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	<title>Wiki - Факультет компьютерных наук - Вклад [ru]</title>
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	<updated>2026-09-21T11:36:00Z</updated>
	<subtitle>Вклад</subtitle>
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	<entry>
		<id>https://wiki.cs.hse.ru/index.php?title=Theory_of_Computation_2021&amp;diff=63243</id>
		<title>Theory of Computation 2021</title>
		<link rel="alternate" type="text/html" href="https://wiki.cs.hse.ru/index.php?title=Theory_of_Computation_2021&amp;diff=63243"/>
		<updated>2021-12-21T10:00:50Z</updated>

		<summary type="html">&lt;p&gt;.obj: /* Exam */&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;= Classes =&lt;br /&gt;
 &lt;br /&gt;
Tuesdays 14:40–17:40, [https://ruz.hse.ru/ruz/main ruz]&lt;br /&gt;
&lt;br /&gt;
Lectures: 14:40 [https://us02web.zoom.us/j/83533615475?pwd=WDU3cHJ5RjREOGd2YU1qdDJCVm1idz09 zoomlink]&lt;br /&gt;
&lt;br /&gt;
Seminars: 16:20 [https://us02web.zoom.us/j/84546220686?pwd=U2dISk5UaFZpdmh3WTdFT3phRVNXZz09 zoomlink]&lt;br /&gt;
&lt;br /&gt;
= Dates and Deadlines =&lt;br /&gt;
Please send your homework by e-mail to both lecturers.&amp;lt;br&amp;gt;&lt;br /&gt;
Homework 1 (problem sets 1–4), deadline: October 5, 14:00; the deadline for the extra problems is &amp;lt;s&amp;gt;November 2&amp;lt;/s&amp;gt; November 8, 14:00&amp;lt;br&amp;gt;&lt;br /&gt;
Homework 2 (problem sets 5–7), deadline: &amp;lt;s&amp;gt;November 2&amp;lt;/s&amp;gt; November 8, 14:00 &amp;lt;br&amp;gt;&lt;br /&gt;
Homework 3, deadline: &amp;lt;s&amp;gt;December 7&amp;lt;/s&amp;gt; December 14, 14:00 &amp;lt;br&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Colloquium: December 7, 14:40–17:40; December 8, 16:30–18:30 &amp;lt;br&amp;gt;&lt;br /&gt;
[https://www.dropbox.com/s/lxyjm6b4xatl0pz/col.pdf?dl=0 Rules and questions]&amp;lt;br&amp;gt;&lt;br /&gt;
Choose your [https://docs.google.com/document/d/1OxiLVx_6LWIJlGP9qjQe1CuBH3BGjk4Q5drHc9r5CE0/ time].&lt;br /&gt;
&lt;br /&gt;
= Grading =&lt;br /&gt;
[https://docs.google.com/spreadsheets/d/1WFBuyjv_D-8EZRhMm39fI_X69daPk2VZwzBXlchW4Mk/edit?usp=sharing Grades]&lt;br /&gt;
&lt;br /&gt;
Colloquium: 35%&amp;lt;br&amp;gt;&lt;br /&gt;
Homework: 35%&amp;lt;br&amp;gt;&lt;br /&gt;
Exam: 30%&lt;br /&gt;
&lt;br /&gt;
== Homework Grading ==&lt;br /&gt;
Some homework assignments contain extra problems. Let us call all other problems regular. The weight of each problem (whether regular or extra) in the overall homework grade is 8/&#039;&#039;n&#039;&#039;, where &#039;&#039;n&#039;&#039; is the total number of regular problems in all homework assignments. Partial credit is possible for some problems.&lt;br /&gt;
&lt;br /&gt;
If you score at least 8 and solve some extra problems that do not contribute to this score, we will evaluate each of these extra problems on the scale [0, 1] and will add two maximal scores to your homework grade.&lt;br /&gt;
&lt;br /&gt;
== Exam ==&lt;br /&gt;
&lt;br /&gt;
December 20, 9:30–12:30, [https://us02web.zoom.us/j/83533615475?pwd=WDU3cHJ5RjREOGd2YU1qdDJCVm1idz09 Zoom]&lt;br /&gt;
&lt;br /&gt;
The exam consists of 8 questions of the same level as the homework.&lt;br /&gt;
&lt;br /&gt;
You may use all notes, books, and other reference materials. However, the solutions you submit must, of course, be your own. You are not allowed to communicate with other students and to use social network sites like Telegram, Facebook, etc. You may not use your phone except in the end of the exam to submit your work.&lt;br /&gt;
&lt;br /&gt;
You must submit your answers in handwriting (exceptions can be asked at the beginning of the exam) by sending scanned or photographed copies to both lecturers.  &lt;br /&gt;
&lt;br /&gt;
We plan to publish the grades on December 21. If you have questions, you can ask them at 13:00 on December 21 via [https://us02web.zoom.us/j/83533615475?pwd=WDU3cHJ5RjREOGd2YU1qdDJCVm1idz09 Zoom].&lt;br /&gt;
&lt;br /&gt;
[https://youtu.be/sKYibeWX5LU Recording] of the consultation (with solutions of problems 11.7, 7.7 and 12.7)&lt;br /&gt;
&lt;br /&gt;
Here is the [https://www.dropbox.com/s/2bt00a3fy28xwsu/exam21_12_20.pdf?dl=0 exam].&lt;br /&gt;
&lt;br /&gt;
= Course Materials =&lt;br /&gt;
&lt;br /&gt;
The main reference is Sipser&#039;s book &amp;quot;Introduction to the theory of computation&amp;quot;, chapters 3, 7–10.&lt;br /&gt;
&lt;br /&gt;
If you need some background in math, consider these two sources:&amp;lt;br&amp;gt;&lt;br /&gt;
[http://www.cs.elte.hu/~lovasz/dmbook.ps Lecture notes: Discrete Mathematics], L. Lovasz, K. Vesztergombi&amp;lt;br&amp;gt;&lt;br /&gt;
[http://rubtsov.su/public/DM-HSE-Draft.pdf Лекции по дискретной математике] (черновик учебника, in Russian)&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
|-&lt;br /&gt;
! Video !! Summary !! Problem list&lt;br /&gt;
|-&lt;br /&gt;
 || 07.09 || Turing machines, multitape Turing machines, connection between them. Universal Turing machine. Examples ([https://www.dropbox.com/s/wna14b7y7nmw3cq/tm.py?dl=0 one], [https://www.dropbox.com/s/wrl3mkeqslj3xtu/wsharpw.py?dl=0 two]). Time and space complexity. Complexity classes P, PSPACE, EXP. || [https://www.dropbox.com/s/37eel2qayios6b3/prob_1.pdf?dl=0 Problem set 1]&lt;br /&gt;
|-&lt;br /&gt;
|| 14.09 ||  Time and space hierarchy theorems. Time and space constructible functions. || [https://www.dropbox.com/s/ow4m1z8u8r211qs/prob_2.pdf?dl=0 Problem set 2]&lt;br /&gt;
|-&lt;br /&gt;
 || 21.09 || Complexity class NP. Examples. Polynomial reductions. NP-hardness and NP-completeness. &lt;br /&gt;
 ||  [https://www.dropbox.com/s/bf68zicg4uh051x/prob_03.pdf?dl=0 Problem set 3]&lt;br /&gt;
|-&lt;br /&gt;
 || 28.09 ||  Non-deterministic TMs. Another definition of NP. Proving NP-hardness by reduction from an NP-complete problem. Examples of NP-complete problems.  || [https://www.dropbox.com/s/g817m6v0ygb8h4n/prob_04.pdf?dl=0 Problem set 4]&lt;br /&gt;
|-&lt;br /&gt;
 || 05.10 || Inclusions between P, NP, and PSPACE. Circuit complexity. Examples. All functions are computed by circuits. Existence of functions with exponential circuit complexity. P is in P/poly.|| [https://www.dropbox.com/s/qkc5p4795rualwn/prob_05.pdf?dl=0 Problem set 5]&lt;br /&gt;
|-&lt;br /&gt;
 || 12.10 || P is a subset of P/poly, Cook–Levin theorem, NP-completeness of: subsetsum, set-splitting, 3-colorability and exactly 1-in-3 SAT.  || [https://www.dropbox.com/s/y2y1lu29936xy9n/prob_06.pdf?dl=0 Problem set 6]&lt;br /&gt;
|-&lt;br /&gt;
 || [https://drive.google.com/drive/folders/1loJWyo9TK6ucCp8RnD3xx3DAVPDs0OiF?usp=sharing 26.10] || Space complexity. Classes L, NL, PSPACE and NPSPACE. Directed Reachability is in SPACE(log^2 n). Configuration graph. Inclusions between time and space classes. TQBF problem, its PSPACE-completeness. PSPACE = NPSPACE. NSPACE(s(n)) is in SPACE(s(n)^2) for space constructible s. || [https://www.dropbox.com/s/b6m0u5vqtutdhq1/prob_07.pdf?dl=0 Problem set 7]&lt;br /&gt;
|- &lt;br /&gt;
|| [https://drive.google.com/drive/folders/1w4W15sPS1nCIpQZQWasqPq8wSVLle5Ik?usp=sharing 02.11] || PSPACE completeness of generalized geography. Oracle computation definitions. There exists an oracle &#039;&#039;A&#039;&#039; for which P&amp;lt;sup&amp;gt;&#039;&#039;A&#039;&#039;&amp;lt;/sup&amp;gt; = NP&amp;lt;sup&amp;gt;&#039;&#039;A&#039;&#039;&amp;lt;/sup&amp;gt;. There is an oracle B such that P&amp;lt;sup&amp;gt;&#039;&#039;B&#039;&#039;&amp;lt;/sup&amp;gt; is not equal to NP&amp;lt;sup&amp;gt;&#039;&#039;B&#039;&#039;&amp;lt;/sup&amp;gt;. || [https://www.dropbox.com/s/bvfrar2p5w3fcie/prob_08.pdf?dl=0 Problem set 8]&lt;br /&gt;
|-&lt;br /&gt;
 || 09.11 || Probabilistic computation. Probabilistic machines, the class BPP, invariance of the definition BPP for different thresholds, RP, coRP, PP, ZPP. BPP is in P/poly. Most of it is also [https://www.youtube.com/watch?v=YSMgVbOqB-8&amp;amp;list=PLm3J0oaFux3YL5vLXpzOyJiLtqLp6dCW2&amp;amp;index=23 here]|| [https://www.dropbox.com/s/dciqvmire4ze4n2/prob_09.pdf?dl=0 Problem set 9]&lt;br /&gt;
|-&lt;br /&gt;
 || [https://youtu.be/ToxNJ9p32Ec 16.11] ||  Streaming algorithms: finding the majority element, computation of the number of different elements &amp;lt;!-- &#039;&#039;F&#039;&#039;&amp;lt;sub&amp;gt;2&amp;lt;/sub&amp;gt;--&amp;gt; in logarithmic space. See Chapts 6.1-6.2 in [https://home.ttic.edu/~avrim/book.pdf foundations of datascience] by Avrim Blum and others. Another nice chapter in [http://theory.stanford.edu/~tim/w15/l/l1.pdf Tim Roughgarden&#039;s lecture notes] || [https://www.dropbox.com/s/ztg8wxuhbkhzh9e/prob_10.pdf?dl=0 Problem set 10]&lt;br /&gt;
|-&lt;br /&gt;
 || [https://drive.google.com/file/d/1mDd3HjabwwzNPMa7oPcnAeHRSymVmsvE/view?usp=sharing 23.11] || Finding the frequent items in streams of data: SpaceSaving and Count-Min Sketch. [https://www.dropbox.com/s/6u27au11u00n59p/tc-11-streaming.pdf?dl=0 Slides] || [https://www.dropbox.com/s/8fvpntf1n4hjoyu/prob_11.pdf?dl=0 Problem set 11]&lt;br /&gt;
|-&lt;br /&gt;
 || [https://youtu.be/H7hF07mMPzk 30.11] || Approximation algorithms. Approximate solutions for Vertex Cover, Weighted Vertex Cover, and TSP. [https://www.dropbox.com/s/wvtcsl6crkj8zeq/tc-12-approximation.pdf?dl=0 Slides.] [https://youtu.be/6ng15Bc8Dlw Seminar.]|| [https://www.dropbox.com/s/qug480ss98pq78p/prob_12.pdf?dl=0 Problem set 12]&lt;br /&gt;
 &lt;br /&gt;
|-&lt;br /&gt;
 || 07.12 || Colloquium. ||&lt;br /&gt;
|-&lt;br /&gt;
 || [https://www.dropbox.com/s/emvoow009xjvf5q/tc-14-clustering.pdf?dl=0 14.12] || Complexity of clustering: an exact algorithm for maximizing the inter-cluster distance and an approximate algorithm for minimizing the intra-class distance.&lt;br /&gt;
 || [https://www.dropbox.com/s/37gdsbv2it8omnm/tc-sample-exam.pdf?dl=0 Sample exam]&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
For interested students, there are 3 lectures in parameterized complexity. &lt;br /&gt;
&lt;br /&gt;
14 Sept: Fixed parameter tracktability and examples, [https://www.dropbox.com/s/zzzaulpmzql7x7u/parameterizedComplexity.pdf?dl=0 presentation]. &lt;br /&gt;
&lt;br /&gt;
21 Sept: Topics from chapters 1 and 2 in &amp;quot;Parameterized algorithms&amp;quot; by Cygan, Fomin and others, 2016.&lt;br /&gt;
&lt;br /&gt;
28 Sept: The W-hierarchy, chapter 13 in the same book.&lt;br /&gt;
&lt;br /&gt;
= Office hours =&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
|-&lt;br /&gt;
!  Person !! Monday !! Tuesday !! Wednesday !! Thursday !! Friday &lt;br /&gt;
|-&lt;br /&gt;
|  [https://www.hse.ru/en/org/persons/160550073 Bruno Bauwens], S834, [https://us02web.zoom.us/j/82300259484?pwd=NWxXekxBeE5yMm9UTmwvLzNNNGlnUT09 Zoom] ||  || ||  ||  || 14:00-20:00&lt;br /&gt;
|-&lt;br /&gt;
|  [https://www.hse.ru/en/staff/obiedkov Sergei Obiedkov], T915, [https://zoom.us/j/99663354582?pwd=K1B5R3NXWEhWbFozR2lqMkFWYW5Ydz09 Zoom] ||  ||  || 16:30–18:00 || 16:30–18:00 ||  &lt;br /&gt;
|}&lt;/div&gt;</summary>
		<author><name>.obj</name></author>
	</entry>
	<entry>
		<id>https://wiki.cs.hse.ru/index.php?title=Theory_of_Computation_2021&amp;diff=63185</id>
		<title>Theory of Computation 2021</title>
		<link rel="alternate" type="text/html" href="https://wiki.cs.hse.ru/index.php?title=Theory_of_Computation_2021&amp;diff=63185"/>
		<updated>2021-12-20T06:29:49Z</updated>

		<summary type="html">&lt;p&gt;.obj: /* Exam */&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;= Classes =&lt;br /&gt;
 &lt;br /&gt;
Tuesdays 14:40–17:40, [https://ruz.hse.ru/ruz/main ruz]&lt;br /&gt;
&lt;br /&gt;
Lectures: 14:40 [https://us02web.zoom.us/j/83533615475?pwd=WDU3cHJ5RjREOGd2YU1qdDJCVm1idz09 zoomlink]&lt;br /&gt;
&lt;br /&gt;
Seminars: 16:20 [https://us02web.zoom.us/j/84546220686?pwd=U2dISk5UaFZpdmh3WTdFT3phRVNXZz09 zoomlink]&lt;br /&gt;
&lt;br /&gt;
= Dates and Deadlines =&lt;br /&gt;
Please send your homework by e-mail to both lecturers.&amp;lt;br&amp;gt;&lt;br /&gt;
Homework 1 (problem sets 1–4), deadline: October 5, 14:00; the deadline for the extra problems is &amp;lt;s&amp;gt;November 2&amp;lt;/s&amp;gt; November 8, 14:00&amp;lt;br&amp;gt;&lt;br /&gt;
Homework 2 (problem sets 5–7), deadline: &amp;lt;s&amp;gt;November 2&amp;lt;/s&amp;gt; November 8, 14:00 &amp;lt;br&amp;gt;&lt;br /&gt;
Homework 3, deadline: &amp;lt;s&amp;gt;December 7&amp;lt;/s&amp;gt; December 14, 14:00 &amp;lt;br&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Colloquium: December 7, 14:40–17:40; December 8, 16:30–18:30 &amp;lt;br&amp;gt;&lt;br /&gt;
[https://www.dropbox.com/s/lxyjm6b4xatl0pz/col.pdf?dl=0 Rules and questions]&amp;lt;br&amp;gt;&lt;br /&gt;
Choose your [https://docs.google.com/document/d/1OxiLVx_6LWIJlGP9qjQe1CuBH3BGjk4Q5drHc9r5CE0/ time].&lt;br /&gt;
&lt;br /&gt;
= Grading =&lt;br /&gt;
[https://docs.google.com/spreadsheets/d/1WFBuyjv_D-8EZRhMm39fI_X69daPk2VZwzBXlchW4Mk/edit?usp=sharing Grades]&lt;br /&gt;
&lt;br /&gt;
Colloquium: 35%&amp;lt;br&amp;gt;&lt;br /&gt;
Homework: 35%&amp;lt;br&amp;gt;&lt;br /&gt;
Exam: 30%&lt;br /&gt;
&lt;br /&gt;
== Homework Grading ==&lt;br /&gt;
Some homework assignments contain extra problems. Let us call all other problems regular. The weight of each problem (whether regular or extra) in the overall homework grade is 8/&#039;&#039;n&#039;&#039;, where &#039;&#039;n&#039;&#039; is the total number of regular problems in all homework assignments. Partial credit is possible for some problems.&lt;br /&gt;
&lt;br /&gt;
If you score at least 8 and solve some extra problems that do not contribute to this score, we will evaluate each of these extra problems on the scale [0, 1] and will add two maximal scores to your homework grade.&lt;br /&gt;
&lt;br /&gt;
== Exam ==&lt;br /&gt;
&lt;br /&gt;
December 20, 9:30–12:30, [https://us02web.zoom.us/j/83533615475?pwd=WDU3cHJ5RjREOGd2YU1qdDJCVm1idz09 Zoom]&lt;br /&gt;
&lt;br /&gt;
The exam consists of 8 questions of the same level as the homework.&lt;br /&gt;
&lt;br /&gt;
You may use all notes, books, and other reference materials. However, the solutions you submit must, of course, be your own. You are not allowed to communicate with other students and to use social network sites like Telegram, Facebook, etc. You may not use your phone except in the end of the exam to submit your work.&lt;br /&gt;
&lt;br /&gt;
You must submit your answers in handwriting (exceptions can be asked at the beginning of the exam) by sending scanned or photographed copies to both lecturers.  &lt;br /&gt;
&lt;br /&gt;
We plan to publish the grades on December 21. If you have questions, you can ask them at 13:00 on December 21 via Zoom (the link will appear here).&lt;br /&gt;
&lt;br /&gt;
[https://youtu.be/sKYibeWX5LU Recording] of the consultation (with solutions of problems 11.7, 7.7 and 12.7)&lt;br /&gt;
&lt;br /&gt;
Here is the [https://www.dropbox.com/s/2bt00a3fy28xwsu/exam21_12_20.pdf?dl=0 exam].&lt;br /&gt;
&lt;br /&gt;
= Course Materials =&lt;br /&gt;
&lt;br /&gt;
The main reference is Sipser&#039;s book &amp;quot;Introduction to the theory of computation&amp;quot;, chapters 3, 7–10.&lt;br /&gt;
&lt;br /&gt;
If you need some background in math, consider these two sources:&amp;lt;br&amp;gt;&lt;br /&gt;
[http://www.cs.elte.hu/~lovasz/dmbook.ps Lecture notes: Discrete Mathematics], L. Lovasz, K. Vesztergombi&amp;lt;br&amp;gt;&lt;br /&gt;
[http://rubtsov.su/public/DM-HSE-Draft.pdf Лекции по дискретной математике] (черновик учебника, in Russian)&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
|-&lt;br /&gt;
! Video !! Summary !! Problem list&lt;br /&gt;
|-&lt;br /&gt;
 || 07.09 || Turing machines, multitape Turing machines, connection between them. Universal Turing machine. Examples ([https://www.dropbox.com/s/wna14b7y7nmw3cq/tm.py?dl=0 one], [https://www.dropbox.com/s/wrl3mkeqslj3xtu/wsharpw.py?dl=0 two]). Time and space complexity. Complexity classes P, PSPACE, EXP. || [https://www.dropbox.com/s/37eel2qayios6b3/prob_1.pdf?dl=0 Problem set 1]&lt;br /&gt;
|-&lt;br /&gt;
|| 14.09 ||  Time and space hierarchy theorems. Time and space constructible functions. || [https://www.dropbox.com/s/ow4m1z8u8r211qs/prob_2.pdf?dl=0 Problem set 2]&lt;br /&gt;
|-&lt;br /&gt;
 || 21.09 || Complexity class NP. Examples. Polynomial reductions. NP-hardness and NP-completeness. &lt;br /&gt;
 ||  [https://www.dropbox.com/s/bf68zicg4uh051x/prob_03.pdf?dl=0 Problem set 3]&lt;br /&gt;
|-&lt;br /&gt;
 || 28.09 ||  Non-deterministic TMs. Another definition of NP. Proving NP-hardness by reduction from an NP-complete problem. Examples of NP-complete problems.  || [https://www.dropbox.com/s/g817m6v0ygb8h4n/prob_04.pdf?dl=0 Problem set 4]&lt;br /&gt;
|-&lt;br /&gt;
 || 05.10 || Inclusions between P, NP, and PSPACE. Circuit complexity. Examples. All functions are computed by circuits. Existence of functions with exponential circuit complexity. P is in P/poly.|| [https://www.dropbox.com/s/qkc5p4795rualwn/prob_05.pdf?dl=0 Problem set 5]&lt;br /&gt;
|-&lt;br /&gt;
 || 12.10 || P is a subset of P/poly, Cook–Levin theorem, NP-completeness of: subsetsum, set-splitting, 3-colorability and exactly 1-in-3 SAT.  || [https://www.dropbox.com/s/y2y1lu29936xy9n/prob_06.pdf?dl=0 Problem set 6]&lt;br /&gt;
|-&lt;br /&gt;
 || [https://drive.google.com/drive/folders/1loJWyo9TK6ucCp8RnD3xx3DAVPDs0OiF?usp=sharing 26.10] || Space complexity. Classes L, NL, PSPACE and NPSPACE. Directed Reachability is in SPACE(log^2 n). Configuration graph. Inclusions between time and space classes. TQBF problem, its PSPACE-completeness. PSPACE = NPSPACE. NSPACE(s(n)) is in SPACE(s(n)^2) for space constructible s. || [https://www.dropbox.com/s/b6m0u5vqtutdhq1/prob_07.pdf?dl=0 Problem set 7]&lt;br /&gt;
|- &lt;br /&gt;
|| [https://drive.google.com/drive/folders/1w4W15sPS1nCIpQZQWasqPq8wSVLle5Ik?usp=sharing 02.11] || PSPACE completeness of generalized geography. Oracle computation definitions. There exists an oracle &#039;&#039;A&#039;&#039; for which P&amp;lt;sup&amp;gt;&#039;&#039;A&#039;&#039;&amp;lt;/sup&amp;gt; = NP&amp;lt;sup&amp;gt;&#039;&#039;A&#039;&#039;&amp;lt;/sup&amp;gt;. There is an oracle B such that P&amp;lt;sup&amp;gt;&#039;&#039;B&#039;&#039;&amp;lt;/sup&amp;gt; is not equal to NP&amp;lt;sup&amp;gt;&#039;&#039;B&#039;&#039;&amp;lt;/sup&amp;gt;. || [https://www.dropbox.com/s/bvfrar2p5w3fcie/prob_08.pdf?dl=0 Problem set 8]&lt;br /&gt;
|-&lt;br /&gt;
 || 09.11 || Probabilistic computation. Probabilistic machines, the class BPP, invariance of the definition BPP for different thresholds, RP, coRP, PP, ZPP. BPP is in P/poly. Most of it is also [https://www.youtube.com/watch?v=YSMgVbOqB-8&amp;amp;list=PLm3J0oaFux3YL5vLXpzOyJiLtqLp6dCW2&amp;amp;index=23 here]|| [https://www.dropbox.com/s/dciqvmire4ze4n2/prob_09.pdf?dl=0 Problem set 9]&lt;br /&gt;
|-&lt;br /&gt;
 || [https://youtu.be/ToxNJ9p32Ec 16.11] ||  Streaming algorithms: finding the majority element, computation of the number of different elements &amp;lt;!-- &#039;&#039;F&#039;&#039;&amp;lt;sub&amp;gt;2&amp;lt;/sub&amp;gt;--&amp;gt; in logarithmic space. See Chapts 6.1-6.2 in [https://home.ttic.edu/~avrim/book.pdf foundations of datascience] by Avrim Blum and others. Another nice chapter in [http://theory.stanford.edu/~tim/w15/l/l1.pdf Tim Roughgarden&#039;s lecture notes] || [https://www.dropbox.com/s/ztg8wxuhbkhzh9e/prob_10.pdf?dl=0 Problem set 10]&lt;br /&gt;
|-&lt;br /&gt;
 || [https://drive.google.com/file/d/1mDd3HjabwwzNPMa7oPcnAeHRSymVmsvE/view?usp=sharing 23.11] || Finding the frequent items in streams of data: SpaceSaving and Count-Min Sketch. [https://www.dropbox.com/s/6u27au11u00n59p/tc-11-streaming.pdf?dl=0 Slides] || [https://www.dropbox.com/s/8fvpntf1n4hjoyu/prob_11.pdf?dl=0 Problem set 11]&lt;br /&gt;
|-&lt;br /&gt;
 || [https://youtu.be/H7hF07mMPzk 30.11] || Approximation algorithms. Approximate solutions for Vertex Cover, Weighted Vertex Cover, and TSP. [https://www.dropbox.com/s/wvtcsl6crkj8zeq/tc-12-approximation.pdf?dl=0 Slides.] [https://youtu.be/6ng15Bc8Dlw Seminar.]|| [https://www.dropbox.com/s/qug480ss98pq78p/prob_12.pdf?dl=0 Problem set 12]&lt;br /&gt;
 &lt;br /&gt;
|-&lt;br /&gt;
 || 07.12 || Colloquium. ||&lt;br /&gt;
|-&lt;br /&gt;
 || [https://www.dropbox.com/s/emvoow009xjvf5q/tc-14-clustering.pdf?dl=0 14.12] || Complexity of clustering: an exact algorithm for maximizing the inter-cluster distance and an approximate algorithm for minimizing the intra-class distance.&lt;br /&gt;
 || [https://www.dropbox.com/s/37gdsbv2it8omnm/tc-sample-exam.pdf?dl=0 Sample exam]&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
For interested students, there are 3 lectures in parameterized complexity. &lt;br /&gt;
&lt;br /&gt;
14 Sept: Fixed parameter tracktability and examples, [https://www.dropbox.com/s/zzzaulpmzql7x7u/parameterizedComplexity.pdf?dl=0 presentation]. &lt;br /&gt;
&lt;br /&gt;
21 Sept: Topics from chapters 1 and 2 in &amp;quot;Parameterized algorithms&amp;quot; by Cygan, Fomin and others, 2016.&lt;br /&gt;
&lt;br /&gt;
28 Sept: The W-hierarchy, chapter 13 in the same book.&lt;br /&gt;
&lt;br /&gt;
= Office hours =&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
|-&lt;br /&gt;
!  Person !! Monday !! Tuesday !! Wednesday !! Thursday !! Friday &lt;br /&gt;
|-&lt;br /&gt;
|  [https://www.hse.ru/en/org/persons/160550073 Bruno Bauwens], S834, [https://us02web.zoom.us/j/82300259484?pwd=NWxXekxBeE5yMm9UTmwvLzNNNGlnUT09 Zoom] ||  || ||  ||  || 14:00-20:00&lt;br /&gt;
|-&lt;br /&gt;
|  [https://www.hse.ru/en/staff/obiedkov Sergei Obiedkov], T915, [https://zoom.us/j/99663354582?pwd=K1B5R3NXWEhWbFozR2lqMkFWYW5Ydz09 Zoom] ||  ||  || 16:30–18:00 || 16:30–18:00 ||  &lt;br /&gt;
|}&lt;/div&gt;</summary>
		<author><name>.obj</name></author>
	</entry>
	<entry>
		<id>https://wiki.cs.hse.ru/index.php?title=Theory_of_Computation_2021&amp;diff=63178</id>
		<title>Theory of Computation 2021</title>
		<link rel="alternate" type="text/html" href="https://wiki.cs.hse.ru/index.php?title=Theory_of_Computation_2021&amp;diff=63178"/>
		<updated>2021-12-19T20:10:30Z</updated>

		<summary type="html">&lt;p&gt;.obj: /* Course Materials */&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;= Classes =&lt;br /&gt;
 &lt;br /&gt;
Tuesdays 14:40–17:40, [https://ruz.hse.ru/ruz/main ruz]&lt;br /&gt;
&lt;br /&gt;
Lectures: 14:40 [https://us02web.zoom.us/j/83533615475?pwd=WDU3cHJ5RjREOGd2YU1qdDJCVm1idz09 zoomlink]&lt;br /&gt;
&lt;br /&gt;
Seminars: 16:20 [https://us02web.zoom.us/j/84546220686?pwd=U2dISk5UaFZpdmh3WTdFT3phRVNXZz09 zoomlink]&lt;br /&gt;
&lt;br /&gt;
= Dates and Deadlines =&lt;br /&gt;
Please send your homework by e-mail to both lecturers.&amp;lt;br&amp;gt;&lt;br /&gt;
Homework 1 (problem sets 1–4), deadline: October 5, 14:00; the deadline for the extra problems is &amp;lt;s&amp;gt;November 2&amp;lt;/s&amp;gt; November 8, 14:00&amp;lt;br&amp;gt;&lt;br /&gt;
Homework 2 (problem sets 5–7), deadline: &amp;lt;s&amp;gt;November 2&amp;lt;/s&amp;gt; November 8, 14:00 &amp;lt;br&amp;gt;&lt;br /&gt;
Homework 3, deadline: &amp;lt;s&amp;gt;December 7&amp;lt;/s&amp;gt; December 14, 14:00 &amp;lt;br&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Colloquium: December 7, 14:40–17:40; December 8, 16:30–18:30 &amp;lt;br&amp;gt;&lt;br /&gt;
[https://www.dropbox.com/s/lxyjm6b4xatl0pz/col.pdf?dl=0 Rules and questions]&amp;lt;br&amp;gt;&lt;br /&gt;
Choose your [https://docs.google.com/document/d/1OxiLVx_6LWIJlGP9qjQe1CuBH3BGjk4Q5drHc9r5CE0/ time].&lt;br /&gt;
&lt;br /&gt;
= Grading =&lt;br /&gt;
[https://docs.google.com/spreadsheets/d/1WFBuyjv_D-8EZRhMm39fI_X69daPk2VZwzBXlchW4Mk/edit?usp=sharing Grades]&lt;br /&gt;
&lt;br /&gt;
Colloquium: 35%&amp;lt;br&amp;gt;&lt;br /&gt;
Homework: 35%&amp;lt;br&amp;gt;&lt;br /&gt;
Exam: 30%&lt;br /&gt;
&lt;br /&gt;
== Homework Grading ==&lt;br /&gt;
Some homework assignments contain extra problems. Let us call all other problems regular. The weight of each problem (whether regular or extra) in the overall homework grade is 8/&#039;&#039;n&#039;&#039;, where &#039;&#039;n&#039;&#039; is the total number of regular problems in all homework assignments. Partial credit is possible for some problems.&lt;br /&gt;
&lt;br /&gt;
If you score at least 8 and solve some extra problems that do not contribute to this score, we will evaluate each of these extra problems on the scale [0, 1] and will add two maximal scores to your homework grade.&lt;br /&gt;
&lt;br /&gt;
== Exam ==&lt;br /&gt;
&lt;br /&gt;
December 20, 9:30–12:30, [https://us02web.zoom.us/j/83533615475?pwd=WDU3cHJ5RjREOGd2YU1qdDJCVm1idz09 Zoom]&lt;br /&gt;
&lt;br /&gt;
The exam consists of 8 questions of the same level as the homework.&lt;br /&gt;
&lt;br /&gt;
You may use all notes, books, and other reference materials. However, the solutions you submit must, of course, be your own. You are not allowed to communicate with other students and to use social network sites like Telegram, Facebook, etc. You may not use your phone except in the end of the exam to submit your work.&lt;br /&gt;
&lt;br /&gt;
You must submit your answers in handwriting (exceptions can be asked at the beginning of the exam) by sending scanned or photographed copies to both lecturers.  &lt;br /&gt;
&lt;br /&gt;
We plan to publish the grades on December 21. If you have questions, you can ask them at 13:00 on December 21 via Zoom (the link will appear here).&lt;br /&gt;
&lt;br /&gt;
[https://youtu.be/sKYibeWX5LU Recording] of the consultation (with solutions of problems 11.7, 7.7 and 12.7)&lt;br /&gt;
&lt;br /&gt;
= Course Materials =&lt;br /&gt;
&lt;br /&gt;
The main reference is Sipser&#039;s book &amp;quot;Introduction to the theory of computation&amp;quot;, chapters 3, 7–10.&lt;br /&gt;
&lt;br /&gt;
If you need some background in math, consider these two sources:&amp;lt;br&amp;gt;&lt;br /&gt;
[http://www.cs.elte.hu/~lovasz/dmbook.ps Lecture notes: Discrete Mathematics], L. Lovasz, K. Vesztergombi&amp;lt;br&amp;gt;&lt;br /&gt;
[http://rubtsov.su/public/DM-HSE-Draft.pdf Лекции по дискретной математике] (черновик учебника, in Russian)&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
|-&lt;br /&gt;
! Video !! Summary !! Problem list&lt;br /&gt;
|-&lt;br /&gt;
 || 07.09 || Turing machines, multitape Turing machines, connection between them. Universal Turing machine. Examples ([https://www.dropbox.com/s/wna14b7y7nmw3cq/tm.py?dl=0 one], [https://www.dropbox.com/s/wrl3mkeqslj3xtu/wsharpw.py?dl=0 two]). Time and space complexity. Complexity classes P, PSPACE, EXP. || [https://www.dropbox.com/s/37eel2qayios6b3/prob_1.pdf?dl=0 Problem set 1]&lt;br /&gt;
|-&lt;br /&gt;
|| 14.09 ||  Time and space hierarchy theorems. Time and space constructible functions. || [https://www.dropbox.com/s/ow4m1z8u8r211qs/prob_2.pdf?dl=0 Problem set 2]&lt;br /&gt;
|-&lt;br /&gt;
 || 21.09 || Complexity class NP. Examples. Polynomial reductions. NP-hardness and NP-completeness. &lt;br /&gt;
 ||  [https://www.dropbox.com/s/bf68zicg4uh051x/prob_03.pdf?dl=0 Problem set 3]&lt;br /&gt;
|-&lt;br /&gt;
 || 28.09 ||  Non-deterministic TMs. Another definition of NP. Proving NP-hardness by reduction from an NP-complete problem. Examples of NP-complete problems.  || [https://www.dropbox.com/s/g817m6v0ygb8h4n/prob_04.pdf?dl=0 Problem set 4]&lt;br /&gt;
|-&lt;br /&gt;
 || 05.10 || Inclusions between P, NP, and PSPACE. Circuit complexity. Examples. All functions are computed by circuits. Existence of functions with exponential circuit complexity. P is in P/poly.|| [https://www.dropbox.com/s/qkc5p4795rualwn/prob_05.pdf?dl=0 Problem set 5]&lt;br /&gt;
|-&lt;br /&gt;
 || 12.10 || P is a subset of P/poly, Cook–Levin theorem, NP-completeness of: subsetsum, set-splitting, 3-colorability and exactly 1-in-3 SAT.  || [https://www.dropbox.com/s/y2y1lu29936xy9n/prob_06.pdf?dl=0 Problem set 6]&lt;br /&gt;
|-&lt;br /&gt;
 || [https://drive.google.com/drive/folders/1loJWyo9TK6ucCp8RnD3xx3DAVPDs0OiF?usp=sharing 26.10] || Space complexity. Classes L, NL, PSPACE and NPSPACE. Directed Reachability is in SPACE(log^2 n). Configuration graph. Inclusions between time and space classes. TQBF problem, its PSPACE-completeness. PSPACE = NPSPACE. NSPACE(s(n)) is in SPACE(s(n)^2) for space constructible s. || [https://www.dropbox.com/s/b6m0u5vqtutdhq1/prob_07.pdf?dl=0 Problem set 7]&lt;br /&gt;
|- &lt;br /&gt;
|| [https://drive.google.com/drive/folders/1w4W15sPS1nCIpQZQWasqPq8wSVLle5Ik?usp=sharing 02.11] || PSPACE completeness of generalized geography. Oracle computation definitions. There exists an oracle &#039;&#039;A&#039;&#039; for which P&amp;lt;sup&amp;gt;&#039;&#039;A&#039;&#039;&amp;lt;/sup&amp;gt; = NP&amp;lt;sup&amp;gt;&#039;&#039;A&#039;&#039;&amp;lt;/sup&amp;gt;. There is an oracle B such that P&amp;lt;sup&amp;gt;&#039;&#039;B&#039;&#039;&amp;lt;/sup&amp;gt; is not equal to NP&amp;lt;sup&amp;gt;&#039;&#039;B&#039;&#039;&amp;lt;/sup&amp;gt;. || [https://www.dropbox.com/s/bvfrar2p5w3fcie/prob_08.pdf?dl=0 Problem set 8]&lt;br /&gt;
|-&lt;br /&gt;
 || 09.11 || Probabilistic computation. Probabilistic machines, the class BPP, invariance of the definition BPP for different thresholds, RP, coRP, PP, ZPP. BPP is in P/poly. Most of it is also [https://www.youtube.com/watch?v=YSMgVbOqB-8&amp;amp;list=PLm3J0oaFux3YL5vLXpzOyJiLtqLp6dCW2&amp;amp;index=23 here]|| [https://www.dropbox.com/s/dciqvmire4ze4n2/prob_09.pdf?dl=0 Problem set 9]&lt;br /&gt;
|-&lt;br /&gt;
 || [https://youtu.be/ToxNJ9p32Ec 16.11] ||  Streaming algorithms: finding the majority element, computation of the number of different elements &amp;lt;!-- &#039;&#039;F&#039;&#039;&amp;lt;sub&amp;gt;2&amp;lt;/sub&amp;gt;--&amp;gt; in logarithmic space. See Chapts 6.1-6.2 in [https://home.ttic.edu/~avrim/book.pdf foundations of datascience] by Avrim Blum and others. Another nice chapter in [http://theory.stanford.edu/~tim/w15/l/l1.pdf Tim Roughgarden&#039;s lecture notes] || [https://www.dropbox.com/s/ztg8wxuhbkhzh9e/prob_10.pdf?dl=0 Problem set 10]&lt;br /&gt;
|-&lt;br /&gt;
 || [https://drive.google.com/file/d/1mDd3HjabwwzNPMa7oPcnAeHRSymVmsvE/view?usp=sharing 23.11] || Finding the frequent items in streams of data: SpaceSaving and Count-Min Sketch. [https://www.dropbox.com/s/6u27au11u00n59p/tc-11-streaming.pdf?dl=0 Slides] || [https://www.dropbox.com/s/8fvpntf1n4hjoyu/prob_11.pdf?dl=0 Problem set 11]&lt;br /&gt;
|-&lt;br /&gt;
 || [https://youtu.be/H7hF07mMPzk 30.11] || Approximation algorithms. Approximate solutions for Vertex Cover, Weighted Vertex Cover, and TSP. [https://www.dropbox.com/s/wvtcsl6crkj8zeq/tc-12-approximation.pdf?dl=0 Slides.] [https://youtu.be/6ng15Bc8Dlw Seminar.]|| [https://www.dropbox.com/s/qug480ss98pq78p/prob_12.pdf?dl=0 Problem set 12]&lt;br /&gt;
 &lt;br /&gt;
|-&lt;br /&gt;
 || 07.12 || Colloquium. ||&lt;br /&gt;
|-&lt;br /&gt;
 || [https://www.dropbox.com/s/emvoow009xjvf5q/tc-14-clustering.pdf?dl=0 14.12] || Complexity of clustering: an exact algorithm for maximizing the inter-cluster distance and an approximate algorithm for minimizing the intra-class distance.&lt;br /&gt;
 || [https://www.dropbox.com/s/37gdsbv2it8omnm/tc-sample-exam.pdf?dl=0 Sample exam]&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
For interested students, there are 3 lectures in parameterized complexity. &lt;br /&gt;
&lt;br /&gt;
14 Sept: Fixed parameter tracktability and examples, [https://www.dropbox.com/s/zzzaulpmzql7x7u/parameterizedComplexity.pdf?dl=0 presentation]. &lt;br /&gt;
&lt;br /&gt;
21 Sept: Topics from chapters 1 and 2 in &amp;quot;Parameterized algorithms&amp;quot; by Cygan, Fomin and others, 2016.&lt;br /&gt;
&lt;br /&gt;
28 Sept: The W-hierarchy, chapter 13 in the same book.&lt;br /&gt;
&lt;br /&gt;
= Office hours =&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
|-&lt;br /&gt;
!  Person !! Monday !! Tuesday !! Wednesday !! Thursday !! Friday &lt;br /&gt;
|-&lt;br /&gt;
|  [https://www.hse.ru/en/org/persons/160550073 Bruno Bauwens], S834, [https://us02web.zoom.us/j/82300259484?pwd=NWxXekxBeE5yMm9UTmwvLzNNNGlnUT09 Zoom] ||  || ||  ||  || 14:00-20:00&lt;br /&gt;
|-&lt;br /&gt;
|  [https://www.hse.ru/en/staff/obiedkov Sergei Obiedkov], T915, [https://zoom.us/j/99663354582?pwd=K1B5R3NXWEhWbFozR2lqMkFWYW5Ydz09 Zoom] ||  ||  || 16:30–18:00 || 16:30–18:00 ||  &lt;br /&gt;
|}&lt;/div&gt;</summary>
		<author><name>.obj</name></author>
	</entry>
	<entry>
		<id>https://wiki.cs.hse.ru/index.php?title=Theory_of_Computation_2021&amp;diff=63177</id>
		<title>Theory of Computation 2021</title>
		<link rel="alternate" type="text/html" href="https://wiki.cs.hse.ru/index.php?title=Theory_of_Computation_2021&amp;diff=63177"/>
		<updated>2021-12-19T19:39:49Z</updated>

		<summary type="html">&lt;p&gt;.obj: /* Exam */&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;= Classes =&lt;br /&gt;
 &lt;br /&gt;
Tuesdays 14:40–17:40, [https://ruz.hse.ru/ruz/main ruz]&lt;br /&gt;
&lt;br /&gt;
Lectures: 14:40 [https://us02web.zoom.us/j/83533615475?pwd=WDU3cHJ5RjREOGd2YU1qdDJCVm1idz09 zoomlink]&lt;br /&gt;
&lt;br /&gt;
Seminars: 16:20 [https://us02web.zoom.us/j/84546220686?pwd=U2dISk5UaFZpdmh3WTdFT3phRVNXZz09 zoomlink]&lt;br /&gt;
&lt;br /&gt;
= Dates and Deadlines =&lt;br /&gt;
Please send your homework by e-mail to both lecturers.&amp;lt;br&amp;gt;&lt;br /&gt;
Homework 1 (problem sets 1–4), deadline: October 5, 14:00; the deadline for the extra problems is &amp;lt;s&amp;gt;November 2&amp;lt;/s&amp;gt; November 8, 14:00&amp;lt;br&amp;gt;&lt;br /&gt;
Homework 2 (problem sets 5–7), deadline: &amp;lt;s&amp;gt;November 2&amp;lt;/s&amp;gt; November 8, 14:00 &amp;lt;br&amp;gt;&lt;br /&gt;
Homework 3, deadline: &amp;lt;s&amp;gt;December 7&amp;lt;/s&amp;gt; December 14, 14:00 &amp;lt;br&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Colloquium: December 7, 14:40–17:40; December 8, 16:30–18:30 &amp;lt;br&amp;gt;&lt;br /&gt;
[https://www.dropbox.com/s/lxyjm6b4xatl0pz/col.pdf?dl=0 Rules and questions]&amp;lt;br&amp;gt;&lt;br /&gt;
Choose your [https://docs.google.com/document/d/1OxiLVx_6LWIJlGP9qjQe1CuBH3BGjk4Q5drHc9r5CE0/ time].&lt;br /&gt;
&lt;br /&gt;
= Grading =&lt;br /&gt;
[https://docs.google.com/spreadsheets/d/1WFBuyjv_D-8EZRhMm39fI_X69daPk2VZwzBXlchW4Mk/edit?usp=sharing Grades]&lt;br /&gt;
&lt;br /&gt;
Colloquium: 35%&amp;lt;br&amp;gt;&lt;br /&gt;
Homework: 35%&amp;lt;br&amp;gt;&lt;br /&gt;
Exam: 30%&lt;br /&gt;
&lt;br /&gt;
== Homework Grading ==&lt;br /&gt;
Some homework assignments contain extra problems. Let us call all other problems regular. The weight of each problem (whether regular or extra) in the overall homework grade is 8/&#039;&#039;n&#039;&#039;, where &#039;&#039;n&#039;&#039; is the total number of regular problems in all homework assignments. Partial credit is possible for some problems.&lt;br /&gt;
&lt;br /&gt;
If you score at least 8 and solve some extra problems that do not contribute to this score, we will evaluate each of these extra problems on the scale [0, 1] and will add two maximal scores to your homework grade.&lt;br /&gt;
&lt;br /&gt;
== Exam ==&lt;br /&gt;
&lt;br /&gt;
December 20, 9:30–12:30, [https://us02web.zoom.us/j/83533615475?pwd=WDU3cHJ5RjREOGd2YU1qdDJCVm1idz09 Zoom]&lt;br /&gt;
&lt;br /&gt;
The exam consists of 8 questions of the same level as the homework.&lt;br /&gt;
&lt;br /&gt;
You may use all notes, books, and other reference materials. However, the solutions you submit must, of course, be your own. You are not allowed to communicate with other students and to use social network sites like Telegram, Facebook, etc. You may not use your phone except in the end of the exam to submit your work.&lt;br /&gt;
&lt;br /&gt;
You must submit your answers in handwriting (exceptions can be asked at the beginning of the exam) by sending scanned or photographed copies to both lecturers.  &lt;br /&gt;
&lt;br /&gt;
We plan to publish the grades on December 21. If you have questions, you can ask them at 13:00 on December 21 via Zoom (the link will appear here).&lt;br /&gt;
&lt;br /&gt;
[https://youtu.be/sKYibeWX5LU Recording] of the consultation (with solutions of problems 11.7, 7.7 and 12.7)&lt;br /&gt;
&lt;br /&gt;
= Course Materials =&lt;br /&gt;
&lt;br /&gt;
The main reference is Sipser&#039;s book &amp;quot;Introduction to the theory of computation&amp;quot;, chapters 3, 7–10.&lt;br /&gt;
&lt;br /&gt;
If you need some background in math, consider these two sources:&amp;lt;br&amp;gt;&lt;br /&gt;
[http://www.cs.elte.hu/~lovasz/dmbook.ps Lecture notes: Discrete Mathematics], L. Lovasz, K. Vesztergombi&amp;lt;br&amp;gt;&lt;br /&gt;
[http://rubtsov.su/public/DM-HSE-Draft.pdf Лекции по дискретной математике] (черновик учебника, in Russian)&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
|-&lt;br /&gt;
! Video !! Summary !! Problem list&lt;br /&gt;
|-&lt;br /&gt;
 || 07.09 || Turing machines, multitape Turing machines, connection between them. Universal Turing machine. Examples ([https://www.dropbox.com/s/wna14b7y7nmw3cq/tm.py?dl=0 one], [https://www.dropbox.com/s/wrl3mkeqslj3xtu/wsharpw.py?dl=0 two]). Time and space complexity. Complexity classes P, PSPACE, EXP. || [https://www.dropbox.com/s/37eel2qayios6b3/prob_1.pdf?dl=0 Problem set 1]&lt;br /&gt;
|-&lt;br /&gt;
|| 14.09 ||  Time and space hierarchy theorem. Time and space constructible functions. || [https://www.dropbox.com/s/ow4m1z8u8r211qs/prob_2.pdf?dl=0 Problem set 2]&lt;br /&gt;
|-&lt;br /&gt;
 || 21.09 || Complexity class NP. Examples. Polynomial reductions. NP-hardness and NP-completeness. &lt;br /&gt;
 ||  [https://www.dropbox.com/s/bf68zicg4uh051x/prob_03.pdf?dl=0 Problem set 3]&lt;br /&gt;
|-&lt;br /&gt;
 || 28.09 ||  Non-deterministic TMs. Another definition of NP. Proving NP-hardness by reduction from an NP-complete problem. Examples of NP-complete problems.  || [https://www.dropbox.com/s/g817m6v0ygb8h4n/prob_04.pdf?dl=0 Problem set 4]&lt;br /&gt;
|-&lt;br /&gt;
 || 05.10 || Inclusions between P, NP, and PSPACE. Circuit complexity. Examples. All functions are computed by circuits. Existence of functions with exponential circuit complexity. P is in P/poly.|| [https://www.dropbox.com/s/qkc5p4795rualwn/prob_05.pdf?dl=0 Problem set 5]&lt;br /&gt;
|-&lt;br /&gt;
 || 12.10 || P is a subset of P/poly, Cook–Levin theorem, NP-completeness of: subsetsum, set-splitting, 3-colorability and exactly 1-in-3 SAT.  || [https://www.dropbox.com/s/y2y1lu29936xy9n/prob_06.pdf?dl=0 Problem set 6]&lt;br /&gt;
|-&lt;br /&gt;
 || [https://drive.google.com/drive/folders/1loJWyo9TK6ucCp8RnD3xx3DAVPDs0OiF?usp=sharing 26.10] || Space complexity. Classes L, NL, PSPACE and NPSPACE. Directed Reachability is in SPACE(log^2 n). Configuration graph. Inclusions between time and space classes. TQBF problem, its PSPACE-completeness. PSPACE = NPSPACE. NSPACE(s(n)) is in SPACE(s(n)^2) for space constructible s. || [https://www.dropbox.com/s/b6m0u5vqtutdhq1/prob_07.pdf?dl=0 Problem set 7]&lt;br /&gt;
|- &lt;br /&gt;
|| [https://drive.google.com/drive/folders/1w4W15sPS1nCIpQZQWasqPq8wSVLle5Ik?usp=sharing 02.11] || PSPACE completeness of generalized geography. Oracle computation definitions. There exists an oracle &#039;&#039;A&#039;&#039; for which P&amp;lt;sup&amp;gt;&#039;&#039;A&#039;&#039;&amp;lt;/sup&amp;gt; = NP&amp;lt;sup&amp;gt;&#039;&#039;A&#039;&#039;&amp;lt;/sup&amp;gt;. There is an oracle B such that P&amp;lt;sup&amp;gt;&#039;&#039;B&#039;&#039;&amp;lt;/sup&amp;gt; is not equal to NP&amp;lt;sup&amp;gt;&#039;&#039;B&#039;&#039;&amp;lt;/sup&amp;gt;. || [https://www.dropbox.com/s/bvfrar2p5w3fcie/prob_08.pdf?dl=0 Problem set 8]&lt;br /&gt;
|-&lt;br /&gt;
 || 09.11 || Probabilistic computation. Probabilistic machines, the class BPP, invariance of the definition BPP for different thresholds, RP, coRP, PP, ZPP. BPP is in P/poly. Most of it is also [https://www.youtube.com/watch?v=YSMgVbOqB-8&amp;amp;list=PLm3J0oaFux3YL5vLXpzOyJiLtqLp6dCW2&amp;amp;index=23 here]|| [https://www.dropbox.com/s/dciqvmire4ze4n2/prob_09.pdf?dl=0 Problem set 9]&lt;br /&gt;
|-&lt;br /&gt;
 || [https://youtu.be/ToxNJ9p32Ec 16.11] ||  Streaming algorithms: finding the majority element, computation of the number of different elements &amp;lt;!-- &#039;&#039;F&#039;&#039;&amp;lt;sub&amp;gt;2&amp;lt;/sub&amp;gt;--&amp;gt; in logarithmic space. See Chapts 6.1-6.2 in [https://home.ttic.edu/~avrim/book.pdf foundations of datascience] by Avrim Blum and others. Another nice chapter in [http://theory.stanford.edu/~tim/w15/l/l1.pdf Tim Roughgarden&#039;s lecture notes] || [https://www.dropbox.com/s/ztg8wxuhbkhzh9e/prob_10.pdf?dl=0 Problem set 10]&lt;br /&gt;
|-&lt;br /&gt;
 || [https://drive.google.com/file/d/1mDd3HjabwwzNPMa7oPcnAeHRSymVmsvE/view?usp=sharing 23.11] || Finding the frequent items in streams of data: SpaceSaving and Count-Min Sketch. [https://www.dropbox.com/s/6u27au11u00n59p/tc-11-streaming.pdf?dl=0 Slides] || [https://www.dropbox.com/s/8fvpntf1n4hjoyu/prob_11.pdf?dl=0 Problem set 11]&lt;br /&gt;
|-&lt;br /&gt;
 || [https://youtu.be/H7hF07mMPzk 30.11] || Approximation algorithms. Approximate solutions for Vertex Cover, Weighted Vertex Cover, and TSP. [https://www.dropbox.com/s/wvtcsl6crkj8zeq/tc-12-approximation.pdf?dl=0 Slides.] [https://youtu.be/6ng15Bc8Dlw Seminar.]|| [https://www.dropbox.com/s/qug480ss98pq78p/prob_12.pdf?dl=0 Problem set 12]&lt;br /&gt;
 &lt;br /&gt;
|-&lt;br /&gt;
 || 07.12 || Colloquium. ||&lt;br /&gt;
|-&lt;br /&gt;
 || [https://www.dropbox.com/s/emvoow009xjvf5q/tc-14-clustering.pdf?dl=0 14.12] || Complexity of clustering: an exact algorithm for maximizing the inter-cluster distance and an approximate algorithm for minimizing the intra-class distance.&lt;br /&gt;
 || [https://www.dropbox.com/s/37gdsbv2it8omnm/tc-sample-exam.pdf?dl=0 Sample exam]&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
For interested students, there are 3 lectures in parameterized complexity. &lt;br /&gt;
&lt;br /&gt;
14 Sept: Fixed parameter tracktability and examples, [https://www.dropbox.com/s/zzzaulpmzql7x7u/parameterizedComplexity.pdf?dl=0 presentation]. &lt;br /&gt;
&lt;br /&gt;
21 Sept: Topics from chapters 1 and 2 in &amp;quot;Parameterized algorithms&amp;quot; by Cygan, Fomin and others, 2016.&lt;br /&gt;
&lt;br /&gt;
28 Sept: The W-hierarchy, chapter 13 in the same book.&lt;br /&gt;
&lt;br /&gt;
= Office hours =&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
|-&lt;br /&gt;
!  Person !! Monday !! Tuesday !! Wednesday !! Thursday !! Friday &lt;br /&gt;
|-&lt;br /&gt;
|  [https://www.hse.ru/en/org/persons/160550073 Bruno Bauwens], S834, [https://us02web.zoom.us/j/82300259484?pwd=NWxXekxBeE5yMm9UTmwvLzNNNGlnUT09 Zoom] ||  || ||  ||  || 14:00-20:00&lt;br /&gt;
|-&lt;br /&gt;
|  [https://www.hse.ru/en/staff/obiedkov Sergei Obiedkov], T915, [https://zoom.us/j/99663354582?pwd=K1B5R3NXWEhWbFozR2lqMkFWYW5Ydz09 Zoom] ||  ||  || 16:30–18:00 || 16:30–18:00 ||  &lt;br /&gt;
|}&lt;/div&gt;</summary>
		<author><name>.obj</name></author>
	</entry>
	<entry>
		<id>https://wiki.cs.hse.ru/index.php?title=Theory_of_Computation_2021&amp;diff=63027</id>
		<title>Theory of Computation 2021</title>
		<link rel="alternate" type="text/html" href="https://wiki.cs.hse.ru/index.php?title=Theory_of_Computation_2021&amp;diff=63027"/>
		<updated>2021-12-16T08:36:54Z</updated>

		<summary type="html">&lt;p&gt;.obj: &lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;= Classes =&lt;br /&gt;
 &lt;br /&gt;
Tuesdays 14:40–17:40, [https://ruz.hse.ru/ruz/main ruz]&lt;br /&gt;
&lt;br /&gt;
Lectures: 14:40 [https://us02web.zoom.us/j/83533615475?pwd=WDU3cHJ5RjREOGd2YU1qdDJCVm1idz09 zoomlink]&lt;br /&gt;
&lt;br /&gt;
Seminars: 16:20 [https://us02web.zoom.us/j/84546220686?pwd=U2dISk5UaFZpdmh3WTdFT3phRVNXZz09 zoomlink]&lt;br /&gt;
&lt;br /&gt;
= Dates and Deadlines =&lt;br /&gt;
Please send your homework by e-mail to both lecturers.&amp;lt;br&amp;gt;&lt;br /&gt;
Homework 1 (problem sets 1–4), deadline: October 5, 14:00; the deadline for the extra problems is &amp;lt;s&amp;gt;November 2&amp;lt;/s&amp;gt; November 8, 14:00&amp;lt;br&amp;gt;&lt;br /&gt;
Homework 2 (problem sets 5–7), deadline: &amp;lt;s&amp;gt;November 2&amp;lt;/s&amp;gt; November 8, 14:00 &amp;lt;br&amp;gt;&lt;br /&gt;
Homework 3, deadline: &amp;lt;s&amp;gt;December 7&amp;lt;/s&amp;gt; December 14, 14:00 &amp;lt;br&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Colloquium: December 7, 14:40–17:40; December 8, 16:30–18:30&#039;&#039;&#039; &amp;lt;br&amp;gt;&lt;br /&gt;
[https://www.dropbox.com/s/lxyjm6b4xatl0pz/col.pdf?dl=0 Rules and questions]&amp;lt;br&amp;gt;&lt;br /&gt;
Choose your [https://docs.google.com/document/d/1OxiLVx_6LWIJlGP9qjQe1CuBH3BGjk4Q5drHc9r5CE0/ time].&lt;br /&gt;
&lt;br /&gt;
= Grading =&lt;br /&gt;
[https://docs.google.com/spreadsheets/d/1WFBuyjv_D-8EZRhMm39fI_X69daPk2VZwzBXlchW4Mk/edit?usp=sharing Grades]&lt;br /&gt;
&lt;br /&gt;
Colloquium: 35%&amp;lt;br&amp;gt;&lt;br /&gt;
Homework: 35%&amp;lt;br&amp;gt;&lt;br /&gt;
Exam: 30%&lt;br /&gt;
&lt;br /&gt;
==Homework Grading==&lt;br /&gt;
Some homework assignments contain extra problems. Let us call all other problems regular. The weight of each problem (whether regular or extra) in the overall homework grade is 8/&#039;&#039;n&#039;&#039;, where &#039;&#039;n&#039;&#039; is the total number of regular problems in all homework assignments. Partial credit is possible for some problems.&lt;br /&gt;
&lt;br /&gt;
If you score at least 8 and solve some extra problems that do not contribute to this score, we will evaluate each of these extra problems on the scale [0, 1] and will add two maximal scores to your homework grade.&lt;br /&gt;
&lt;br /&gt;
== Exam ==&lt;br /&gt;
&lt;br /&gt;
December 20, 9:30–12:30, [https://us02web.zoom.us/j/83533615475?pwd=WDU3cHJ5RjREOGd2YU1qdDJCVm1idz09 Zoom]&lt;br /&gt;
&lt;br /&gt;
The exam consists of 7 or 8 questions of the same level as the homework.&lt;br /&gt;
&lt;br /&gt;
You may use all course materials (seminar sheets, Sipser&#039;s book, etc). You are not allowed to communicate with other students and to use social network sites like Telegram, Facebook, etc. You may not use your phone except in the end of the exam to submit your work.&lt;br /&gt;
&lt;br /&gt;
You must submit your answers in handwriting (exceptions can be asked at the beginning of the exam) by sending scanned or photographed copies to both lecturers.  &lt;br /&gt;
&lt;br /&gt;
We plan to publish the grades on December 21. If you have questions, you can ask them at 13:00 on December 21 via Zoom (the link will appear here).&lt;br /&gt;
&lt;br /&gt;
= Course Materials =&lt;br /&gt;
&lt;br /&gt;
The main reference is Sipser&#039;s book &amp;quot;Introduction to the theory of computation&amp;quot;, chapters 3, 7–10.&lt;br /&gt;
&lt;br /&gt;
If you need some background in math, consider these two sources:&amp;lt;br&amp;gt;&lt;br /&gt;
[http://www.cs.elte.hu/~lovasz/dmbook.ps Lecture notes: Discrete Mathematics], L. Lovasz, K. Vesztergombi&amp;lt;br&amp;gt;&lt;br /&gt;
[http://rubtsov.su/public/DM-HSE-Draft.pdf Лекции по дискретной математике] (черновик учебника, in Russian)&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
|-&lt;br /&gt;
! Video !! Summary !! Problem list&lt;br /&gt;
|-&lt;br /&gt;
 || 07.09 || Turing machines, multitape Turing machines, connection between them. Universal Turing machine. Examples ([https://www.dropbox.com/s/wna14b7y7nmw3cq/tm.py?dl=0 one], [https://www.dropbox.com/s/wrl3mkeqslj3xtu/wsharpw.py?dl=0 two]). Time and space complexity. Complexity classes P, PSPACE, EXP. || [https://www.dropbox.com/s/37eel2qayios6b3/prob_1.pdf?dl=0 Problem set 1]&lt;br /&gt;
|-&lt;br /&gt;
|| 14.09 ||  Time and space hierarchy theorem. Time and space constructible functions. || [https://www.dropbox.com/s/ow4m1z8u8r211qs/prob_2.pdf?dl=0 Problem set 2]&lt;br /&gt;
|-&lt;br /&gt;
 || 21.09 || Complexity class NP. Examples. Polynomial reductions. NP-hardness and NP-completeness. &lt;br /&gt;
 ||  [https://www.dropbox.com/s/bf68zicg4uh051x/prob_03.pdf?dl=0 Problem set 3]&lt;br /&gt;
|-&lt;br /&gt;
 || 28.09 ||  Non-deterministic TMs. Another definition of NP. Proving NP-hardness by reduction from an NP-complete problem. Examples of NP-complete problems.  || [https://www.dropbox.com/s/g817m6v0ygb8h4n/prob_04.pdf?dl=0 Problem set 4]&lt;br /&gt;
|-&lt;br /&gt;
 || 05.10 || Inclusions between P, NP, and PSPACE. Circuit complexity. Examples. All functions are computed by circuits. Existence of functions with exponential circuit complexity. P is in P/poly.|| [https://www.dropbox.com/s/qkc5p4795rualwn/prob_05.pdf?dl=0 Problem set 5]&lt;br /&gt;
|-&lt;br /&gt;
 || 12.10 || P is a subset of P/poly, Cook–Levin theorem, NP-completeness of: subsetsum, set-splitting, 3-colorability and exactly 1-in-3 SAT.  || [https://www.dropbox.com/s/y2y1lu29936xy9n/prob_06.pdf?dl=0 Problem set 6]&lt;br /&gt;
|-&lt;br /&gt;
 || [https://drive.google.com/drive/folders/1loJWyo9TK6ucCp8RnD3xx3DAVPDs0OiF?usp=sharing 26.10] || Space complexity. Classes L, NL, PSPACE and NPSPACE. Directed Reachability is in SPACE(log^2 n). Configuration graph. Inclusions between time and space classes. TQBF problem, its PSPACE-completeness. PSPACE = NPSPACE. NSPACE(s(n)) is in SPACE(s(n)^2) for space constructible s. || [https://www.dropbox.com/s/b6m0u5vqtutdhq1/prob_07.pdf?dl=0 Problem set 7]&lt;br /&gt;
|- &lt;br /&gt;
|| [https://drive.google.com/drive/folders/1w4W15sPS1nCIpQZQWasqPq8wSVLle5Ik?usp=sharing 02.11] || PSPACE completeness of generalized geography. Oracle computation definitions. There exists an oracle &#039;&#039;A&#039;&#039; for which P&amp;lt;sup&amp;gt;&#039;&#039;A&#039;&#039;&amp;lt;/sup&amp;gt; = NP&amp;lt;sup&amp;gt;&#039;&#039;A&#039;&#039;&amp;lt;/sup&amp;gt;. There is an oracle B such that P&amp;lt;sup&amp;gt;&#039;&#039;B&#039;&#039;&amp;lt;/sup&amp;gt; is not equal to NP&amp;lt;sup&amp;gt;&#039;&#039;B&#039;&#039;&amp;lt;/sup&amp;gt;. || [https://www.dropbox.com/s/bvfrar2p5w3fcie/prob_08.pdf?dl=0 Problem set 8]&lt;br /&gt;
|-&lt;br /&gt;
 || 09.11 || Probabilistic computation. Probabilistic machines, the class BPP, invariance of the definition BPP for different thresholds, RP, coRP, PP, ZPP. BPP is in P/poly. Most of it is also [https://www.youtube.com/watch?v=YSMgVbOqB-8&amp;amp;list=PLm3J0oaFux3YL5vLXpzOyJiLtqLp6dCW2&amp;amp;index=23 here]|| [https://www.dropbox.com/s/dciqvmire4ze4n2/prob_09.pdf?dl=0 Problem set 9]&lt;br /&gt;
|-&lt;br /&gt;
 || [https://youtu.be/ToxNJ9p32Ec 16.11] ||  Streaming algorithms: finding the majority element, computation of the number of different elements &amp;lt;!-- &#039;&#039;F&#039;&#039;&amp;lt;sub&amp;gt;2&amp;lt;/sub&amp;gt;--&amp;gt; in logarithmic space. See Chapts 6.1-6.2 in [https://home.ttic.edu/~avrim/book.pdf foundations of datascience] by Avrim Blum and others. Another nice chapter in [http://theory.stanford.edu/~tim/w15/l/l1.pdf Tim Roughgarden&#039;s lecture notes] || [https://www.dropbox.com/s/ztg8wxuhbkhzh9e/prob_10.pdf?dl=0 Problem set 10]&lt;br /&gt;
|-&lt;br /&gt;
 || [https://drive.google.com/file/d/1mDd3HjabwwzNPMa7oPcnAeHRSymVmsvE/view?usp=sharing 23.11] || Finding the frequent items in streams of data: SpaceSaving and Count-Min Sketch. [https://www.dropbox.com/s/6u27au11u00n59p/tc-11-streaming.pdf?dl=0 Slides] || [https://www.dropbox.com/s/8fvpntf1n4hjoyu/prob_11.pdf?dl=0 Problem set 11]&lt;br /&gt;
|-&lt;br /&gt;
 || [https://youtu.be/H7hF07mMPzk 30.11] || Approximation algorithms. Approximate solutions for Vertex Cover, Weighted Vertex Cover, and TSP. [https://www.dropbox.com/s/wvtcsl6crkj8zeq/tc-12-approximation.pdf?dl=0 Slides.] [https://youtu.be/6ng15Bc8Dlw Seminar.]|| [https://www.dropbox.com/s/qug480ss98pq78p/prob_12.pdf?dl=0 Problem set 12]&lt;br /&gt;
 &lt;br /&gt;
|-&lt;br /&gt;
 || 07.12 || Colloquium. ||&lt;br /&gt;
|-&lt;br /&gt;
 || [https://www.dropbox.com/s/emvoow009xjvf5q/tc-14-clustering.pdf?dl=0 14.12] || Complexity of clustering: an exact algorithm for maximizing the inter-cluster distance and an approximate algorithm for minimizing the intra-class distance.&lt;br /&gt;
 || [https://www.dropbox.com/s/37gdsbv2it8omnm/tc-sample-exam.pdf?dl=0 Sample exam]&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
For interested students, there are 3 lectures in parameterized complexity. &lt;br /&gt;
&lt;br /&gt;
14 Sept: Fixed parameter tracktability and examples, [https://www.dropbox.com/s/zzzaulpmzql7x7u/parameterizedComplexity.pdf?dl=0 presentation]. &lt;br /&gt;
&lt;br /&gt;
21 Sept: Topics from chapters 1 and 2 in &amp;quot;Parameterized algorithms&amp;quot; by Cygan, Fomin and others, 2016.&lt;br /&gt;
&lt;br /&gt;
28 Sept: The W-hierarchy, chapter 13 in the same book.&lt;br /&gt;
&lt;br /&gt;
= Office hours =&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
|-&lt;br /&gt;
!  Person !! Monday !! Tuesday !! Wednesday !! Thursday !! Friday &lt;br /&gt;
|-&lt;br /&gt;
|  [https://www.hse.ru/en/org/persons/160550073 Bruno Bauwens], S834, [https://us02web.zoom.us/j/82300259484?pwd=NWxXekxBeE5yMm9UTmwvLzNNNGlnUT09 Zoom] ||  || ||  ||  || 14:00-20:00&lt;br /&gt;
|-&lt;br /&gt;
|  [https://www.hse.ru/en/staff/obiedkov Sergei Obiedkov], T915, [https://zoom.us/j/99663354582?pwd=K1B5R3NXWEhWbFozR2lqMkFWYW5Ydz09 Zoom] ||  ||  || 16:30–18:00 || 16:30–18:00 ||  &lt;br /&gt;
|}&lt;/div&gt;</summary>
		<author><name>.obj</name></author>
	</entry>
	<entry>
		<id>https://wiki.cs.hse.ru/index.php?title=Theory_of_Computation_2021&amp;diff=63026</id>
		<title>Theory of Computation 2021</title>
		<link rel="alternate" type="text/html" href="https://wiki.cs.hse.ru/index.php?title=Theory_of_Computation_2021&amp;diff=63026"/>
		<updated>2021-12-16T08:35:00Z</updated>

		<summary type="html">&lt;p&gt;.obj: &lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;= Classes =&lt;br /&gt;
 &lt;br /&gt;
Tuesdays 14:40–17:40, [https://ruz.hse.ru/ruz/main ruz]&lt;br /&gt;
&lt;br /&gt;
Lectures: 14:40 [https://us02web.zoom.us/j/83533615475?pwd=WDU3cHJ5RjREOGd2YU1qdDJCVm1idz09 zoomlink]&lt;br /&gt;
&lt;br /&gt;
Seminars: 16:20 [https://us02web.zoom.us/j/84546220686?pwd=U2dISk5UaFZpdmh3WTdFT3phRVNXZz09 zoomlink]&lt;br /&gt;
&lt;br /&gt;
= Dates and Deadlines =&lt;br /&gt;
Please send your homework by e-mail to both lecturers.&amp;lt;br&amp;gt;&lt;br /&gt;
Homework 1 (problem sets 1–4), deadline: October 5, 14:00; the deadline for the extra problems is &amp;lt;s&amp;gt;November 2&amp;lt;/s&amp;gt; November 8, 14:00&amp;lt;br&amp;gt;&lt;br /&gt;
Homework 2 (problem sets 5–7), deadline: &amp;lt;s&amp;gt;November 2&amp;lt;/s&amp;gt; November 8, 14:00 &amp;lt;br&amp;gt;&lt;br /&gt;
Homework 3, deadline: &amp;lt;s&amp;gt;December 7&amp;lt;/s&amp;gt; December 14, 14:00 &amp;lt;br&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Colloquium: December 7, 14:40–17:40; December 8, 16:30–18:30&#039;&#039;&#039; &amp;lt;br&amp;gt;&lt;br /&gt;
[https://www.dropbox.com/s/lxyjm6b4xatl0pz/col.pdf?dl=0 Rules and questions]&amp;lt;br&amp;gt;&lt;br /&gt;
Choose your [https://docs.google.com/document/d/1OxiLVx_6LWIJlGP9qjQe1CuBH3BGjk4Q5drHc9r5CE0/ time].&lt;br /&gt;
&lt;br /&gt;
= Grading =&lt;br /&gt;
[https://docs.google.com/spreadsheets/d/1WFBuyjv_D-8EZRhMm39fI_X69daPk2VZwzBXlchW4Mk/edit?usp=sharing Grades]&lt;br /&gt;
&lt;br /&gt;
Colloquium: 35%&amp;lt;br&amp;gt;&lt;br /&gt;
Homework: 35%&amp;lt;br&amp;gt;&lt;br /&gt;
Exam: 30%&lt;br /&gt;
&lt;br /&gt;
==Homework Grading==&lt;br /&gt;
Some homework assignments contain extra problems. Let us call all other problems regular. The weight of each problem (whether regular or extra) in the overall homework grade is 8/&#039;&#039;n&#039;&#039;, where &#039;&#039;n&#039;&#039; is the total number of regular problems in all homework assignments. Partial credit is possible for some problems.&lt;br /&gt;
&lt;br /&gt;
If you score at least 8 and solve some extra problems that do not contribute to this score, we will evaluate each of these extra problems on the scale [0, 1] and will add two maximal scores to your homework grade.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
== Exam ==&lt;br /&gt;
&lt;br /&gt;
December 20, 9:30–12:30, [https://us02web.zoom.us/j/83533615475?pwd=WDU3cHJ5RjREOGd2YU1qdDJCVm1idz09 Zoom]&lt;br /&gt;
&lt;br /&gt;
The exam consists of 7 or 8 questions of the same level as the homework.&lt;br /&gt;
&lt;br /&gt;
You may use all course materials (seminar sheets, Sipser&#039;s book, etc). You are not allowed to communicate with other students and to use social network sites like Telegram, Facebook, etc. You may not use your phone except in the end of the exam to submit your work.&lt;br /&gt;
&lt;br /&gt;
You must submit your answers in handwriting (exceptions can be asked at the beginning of the exam) by sending scanned or photographed copies to both lecturers.  &lt;br /&gt;
&lt;br /&gt;
We plan to publish the grades on December 21. If you have questions, you can ask them at 13:00 on December 21 via Zoom (the link will appear here).&lt;br /&gt;
&lt;br /&gt;
= Course Materials =&lt;br /&gt;
&lt;br /&gt;
The main reference is Sipser&#039;s book &amp;quot;Introduction to the theory of computation&amp;quot;, chapters 3, 7–10.&lt;br /&gt;
&lt;br /&gt;
If you need some background in math, consider these two sources:&amp;lt;br&amp;gt;&lt;br /&gt;
[http://www.cs.elte.hu/~lovasz/dmbook.ps Lecture notes: Discrete Mathematics], L. Lovasz, K. Vesztergombi&amp;lt;br&amp;gt;&lt;br /&gt;
[http://rubtsov.su/public/DM-HSE-Draft.pdf Лекции по дискретной математике] (черновик учебника, in Russian)&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
|-&lt;br /&gt;
! Video !! Summary !! Problem list&lt;br /&gt;
|-&lt;br /&gt;
 || 07.09 || Turing machines, multitape Turing machines, connection between them. Universal Turing machine. Examples ([https://www.dropbox.com/s/wna14b7y7nmw3cq/tm.py?dl=0 one], [https://www.dropbox.com/s/wrl3mkeqslj3xtu/wsharpw.py?dl=0 two]). Time and space complexity. Complexity classes P, PSPACE, EXP. || [https://www.dropbox.com/s/37eel2qayios6b3/prob_1.pdf?dl=0 Problem set 1]&lt;br /&gt;
|-&lt;br /&gt;
|| 14.09 ||  Time and space hierarchy theorem. Time and space constructible functions. || [https://www.dropbox.com/s/ow4m1z8u8r211qs/prob_2.pdf?dl=0 Problem set 2]&lt;br /&gt;
|-&lt;br /&gt;
 || 21.09 || Complexity class NP. Examples. Polynomial reductions. NP-hardness and NP-completeness. &lt;br /&gt;
 ||  [https://www.dropbox.com/s/bf68zicg4uh051x/prob_03.pdf?dl=0 Problem set 3]&lt;br /&gt;
|-&lt;br /&gt;
 || 28.09 ||  Non-deterministic TMs. Another definition of NP. Proving NP-hardness by reduction from an NP-complete problem. Examples of NP-complete problems.  || [https://www.dropbox.com/s/g817m6v0ygb8h4n/prob_04.pdf?dl=0 Problem set 4]&lt;br /&gt;
|-&lt;br /&gt;
 || 05.10 || Inclusions between P, NP, and PSPACE. Circuit complexity. Examples. All functions are computed by circuits. Existence of functions with exponential circuit complexity. P is in P/poly.|| [https://www.dropbox.com/s/qkc5p4795rualwn/prob_05.pdf?dl=0 Problem set 5]&lt;br /&gt;
|-&lt;br /&gt;
 || 12.10 || P is a subset of P/poly, Cook–Levin theorem, NP-completeness of: subsetsum, set-splitting, 3-colorability and exactly 1-in-3 SAT.  || [https://www.dropbox.com/s/y2y1lu29936xy9n/prob_06.pdf?dl=0 Problem set 6]&lt;br /&gt;
|-&lt;br /&gt;
 || [https://drive.google.com/drive/folders/1loJWyo9TK6ucCp8RnD3xx3DAVPDs0OiF?usp=sharing 26.10] || Space complexity. Classes L, NL, PSPACE and NPSPACE. Directed Reachability is in SPACE(log^2 n). Configuration graph. Inclusions between time and space classes. TQBF problem, its PSPACE-completeness. PSPACE = NPSPACE. NSPACE(s(n)) is in SPACE(s(n)^2) for space constructible s. || [https://www.dropbox.com/s/b6m0u5vqtutdhq1/prob_07.pdf?dl=0 Problem set 7]&lt;br /&gt;
|- &lt;br /&gt;
|| [https://drive.google.com/drive/folders/1w4W15sPS1nCIpQZQWasqPq8wSVLle5Ik?usp=sharing 02.11] || PSPACE completeness of generalized geography. Oracle computation definitions. There exists an oracle &#039;&#039;A&#039;&#039; for which P&amp;lt;sup&amp;gt;&#039;&#039;A&#039;&#039;&amp;lt;/sup&amp;gt; = NP&amp;lt;sup&amp;gt;&#039;&#039;A&#039;&#039;&amp;lt;/sup&amp;gt;. There is an oracle B such that P&amp;lt;sup&amp;gt;&#039;&#039;B&#039;&#039;&amp;lt;/sup&amp;gt; is not equal to NP&amp;lt;sup&amp;gt;&#039;&#039;B&#039;&#039;&amp;lt;/sup&amp;gt;. || [https://www.dropbox.com/s/bvfrar2p5w3fcie/prob_08.pdf?dl=0 Problem set 8]&lt;br /&gt;
|-&lt;br /&gt;
 || 09.11 || Probabilistic computation. Probabilistic machines, the class BPP, invariance of the definition BPP for different thresholds, RP, coRP, PP, ZPP. BPP is in P/poly. Most of it is also [https://www.youtube.com/watch?v=YSMgVbOqB-8&amp;amp;list=PLm3J0oaFux3YL5vLXpzOyJiLtqLp6dCW2&amp;amp;index=23 here]|| [https://www.dropbox.com/s/dciqvmire4ze4n2/prob_09.pdf?dl=0 Problem set 9]&lt;br /&gt;
|-&lt;br /&gt;
 || [https://youtu.be/ToxNJ9p32Ec 16.11] ||  Streaming algorithms: finding the majority element, computation of the number of different elements &amp;lt;!-- &#039;&#039;F&#039;&#039;&amp;lt;sub&amp;gt;2&amp;lt;/sub&amp;gt;--&amp;gt; in logarithmic space. See Chapts 6.1-6.2 in [https://home.ttic.edu/~avrim/book.pdf foundations of datascience] by Avrim Blum and others. Another nice chapter in [http://theory.stanford.edu/~tim/w15/l/l1.pdf Tim Roughgarden&#039;s lecture notes] || [https://www.dropbox.com/s/ztg8wxuhbkhzh9e/prob_10.pdf?dl=0 Problem set 10]&lt;br /&gt;
|-&lt;br /&gt;
 || [https://drive.google.com/file/d/1mDd3HjabwwzNPMa7oPcnAeHRSymVmsvE/view?usp=sharing 23.11] || Finding the frequent items in streams of data: SpaceSaving and Count-Min Sketch. [https://www.dropbox.com/s/6u27au11u00n59p/tc-11-streaming.pdf?dl=0 Slides] || [https://www.dropbox.com/s/8fvpntf1n4hjoyu/prob_11.pdf?dl=0 Problem set 11]&lt;br /&gt;
|-&lt;br /&gt;
 || [https://youtu.be/H7hF07mMPzk 30.11] || Approximation algorithms. Approximate solutions for Vertex Cover, Weighted Vertex Cover, and TSP. [https://www.dropbox.com/s/wvtcsl6crkj8zeq/tc-12-approximation.pdf?dl=0 Slides.] [https://youtu.be/6ng15Bc8Dlw Seminar.]|| [https://www.dropbox.com/s/qug480ss98pq78p/prob_12.pdf?dl=0 Problem set 12]&lt;br /&gt;
 &lt;br /&gt;
|-&lt;br /&gt;
 || 07.12 || Colloquium. ||&lt;br /&gt;
|-&lt;br /&gt;
 || [https://www.dropbox.com/s/emvoow009xjvf5q/tc-14-clustering.pdf?dl=0 14.12] || Complexity of clustering: an exact algorithm for maximizing the inter-cluster distance and an approximate algorithm for minimizing the intra-class distance.&lt;br /&gt;
 || [https://www.dropbox.com/s/37gdsbv2it8omnm/tc-sample-exam.pdf?dl=0 Sample exam]&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
For interested students, there are 3 lectures in parameterized complexity. &lt;br /&gt;
&lt;br /&gt;
14 Sept: Fixed parameter tracktability and examples, [https://www.dropbox.com/s/zzzaulpmzql7x7u/parameterizedComplexity.pdf?dl=0 presentation]. &lt;br /&gt;
&lt;br /&gt;
21 Sept: Topics from chapters 1 and 2 in &amp;quot;Parameterized algorithms&amp;quot; by Cygan, Fomin and others, 2016.&lt;br /&gt;
&lt;br /&gt;
28 Sept: The W-hierarchy, chapter 13 in the same book.&lt;br /&gt;
&lt;br /&gt;
= Office hours =&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
|-&lt;br /&gt;
!  Person !! Monday !! Tuesday !! Wednesday !! Thursday !! Friday &lt;br /&gt;
|-&lt;br /&gt;
|  [https://www.hse.ru/en/org/persons/160550073 Bruno Bauwens], S834, [https://us02web.zoom.us/j/82300259484?pwd=NWxXekxBeE5yMm9UTmwvLzNNNGlnUT09 Zoom] ||  || ||  ||  || 14:00-20:00&lt;br /&gt;
|-&lt;br /&gt;
|  [https://www.hse.ru/en/staff/obiedkov Sergei Obiedkov], T915, [https://zoom.us/j/99663354582?pwd=K1B5R3NXWEhWbFozR2lqMkFWYW5Ydz09 Zoom] ||  ||  || 16:30–18:00 || 16:30–18:00 ||  &lt;br /&gt;
|}&lt;/div&gt;</summary>
		<author><name>.obj</name></author>
	</entry>
	<entry>
		<id>https://wiki.cs.hse.ru/index.php?title=Theory_of_Computation_2021&amp;diff=62987</id>
		<title>Theory of Computation 2021</title>
		<link rel="alternate" type="text/html" href="https://wiki.cs.hse.ru/index.php?title=Theory_of_Computation_2021&amp;diff=62987"/>
		<updated>2021-12-14T21:59:28Z</updated>

		<summary type="html">&lt;p&gt;.obj: /* Course Materials */&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;= Classes =&lt;br /&gt;
 &lt;br /&gt;
Tuesdays 14:40–17:40, [https://ruz.hse.ru/ruz/main ruz]&lt;br /&gt;
&lt;br /&gt;
Lectures: 14:40 [https://us02web.zoom.us/j/83533615475?pwd=WDU3cHJ5RjREOGd2YU1qdDJCVm1idz09 zoomlink]&lt;br /&gt;
&lt;br /&gt;
Seminars: 16:20 [https://us02web.zoom.us/j/84546220686?pwd=U2dISk5UaFZpdmh3WTdFT3phRVNXZz09 zoomlink]&lt;br /&gt;
&lt;br /&gt;
= Dates and Deadlines =&lt;br /&gt;
Please send your homework by e-mail to both lecturers.&amp;lt;br&amp;gt;&lt;br /&gt;
Homework 1 (problem sets 1–4), deadline: October 5, 14:00; the deadline for the extra problems is &amp;lt;s&amp;gt;November 2&amp;lt;/s&amp;gt; November 8, 14:00&amp;lt;br&amp;gt;&lt;br /&gt;
Homework 2 (problem sets 5–7), deadline: &amp;lt;s&amp;gt;November 2&amp;lt;/s&amp;gt; November 8, 14:00 &amp;lt;br&amp;gt;&lt;br /&gt;
Homework 3, deadline: &amp;lt;s&amp;gt;December 7&amp;lt;/s&amp;gt; December 14, 14:00 &amp;lt;br&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Colloquium: December 7, 14:40–17:40; December 8, 16:30–18:30&#039;&#039;&#039; &amp;lt;br&amp;gt;&lt;br /&gt;
[https://www.dropbox.com/s/lxyjm6b4xatl0pz/col.pdf?dl=0 Rules and questions]&amp;lt;br&amp;gt;&lt;br /&gt;
Choose your [https://docs.google.com/document/d/1OxiLVx_6LWIJlGP9qjQe1CuBH3BGjk4Q5drHc9r5CE0/ time].&lt;br /&gt;
&lt;br /&gt;
= Grading =&lt;br /&gt;
[https://docs.google.com/spreadsheets/d/1WFBuyjv_D-8EZRhMm39fI_X69daPk2VZwzBXlchW4Mk/edit?usp=sharing Grades]&lt;br /&gt;
&lt;br /&gt;
Colloquium: 35%&amp;lt;br&amp;gt;&lt;br /&gt;
Homework: 35%&amp;lt;br&amp;gt;&lt;br /&gt;
Exam: 30%&lt;br /&gt;
&lt;br /&gt;
==Homework Grading==&lt;br /&gt;
Some homework assignments contain extra problems. Let us call all other problems regular. The weight of each problem (whether regular or extra) in the overall homework grade is 8/&#039;&#039;n&#039;&#039;, where &#039;&#039;n&#039;&#039; is the total number of regular problems in all homework assignments. Partial credit is possible for some problems.&lt;br /&gt;
&lt;br /&gt;
If you score at least 8 and solve some extra problems that do not contribute to this score, we will evaluate each of these extra problems on the scale [0, 1] and will add two maximal scores to your homework grade.&lt;br /&gt;
&lt;br /&gt;
= Course Materials =&lt;br /&gt;
&lt;br /&gt;
The main reference is Sipser&#039;s book &amp;quot;Introduction to the theory of computation&amp;quot;, chapters 3, 7–10.&lt;br /&gt;
&lt;br /&gt;
If you need some background in math, consider these two sources:&amp;lt;br&amp;gt;&lt;br /&gt;
[http://www.cs.elte.hu/~lovasz/dmbook.ps Lecture notes: Discrete Mathematics], L. Lovasz, K. Vesztergombi&amp;lt;br&amp;gt;&lt;br /&gt;
[http://rubtsov.su/public/DM-HSE-Draft.pdf Лекции по дискретной математике] (черновик учебника, in Russian)&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
|-&lt;br /&gt;
! Video !! Summary !! Problem list&lt;br /&gt;
|-&lt;br /&gt;
 || 07.09 || Turing machines, multitape Turing machines, connection between them. Universal Turing machine. Examples ([https://www.dropbox.com/s/wna14b7y7nmw3cq/tm.py?dl=0 one], [https://www.dropbox.com/s/wrl3mkeqslj3xtu/wsharpw.py?dl=0 two]). Time and space complexity. Complexity classes P, PSPACE, EXP. || [https://www.dropbox.com/s/37eel2qayios6b3/prob_1.pdf?dl=0 Problem set 1]&lt;br /&gt;
|-&lt;br /&gt;
|| 14.09 ||  Time and space hierarchy theorem. Time and space constructible functions. || [https://www.dropbox.com/s/ow4m1z8u8r211qs/prob_2.pdf?dl=0 Problem set 2]&lt;br /&gt;
|-&lt;br /&gt;
 || 21.09 || Complexity class NP. Examples. Polynomial reductions. NP-hardness and NP-completeness. &lt;br /&gt;
 ||  [https://www.dropbox.com/s/bf68zicg4uh051x/prob_03.pdf?dl=0 Problem set 3]&lt;br /&gt;
|-&lt;br /&gt;
 || 28.09 ||  Non-deterministic TMs. Another definition of NP. Proving NP-hardness by reduction from an NP-complete problem. Examples of NP-complete problems.  || [https://www.dropbox.com/s/g817m6v0ygb8h4n/prob_04.pdf?dl=0 Problem set 4]&lt;br /&gt;
|-&lt;br /&gt;
 || 05.10 || Inclusions between P, NP, and PSPACE. Circuit complexity. Examples. All functions are computed by circuits. Existence of functions with exponential circuit complexity. P is in P/poly.|| [https://www.dropbox.com/s/qkc5p4795rualwn/prob_05.pdf?dl=0 Problem set 5]&lt;br /&gt;
|-&lt;br /&gt;
 || 12.10 || P is a subset of P/poly, Cook–Levin theorem, NP-completeness of: subsetsum, set-splitting, 3-colorability and exactly 1-in-3 SAT.  || [https://www.dropbox.com/s/y2y1lu29936xy9n/prob_06.pdf?dl=0 Problem set 6]&lt;br /&gt;
|-&lt;br /&gt;
 || [https://drive.google.com/drive/folders/1loJWyo9TK6ucCp8RnD3xx3DAVPDs0OiF?usp=sharing 26.10] || Space complexity. Classes L, NL, PSPACE and NPSPACE. Directed Reachability is in SPACE(log^2 n). Configuration graph. Inclusions between time and space classes. TQBF problem, its PSPACE-completeness. PSPACE = NPSPACE. NSPACE(s(n)) is in SPACE(s(n)^2) for space constructible s. || [https://www.dropbox.com/s/b6m0u5vqtutdhq1/prob_07.pdf?dl=0 Problem set 7]&lt;br /&gt;
|- &lt;br /&gt;
|| [https://drive.google.com/drive/folders/1w4W15sPS1nCIpQZQWasqPq8wSVLle5Ik?usp=sharing 02.11] || PSPACE completeness of generalized geography. Oracle computation definitions. There exists an oracle &#039;&#039;A&#039;&#039; for which P&amp;lt;sup&amp;gt;&#039;&#039;A&#039;&#039;&amp;lt;/sup&amp;gt; = NP&amp;lt;sup&amp;gt;&#039;&#039;A&#039;&#039;&amp;lt;/sup&amp;gt;. There is an oracle B such that P&amp;lt;sup&amp;gt;&#039;&#039;B&#039;&#039;&amp;lt;/sup&amp;gt; is not equal to NP&amp;lt;sup&amp;gt;&#039;&#039;B&#039;&#039;&amp;lt;/sup&amp;gt;. || [https://www.dropbox.com/s/bvfrar2p5w3fcie/prob_08.pdf?dl=0 Problem set 8]&lt;br /&gt;
|-&lt;br /&gt;
 || 09.11 || Probabilistic computation. Probabilistic machines, the class BPP, invariance of the definition BPP for different thresholds, RP, coRP, PP, ZPP. BPP is in P/poly. Most of it is also [https://www.youtube.com/watch?v=YSMgVbOqB-8&amp;amp;list=PLm3J0oaFux3YL5vLXpzOyJiLtqLp6dCW2&amp;amp;index=23 here]|| [https://www.dropbox.com/s/dciqvmire4ze4n2/prob_09.pdf?dl=0 Problem set 9]&lt;br /&gt;
|-&lt;br /&gt;
 || [https://youtu.be/ToxNJ9p32Ec 16.11] ||  Streaming algorithms: finding the majority element, computation of the number of different elements &amp;lt;!-- &#039;&#039;F&#039;&#039;&amp;lt;sub&amp;gt;2&amp;lt;/sub&amp;gt;--&amp;gt; in logarithmic space. See Chapts 6.1-6.2 in [https://home.ttic.edu/~avrim/book.pdf foundations of datascience] by Avrim Blum and others. Another nice chapter in [http://theory.stanford.edu/~tim/w15/l/l1.pdf Tim Roughgarden&#039;s lecture notes] || [https://www.dropbox.com/s/ztg8wxuhbkhzh9e/prob_10.pdf?dl=0 Problem set 10]&lt;br /&gt;
|-&lt;br /&gt;
 || [https://drive.google.com/file/d/1mDd3HjabwwzNPMa7oPcnAeHRSymVmsvE/view?usp=sharing 23.11] || Finding the frequent items in streams of data: SpaceSaving and Count-Min Sketch. [https://www.dropbox.com/s/6u27au11u00n59p/tc-11-streaming.pdf?dl=0 Slides] || [https://www.dropbox.com/s/8fvpntf1n4hjoyu/prob_11.pdf?dl=0 Problem set 11]&lt;br /&gt;
|-&lt;br /&gt;
 || [https://youtu.be/H7hF07mMPzk 30.11] || Approximation algorithms. Approximate solutions for Vertex Cover, Weighted Vertex Cover, and TSP. [https://www.dropbox.com/s/wvtcsl6crkj8zeq/tc-12-approximation.pdf?dl=0 Slides.] [https://youtu.be/6ng15Bc8Dlw Seminar.]|| [https://www.dropbox.com/s/qug480ss98pq78p/prob_12.pdf?dl=0 Problem set 12]&lt;br /&gt;
 &lt;br /&gt;
|-&lt;br /&gt;
 || 07.12 || Colloquium. ||&lt;br /&gt;
|-&lt;br /&gt;
 || [https://www.dropbox.com/s/emvoow009xjvf5q/tc-14-clustering.pdf?dl=0 14.12] || Complexity of clustering: an exact algorithm for maximizing the inter-cluster distance and an approximate algorithm for minimizing the intra-class distance.&lt;br /&gt;
 || [https://www.dropbox.com/s/37gdsbv2it8omnm/tc-sample-exam.pdf?dl=0 Sample exam]&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
For interested students, there are 3 lectures in parameterized complexity. &lt;br /&gt;
&lt;br /&gt;
14 Sept: Fixed parameter tracktability and examples, [https://www.dropbox.com/s/zzzaulpmzql7x7u/parameterizedComplexity.pdf?dl=0 presentation]. &lt;br /&gt;
&lt;br /&gt;
21 Sept: Topics from chapters 1 and 2 in &amp;quot;Parameterized algorithms&amp;quot; by Cygan, Fomin and others, 2016.&lt;br /&gt;
&lt;br /&gt;
28 Sept: The W-hierarchy, chapter 13 in the same book.&lt;br /&gt;
&lt;br /&gt;
= Office hours =&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
|-&lt;br /&gt;
!  Person !! Monday !! Tuesday !! Wednesday !! Thursday !! Friday &lt;br /&gt;
|-&lt;br /&gt;
|  [https://www.hse.ru/en/org/persons/160550073 Bruno Bauwens], S834, [https://us02web.zoom.us/j/82300259484?pwd=NWxXekxBeE5yMm9UTmwvLzNNNGlnUT09 Zoom] ||  || ||  ||  || 14:00-20:00&lt;br /&gt;
|-&lt;br /&gt;
|  [https://www.hse.ru/en/staff/obiedkov Sergei Obiedkov], T915, [https://zoom.us/j/99663354582?pwd=K1B5R3NXWEhWbFozR2lqMkFWYW5Ydz09 Zoom] ||  ||  || 16:30–18:00 || 16:30–18:00 ||  &lt;br /&gt;
|}&lt;/div&gt;</summary>
		<author><name>.obj</name></author>
	</entry>
	<entry>
		<id>https://wiki.cs.hse.ru/index.php?title=Theory_of_Computation_2021&amp;diff=62970</id>
		<title>Theory of Computation 2021</title>
		<link rel="alternate" type="text/html" href="https://wiki.cs.hse.ru/index.php?title=Theory_of_Computation_2021&amp;diff=62970"/>
		<updated>2021-12-14T13:16:42Z</updated>

		<summary type="html">&lt;p&gt;.obj: /* Course Materials */&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;= Classes =&lt;br /&gt;
 &lt;br /&gt;
Tuesdays 14:40–17:40, [https://ruz.hse.ru/ruz/main ruz]&lt;br /&gt;
&lt;br /&gt;
Lectures: 14:40 [https://us02web.zoom.us/j/83533615475?pwd=WDU3cHJ5RjREOGd2YU1qdDJCVm1idz09 zoomlink]&lt;br /&gt;
&lt;br /&gt;
Seminars: 16:20 [https://us02web.zoom.us/j/84546220686?pwd=U2dISk5UaFZpdmh3WTdFT3phRVNXZz09 zoomlink]&lt;br /&gt;
&lt;br /&gt;
= Dates and Deadlines =&lt;br /&gt;
Please send your homework by e-mail to both lecturers.&amp;lt;br&amp;gt;&lt;br /&gt;
Homework 1 (problem sets 1–4), deadline: October 5, 14:00; the deadline for the extra problems is &amp;lt;s&amp;gt;November 2&amp;lt;/s&amp;gt; November 8, 14:00&amp;lt;br&amp;gt;&lt;br /&gt;
Homework 2 (problem sets 5–7), deadline: &amp;lt;s&amp;gt;November 2&amp;lt;/s&amp;gt; November 8, 14:00 &amp;lt;br&amp;gt;&lt;br /&gt;
Homework 3, deadline: &amp;lt;s&amp;gt;December 7&amp;lt;/s&amp;gt; December 14, 14:00 &amp;lt;br&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Colloquium: December 7, 14:40–17:40; December 8, 16:30–18:30&#039;&#039;&#039; &amp;lt;br&amp;gt;&lt;br /&gt;
[https://www.dropbox.com/s/lxyjm6b4xatl0pz/col.pdf?dl=0 Rules and questions]&amp;lt;br&amp;gt;&lt;br /&gt;
Choose your [https://docs.google.com/document/d/1OxiLVx_6LWIJlGP9qjQe1CuBH3BGjk4Q5drHc9r5CE0/ time].&lt;br /&gt;
&lt;br /&gt;
= Grading =&lt;br /&gt;
[https://docs.google.com/spreadsheets/d/1WFBuyjv_D-8EZRhMm39fI_X69daPk2VZwzBXlchW4Mk/edit?usp=sharing Grades]&lt;br /&gt;
&lt;br /&gt;
Colloquium: 35%&amp;lt;br&amp;gt;&lt;br /&gt;
Homework: 35%&amp;lt;br&amp;gt;&lt;br /&gt;
Exam: 30%&lt;br /&gt;
&lt;br /&gt;
==Homework Grading==&lt;br /&gt;
Some homework assignments contain extra problems. Let us call all other problems regular. The weight of each problem (whether regular or extra) in the overall homework grade is 8/&#039;&#039;n&#039;&#039;, where &#039;&#039;n&#039;&#039; is the total number of regular problems in all homework assignments. Partial credit is possible for some problems.&lt;br /&gt;
&lt;br /&gt;
If you score at least 8 and solve some extra problems that do not contribute to this score, we will evaluate each of these extra problems on the scale [0, 1] and will add two maximal scores to your homework grade.&lt;br /&gt;
&lt;br /&gt;
= Course Materials =&lt;br /&gt;
&lt;br /&gt;
The main reference is Sipser&#039;s book &amp;quot;Introduction to the theory of computation&amp;quot;, chapters 3, 7–10.&lt;br /&gt;
&lt;br /&gt;
If you need some background in math, consider these two sources:&amp;lt;br&amp;gt;&lt;br /&gt;
[http://www.cs.elte.hu/~lovasz/dmbook.ps Lecture notes: Discrete Mathematics], L. Lovasz, K. Vesztergombi&amp;lt;br&amp;gt;&lt;br /&gt;
[http://rubtsov.su/public/DM-HSE-Draft.pdf Лекции по дискретной математике] (черновик учебника, in Russian)&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
|-&lt;br /&gt;
! Video !! Summary !! Problem list&lt;br /&gt;
|-&lt;br /&gt;
 || 07.09 || Turing machines, multitape Turing machines, connection between them. Universal Turing machine. Examples ([https://www.dropbox.com/s/wna14b7y7nmw3cq/tm.py?dl=0 one], [https://www.dropbox.com/s/wrl3mkeqslj3xtu/wsharpw.py?dl=0 two]). Time and space complexity. Complexity classes P, PSPACE, EXP. || [https://www.dropbox.com/s/37eel2qayios6b3/prob_1.pdf?dl=0 Problem set 1]&lt;br /&gt;
|-&lt;br /&gt;
|| 14.09 ||  Time and space hierarchy theorem. Time and space constructible functions. || [https://www.dropbox.com/s/ow4m1z8u8r211qs/prob_2.pdf?dl=0 Problem set 2]&lt;br /&gt;
|-&lt;br /&gt;
 || 21.09 || Complexity class NP. Examples. Polynomial reductions. NP-hardness and NP-completeness. &lt;br /&gt;
 ||  [https://www.dropbox.com/s/bf68zicg4uh051x/prob_03.pdf?dl=0 Problem set 3]&lt;br /&gt;
|-&lt;br /&gt;
 || 28.09 ||  Non-deterministic TMs. Another definition of NP. Proving NP-hardness by reduction from an NP-complete problem. Examples of NP-complete problems.  || [https://www.dropbox.com/s/g817m6v0ygb8h4n/prob_04.pdf?dl=0 Problem set 4]&lt;br /&gt;
|-&lt;br /&gt;
 || 05.10 || Inclusions between P, NP, and PSPACE. Circuit complexity. Examples. All functions are computed by circuits. Existence of functions with exponential circuit complexity. P is in P/poly.|| [https://www.dropbox.com/s/qkc5p4795rualwn/prob_05.pdf?dl=0 Problem set 5]&lt;br /&gt;
|-&lt;br /&gt;
 || 12.10 || P is a subset of P/poly, Cook–Levin theorem, NP-completeness of: subsetsum, set-splitting, 3-colorability and exactly 1-in-3 SAT.  || [https://www.dropbox.com/s/y2y1lu29936xy9n/prob_06.pdf?dl=0 Problem set 6]&lt;br /&gt;
|-&lt;br /&gt;
 || [https://drive.google.com/drive/folders/1loJWyo9TK6ucCp8RnD3xx3DAVPDs0OiF?usp=sharing 26.10] || Space complexity. Classes L, NL, PSPACE and NPSPACE. Directed Reachability is in SPACE(log^2 n). Configuration graph. Inclusions between time and space classes. TQBF problem, its PSPACE-completeness. PSPACE = NPSPACE. NSPACE(s(n)) is in SPACE(s(n)^2) for space constructible s. || [https://www.dropbox.com/s/b6m0u5vqtutdhq1/prob_07.pdf?dl=0 Problem set 7]&lt;br /&gt;
|- &lt;br /&gt;
|| [https://drive.google.com/drive/folders/1w4W15sPS1nCIpQZQWasqPq8wSVLle5Ik?usp=sharing 02.11] || PSPACE completeness of generalized geography. Oracle computation definitions. There exists an oracle &#039;&#039;A&#039;&#039; for which P&amp;lt;sup&amp;gt;&#039;&#039;A&#039;&#039;&amp;lt;/sup&amp;gt; = NP&amp;lt;sup&amp;gt;&#039;&#039;A&#039;&#039;&amp;lt;/sup&amp;gt;. There is an oracle B such that P&amp;lt;sup&amp;gt;&#039;&#039;B&#039;&#039;&amp;lt;/sup&amp;gt; is not equal to NP&amp;lt;sup&amp;gt;&#039;&#039;B&#039;&#039;&amp;lt;/sup&amp;gt;. || [https://www.dropbox.com/s/bvfrar2p5w3fcie/prob_08.pdf?dl=0 Problem set 8]&lt;br /&gt;
|-&lt;br /&gt;
 || 09.11 || Probabilistic computation. Probabilistic machines, the class BPP, invariance of the definition BPP for different thresholds, RP, coRP, PP, ZPP. BPP is in P/poly. Most of it is also [https://www.youtube.com/watch?v=YSMgVbOqB-8&amp;amp;list=PLm3J0oaFux3YL5vLXpzOyJiLtqLp6dCW2&amp;amp;index=23 here]|| [https://www.dropbox.com/s/dciqvmire4ze4n2/prob_09.pdf?dl=0 Problem set 9]&lt;br /&gt;
|-&lt;br /&gt;
 || [https://youtu.be/ToxNJ9p32Ec 16.11] ||  Streaming algorithms: finding the majority element, computation of the number of different elements &amp;lt;!-- &#039;&#039;F&#039;&#039;&amp;lt;sub&amp;gt;2&amp;lt;/sub&amp;gt;--&amp;gt; in logarithmic space. See Chapts 6.1-6.2 in [https://home.ttic.edu/~avrim/book.pdf foundations of datascience] by Avrim Blum and others. Another nice chapter in [http://theory.stanford.edu/~tim/w15/l/l1.pdf Tim Roughgarden&#039;s lecture notes] || [https://www.dropbox.com/s/ztg8wxuhbkhzh9e/prob_10.pdf?dl=0 Problem set 10]&lt;br /&gt;
|-&lt;br /&gt;
 || [https://drive.google.com/file/d/1mDd3HjabwwzNPMa7oPcnAeHRSymVmsvE/view?usp=sharing 23.11] || Finding the frequent items in streams of data: SpaceSaving and Count-Min Sketch. [https://www.dropbox.com/s/6u27au11u00n59p/tc-11-streaming.pdf?dl=0 Slides] || [https://www.dropbox.com/s/8fvpntf1n4hjoyu/prob_11.pdf?dl=0 Problem set 11]&lt;br /&gt;
|-&lt;br /&gt;
 || [https://youtu.be/H7hF07mMPzk 30.11] || Approximation algorithms. Approximate solutions for Vertex Cover, Weighted Vertex Cover, and TSP. [https://www.dropbox.com/s/wvtcsl6crkj8zeq/tc-12-approximation.pdf?dl=0 Slides.] [https://youtu.be/6ng15Bc8Dlw Seminar.]|| [https://www.dropbox.com/s/qug480ss98pq78p/prob_12.pdf?dl=0 Problem set 12]&lt;br /&gt;
 &lt;br /&gt;
|-&lt;br /&gt;
 || 07.12 || Colloquium. ||&lt;br /&gt;
|-&lt;br /&gt;
 || 14.12 || Complexity of clustering: an exact algorithm for maximizing the inter-cluster distance and an approximate algorithm for minimizing the intra-class distance.&lt;br /&gt;
 || [https://www.dropbox.com/s/37gdsbv2it8omnm/tc-sample-exam.pdf?dl=0 Sample exam]&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
For interested students, there are 3 lectures in parameterized complexity. &lt;br /&gt;
&lt;br /&gt;
14 Sept: Fixed parameter tracktability and examples, [https://www.dropbox.com/s/zzzaulpmzql7x7u/parameterizedComplexity.pdf?dl=0 presentation]. &lt;br /&gt;
&lt;br /&gt;
21 Sept: Topics from chapters 1 and 2 in &amp;quot;Parameterized algorithms&amp;quot; by Cygan, Fomin and others, 2016.&lt;br /&gt;
&lt;br /&gt;
28 Sept: The W-hierarchy, chapter 13 in the same book.&lt;br /&gt;
&lt;br /&gt;
= Office hours =&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
|-&lt;br /&gt;
!  Person !! Monday !! Tuesday !! Wednesday !! Thursday !! Friday &lt;br /&gt;
|-&lt;br /&gt;
|  [https://www.hse.ru/en/org/persons/160550073 Bruno Bauwens], S834, [https://us02web.zoom.us/j/82300259484?pwd=NWxXekxBeE5yMm9UTmwvLzNNNGlnUT09 Zoom] ||  || ||  ||  || 14:00-20:00&lt;br /&gt;
|-&lt;br /&gt;
|  [https://www.hse.ru/en/staff/obiedkov Sergei Obiedkov], T915, [https://zoom.us/j/99663354582?pwd=K1B5R3NXWEhWbFozR2lqMkFWYW5Ydz09 Zoom] ||  ||  || 16:30–18:00 || 16:30–18:00 ||  &lt;br /&gt;
|}&lt;/div&gt;</summary>
		<author><name>.obj</name></author>
	</entry>
	<entry>
		<id>https://wiki.cs.hse.ru/index.php?title=Theory_of_Computation_2021&amp;diff=62590</id>
		<title>Theory of Computation 2021</title>
		<link rel="alternate" type="text/html" href="https://wiki.cs.hse.ru/index.php?title=Theory_of_Computation_2021&amp;diff=62590"/>
		<updated>2021-12-07T08:48:27Z</updated>

		<summary type="html">&lt;p&gt;.obj: /* Homework Grading */&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;= Classes =&lt;br /&gt;
 &lt;br /&gt;
Tuesdays 14:40–17:40, [https://ruz.hse.ru/ruz/main ruz]&lt;br /&gt;
&lt;br /&gt;
Lectures: 14:40 [https://us02web.zoom.us/j/83533615475?pwd=WDU3cHJ5RjREOGd2YU1qdDJCVm1idz09 zoomlink]&lt;br /&gt;
&lt;br /&gt;
Seminars: 16:20 [https://us02web.zoom.us/j/84546220686?pwd=U2dISk5UaFZpdmh3WTdFT3phRVNXZz09 zoomlink]&lt;br /&gt;
&lt;br /&gt;
= Dates and Deadlines =&lt;br /&gt;
Please send your homework by e-mail to both lecturers.&amp;lt;br&amp;gt;&lt;br /&gt;
Homework 1 (problem sets 1–4), deadline: October 5, 14:00; the deadline for the extra problems is &amp;lt;s&amp;gt;November 2&amp;lt;/s&amp;gt; November 8, 14:00&amp;lt;br&amp;gt;&lt;br /&gt;
Homework 2 (problem sets 5–7), deadline: &amp;lt;s&amp;gt;November 2&amp;lt;/s&amp;gt; November 8, 14:00 &amp;lt;br&amp;gt;&lt;br /&gt;
Homework 3, deadline: &amp;lt;s&amp;gt;December 7&amp;lt;/s&amp;gt; December 14, 14:00 &amp;lt;br&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Colloquium: December 7, 14:40–17:40; December 8, 16:30–18:30&#039;&#039;&#039; &amp;lt;br&amp;gt;&lt;br /&gt;
[https://www.dropbox.com/s/lxyjm6b4xatl0pz/col.pdf?dl=0 Rules and questions]&amp;lt;br&amp;gt;&lt;br /&gt;
Choose your [https://docs.google.com/document/d/1OxiLVx_6LWIJlGP9qjQe1CuBH3BGjk4Q5drHc9r5CE0/ time].&lt;br /&gt;
&lt;br /&gt;
= Grading =&lt;br /&gt;
[https://docs.google.com/spreadsheets/d/1WFBuyjv_D-8EZRhMm39fI_X69daPk2VZwzBXlchW4Mk/edit?usp=sharing Grades]&lt;br /&gt;
&lt;br /&gt;
Colloquium: 35%&amp;lt;br&amp;gt;&lt;br /&gt;
Homework: 35%&amp;lt;br&amp;gt;&lt;br /&gt;
Exam: 30%&lt;br /&gt;
&lt;br /&gt;
==Homework Grading==&lt;br /&gt;
Some homework assignments contain extra problems. Let us call all other problems regular. The weight of each problem (whether regular or extra) in the overall homework grade is 8/&#039;&#039;n&#039;&#039;, where &#039;&#039;n&#039;&#039; is the total number of regular problems in all homework assignments. Partial credit is possible for some problems.&lt;br /&gt;
&lt;br /&gt;
If you score at least 8 and solve some extra problems that do not contribute to this score, we will evaluate each of these extra problems on the scale [0, 1] and will add two maximal scores to your homework grade.&lt;br /&gt;
&lt;br /&gt;
= Course Materials =&lt;br /&gt;
&lt;br /&gt;
The main reference is Sipser&#039;s book &amp;quot;Introduction to the theory of computation&amp;quot;, chapters 3, 7–10.&lt;br /&gt;
&lt;br /&gt;
If you need some background in math, consider these two sources:&amp;lt;br&amp;gt;&lt;br /&gt;
[http://www.cs.elte.hu/~lovasz/dmbook.ps Lecture notes: Discrete Mathematics], L. Lovasz, K. Vesztergombi&amp;lt;br&amp;gt;&lt;br /&gt;
[http://rubtsov.su/public/DM-HSE-Draft.pdf Лекции по дискретной математике] (черновик учебника, in Russian)&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
|-&lt;br /&gt;
! Video !! Summary !! Problem list&lt;br /&gt;
|-&lt;br /&gt;
 || 07.09 || Turing machines, multitape Turing machines, connection between them. Universal Turing machine. Examples ([https://www.dropbox.com/s/wna14b7y7nmw3cq/tm.py?dl=0 one], [https://www.dropbox.com/s/wrl3mkeqslj3xtu/wsharpw.py?dl=0 two]). Time and space complexity. Complexity classes P, PSPACE, EXP. || [https://www.dropbox.com/s/37eel2qayios6b3/prob_1.pdf?dl=0 Problem set 1]&lt;br /&gt;
|-&lt;br /&gt;
|| 14.09 ||  Time and space hierarchy theorem. Time and space constructible functions. || [https://www.dropbox.com/s/ow4m1z8u8r211qs/prob_2.pdf?dl=0 Problem set 2]&lt;br /&gt;
|-&lt;br /&gt;
 || 21.09 || Complexity class NP. Examples. Polynomial reductions. NP-hardness and NP-completeness. &lt;br /&gt;
 ||  [https://www.dropbox.com/s/bf68zicg4uh051x/prob_03.pdf?dl=0 Problem set 3]&lt;br /&gt;
|-&lt;br /&gt;
 || 28.09 ||  Non-deterministic TMs. Another definition of NP. Proving NP-hardness by reduction from an NP-complete problem. Examples of NP-complete problems.  || [https://www.dropbox.com/s/g817m6v0ygb8h4n/prob_04.pdf?dl=0 Problem set 4]&lt;br /&gt;
|-&lt;br /&gt;
 || 05.10 || Inclusions between P, NP, and PSPACE. Circuit complexity. Examples. All functions are computed by circuits. Existence of functions with exponential circuit complexity. P is in P/poly.|| [https://www.dropbox.com/s/qkc5p4795rualwn/prob_05.pdf?dl=0 Problem set 5]&lt;br /&gt;
|-&lt;br /&gt;
 || 12.10 || P is a subset of P/poly, Cook–Levin theorem, NP-completeness of: subsetsum, set-splitting, 3-colorability and exactly 1-in-3 SAT.  || [https://www.dropbox.com/s/y2y1lu29936xy9n/prob_06.pdf?dl=0 Problem set 6]&lt;br /&gt;
|-&lt;br /&gt;
 || [https://drive.google.com/drive/folders/1loJWyo9TK6ucCp8RnD3xx3DAVPDs0OiF?usp=sharing 26.10] || Space complexity. Classes L, NL, PSPACE and NPSPACE. Directed Reachability is in SPACE(log^2 n). Configuration graph. Inclusions between time and space classes. TQBF problem, its PSPACE-completeness. PSPACE = NPSPACE. NSPACE(s(n)) is in SPACE(s(n)^2) for space constructible s. || [https://www.dropbox.com/s/b6m0u5vqtutdhq1/prob_07.pdf?dl=0 Problem set 7]&lt;br /&gt;
|- &lt;br /&gt;
|| [https://drive.google.com/drive/folders/1w4W15sPS1nCIpQZQWasqPq8wSVLle5Ik?usp=sharing 02.11] || PSPACE completeness of generalized geography. Oracle computation definitions. There exists an oracle &#039;&#039;A&#039;&#039; for which P&amp;lt;sup&amp;gt;&#039;&#039;A&#039;&#039;&amp;lt;/sup&amp;gt; = NP&amp;lt;sup&amp;gt;&#039;&#039;A&#039;&#039;&amp;lt;/sup&amp;gt;. There is an oracle B such that P&amp;lt;sup&amp;gt;&#039;&#039;B&#039;&#039;&amp;lt;/sup&amp;gt; is not equal to NP&amp;lt;sup&amp;gt;&#039;&#039;B&#039;&#039;&amp;lt;/sup&amp;gt;. || [https://www.dropbox.com/s/bvfrar2p5w3fcie/prob_08.pdf?dl=0 Problem set 8]&lt;br /&gt;
|-&lt;br /&gt;
 || 09.11 || Probabilistic computation. Probabilistic machines, the class BPP, invariance of the definition BPP for different thresholds, RP, coRP, PP, ZPP. BPP is in P/poly. Most of it is also [https://www.youtube.com/watch?v=YSMgVbOqB-8&amp;amp;list=PLm3J0oaFux3YL5vLXpzOyJiLtqLp6dCW2&amp;amp;index=23 here]|| [https://www.dropbox.com/s/dciqvmire4ze4n2/prob_09.pdf?dl=0 Problem set 9]&lt;br /&gt;
|-&lt;br /&gt;
 || [https://youtu.be/ToxNJ9p32Ec 16.11] ||  Streaming algorithms: finding the majority element, computation of the number of different elements &amp;lt;!-- &#039;&#039;F&#039;&#039;&amp;lt;sub&amp;gt;2&amp;lt;/sub&amp;gt;--&amp;gt; in logarithmic space. See Chapts 6.1-6.2 in [https://home.ttic.edu/~avrim/book.pdf foundations of datascience] by Avrim Blum and others. Another nice chapter in [http://theory.stanford.edu/~tim/w15/l/l1.pdf Tim Roughgarden&#039;s lecture notes] || [https://www.dropbox.com/s/ztg8wxuhbkhzh9e/prob_10.pdf?dl=0 Problem set 10]&lt;br /&gt;
|-&lt;br /&gt;
 || [https://drive.google.com/file/d/1mDd3HjabwwzNPMa7oPcnAeHRSymVmsvE/view?usp=sharing 23.11] || Finding the frequent items in streams of data: SpaceSaving and Count-Min Sketch. [https://www.dropbox.com/s/6u27au11u00n59p/tc-11-streaming.pdf?dl=0 Slides] || [https://www.dropbox.com/s/8fvpntf1n4hjoyu/prob_11.pdf?dl=0 Problem set 11]&lt;br /&gt;
|-&lt;br /&gt;
 || [https://youtu.be/H7hF07mMPzk 30.11] || Approximation algorithms. Approximate solutions for Vertex Cover, Weighted Vertex Cover, and TSP. [https://www.dropbox.com/s/wvtcsl6crkj8zeq/tc-12-approximation.pdf?dl=0 Slides.] [https://youtu.be/6ng15Bc8Dlw Seminar.]|| [https://www.dropbox.com/s/qug480ss98pq78p/prob_12.pdf?dl=0 Problem set 12]&lt;br /&gt;
 &lt;br /&gt;
|-&lt;br /&gt;
 || 07.12 || Colloquium. ||&lt;br /&gt;
|-&lt;br /&gt;
 || 14.12 || Complexity of clustering: an exact algorithm for maximizing the inter-cluster distance and an approximate algorithm for minimizing the intra-class distance.&lt;br /&gt;
 || &lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
For interested students, there are 3 lectures in parameterized complexity. &lt;br /&gt;
&lt;br /&gt;
14 Sept: Fixed parameter tracktability and examples, [https://www.dropbox.com/s/zzzaulpmzql7x7u/parameterizedComplexity.pdf?dl=0 presentation]. &lt;br /&gt;
&lt;br /&gt;
21 Sept: Topics from chapters 1 and 2 in &amp;quot;Parameterized algorithms&amp;quot; by Cygan, Fomin and others, 2016.&lt;br /&gt;
&lt;br /&gt;
28 Sept: The W-hierarchy, chapter 13 in the same book.&lt;br /&gt;
&lt;br /&gt;
= Office hours =&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
|-&lt;br /&gt;
!  Person !! Monday !! Tuesday !! Wednesday !! Thursday !! Friday &lt;br /&gt;
|-&lt;br /&gt;
|  [https://www.hse.ru/en/org/persons/160550073 Bruno Bauwens], S834, [https://us02web.zoom.us/j/82300259484?pwd=NWxXekxBeE5yMm9UTmwvLzNNNGlnUT09 Zoom] ||  || ||  ||  || 14:00-20:00&lt;br /&gt;
|-&lt;br /&gt;
|  [https://www.hse.ru/en/staff/obiedkov Sergei Obiedkov], T915, [https://zoom.us/j/99663354582?pwd=K1B5R3NXWEhWbFozR2lqMkFWYW5Ydz09 Zoom] ||  ||  || 16:30–18:00 || 16:30–18:00 ||  &lt;br /&gt;
|}&lt;/div&gt;</summary>
		<author><name>.obj</name></author>
	</entry>
	<entry>
		<id>https://wiki.cs.hse.ru/index.php?title=Theory_of_Computation_2021&amp;diff=62420</id>
		<title>Theory of Computation 2021</title>
		<link rel="alternate" type="text/html" href="https://wiki.cs.hse.ru/index.php?title=Theory_of_Computation_2021&amp;diff=62420"/>
		<updated>2021-12-03T22:23:11Z</updated>

		<summary type="html">&lt;p&gt;.obj: /* Course Materials */&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;= Classes =&lt;br /&gt;
 &lt;br /&gt;
Tuesdays 14:40–17:40, [https://ruz.hse.ru/ruz/main ruz]&lt;br /&gt;
&lt;br /&gt;
Lectures: 14:40 [https://us02web.zoom.us/j/83533615475?pwd=WDU3cHJ5RjREOGd2YU1qdDJCVm1idz09 zoomlink]&lt;br /&gt;
&lt;br /&gt;
Seminars: 16:20 [https://us02web.zoom.us/j/84546220686?pwd=U2dISk5UaFZpdmh3WTdFT3phRVNXZz09 zoomlink]&lt;br /&gt;
&lt;br /&gt;
= Dates and Deadlines =&lt;br /&gt;
Please send your homework by e-mail to both lecturers.&amp;lt;br&amp;gt;&lt;br /&gt;
Homework 1 (problem sets 1–4), deadline: October 5, 14:00; the deadline for the extra problems is &amp;lt;s&amp;gt;November 2&amp;lt;/s&amp;gt; November 8, 14:00&amp;lt;br&amp;gt;&lt;br /&gt;
Homework 2 (problem sets 5–7), deadline: &amp;lt;s&amp;gt;November 2&amp;lt;/s&amp;gt; November 8, 14:00 &amp;lt;br&amp;gt;&lt;br /&gt;
Homework 3, deadline: December 7, 14:00 &amp;lt;br&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Colloquium: December 7, 14:40–17:40; December 8, 16:30–18:30&#039;&#039;&#039; &amp;lt;br&amp;gt;&lt;br /&gt;
[https://www.dropbox.com/s/lxyjm6b4xatl0pz/col.pdf?dl=0 Rules and questions]&amp;lt;br&amp;gt;&lt;br /&gt;
Choose your [https://docs.google.com/document/d/1OxiLVx_6LWIJlGP9qjQe1CuBH3BGjk4Q5drHc9r5CE0/ time].&lt;br /&gt;
&lt;br /&gt;
= Grading =&lt;br /&gt;
[https://docs.google.com/spreadsheets/d/1WFBuyjv_D-8EZRhMm39fI_X69daPk2VZwzBXlchW4Mk/edit?usp=sharing Grades]&lt;br /&gt;
&lt;br /&gt;
Colloquium: 35%&amp;lt;br&amp;gt;&lt;br /&gt;
Homework: 35%&amp;lt;br&amp;gt;&lt;br /&gt;
Exam: 30%&lt;br /&gt;
&lt;br /&gt;
==Homework Grading==&lt;br /&gt;
Some homework assignments contain extra problems. Let us call all other problems normal. The weight of each problem (whether normal or extra) in the overall homework grade is 8/&#039;&#039;n&#039;&#039;, where &#039;&#039;n&#039;&#039; is the total number of normal problems in all homework assignments. Partial credit is possible for some problems.&lt;br /&gt;
&lt;br /&gt;
If you score at least 8 and solve some extra problems that do not contribute to this score, we will evaluate each of these extra problems on the scale [0, 1] and will add two maximal scores to your homework grade.&lt;br /&gt;
&lt;br /&gt;
= Course Materials =&lt;br /&gt;
&lt;br /&gt;
The main reference is Sipser&#039;s book &amp;quot;Introduction to the theory of computation&amp;quot;, chapters 3, 7–10.&lt;br /&gt;
&lt;br /&gt;
If you need some background in math, consider these two sources:&amp;lt;br&amp;gt;&lt;br /&gt;
[http://www.cs.elte.hu/~lovasz/dmbook.ps Lecture notes: Discrete Mathematics], L. Lovasz, K. Vesztergombi&amp;lt;br&amp;gt;&lt;br /&gt;
[http://rubtsov.su/public/DM-HSE-Draft.pdf Лекции по дискретной математике] (черновик учебника, in Russian)&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
|-&lt;br /&gt;
! Video !! Summary !! Problem list&lt;br /&gt;
|-&lt;br /&gt;
 || 07.09 || Turing machines, multitape Turing machines, connection between them. Universal Turing machine. Examples ([https://www.dropbox.com/s/wna14b7y7nmw3cq/tm.py?dl=0 one], [https://www.dropbox.com/s/wrl3mkeqslj3xtu/wsharpw.py?dl=0 two]). Time and space complexity. Complexity classes P, PSPACE, EXP. || [https://www.dropbox.com/s/37eel2qayios6b3/prob_1.pdf?dl=0 Problem set 1]&lt;br /&gt;
|-&lt;br /&gt;
|| 14.09 ||  Time and space hierarchy theorem. Time and space constructible functions. || [https://www.dropbox.com/s/ow4m1z8u8r211qs/prob_2.pdf?dl=0 Problem set 2]&lt;br /&gt;
|-&lt;br /&gt;
 || 21.09 || Complexity class NP. Examples. Polynomial reductions. NP-hardness and NP-completeness. &lt;br /&gt;
 ||  [https://www.dropbox.com/s/bf68zicg4uh051x/prob_03.pdf?dl=0 Problem set 3]&lt;br /&gt;
|-&lt;br /&gt;
 || 28.09 ||  Non-deterministic TMs. Another definition of NP. Proving NP-hardness by reduction from an NP-complete problem. Examples of NP-complete problems.  || [https://www.dropbox.com/s/g817m6v0ygb8h4n/prob_04.pdf?dl=0 Problem set 4]&lt;br /&gt;
|-&lt;br /&gt;
 || 05.10 || Inclusions between P, NP, and PSPACE. Circuit complexity. Examples. All functions are computed by circuits. Existence of functions with exponential circuit complexity. P is in P/poly.|| [https://www.dropbox.com/s/qkc5p4795rualwn/prob_05.pdf?dl=0 Problem set 5]&lt;br /&gt;
|-&lt;br /&gt;
 || 12.10 || P is a subset of P/poly, Cook–Levin theorem, NP-completeness of: subsetsum, set-splitting, 3-colorability and exactly 1-in-3 SAT.  || [https://www.dropbox.com/s/y2y1lu29936xy9n/prob_06.pdf?dl=0 Problem set 6]&lt;br /&gt;
|-&lt;br /&gt;
 || [https://drive.google.com/drive/folders/1loJWyo9TK6ucCp8RnD3xx3DAVPDs0OiF?usp=sharing 26.10] || Space complexity. Classes L, NL, PSPACE and NPSPACE. Directed Reachability is in SPACE(log^2 n). Configuration graph. Inclusions between time and space classes. TQBF problem, its PSPACE-completeness. PSPACE = NPSPACE. NSPACE(s(n)) is in SPACE(s(n)^2) for space constructible s. || [https://www.dropbox.com/s/b6m0u5vqtutdhq1/prob_07.pdf?dl=0 Problem set 7]&lt;br /&gt;
|- &lt;br /&gt;
|| [https://drive.google.com/drive/folders/1w4W15sPS1nCIpQZQWasqPq8wSVLle5Ik?usp=sharing 02.11] || PSPACE completeness of generalized geography. Oracle computation definitions. There exists an oracle &#039;&#039;A&#039;&#039; for which P&amp;lt;sup&amp;gt;&#039;&#039;A&#039;&#039;&amp;lt;/sup&amp;gt; = NP&amp;lt;sup&amp;gt;&#039;&#039;A&#039;&#039;&amp;lt;/sup&amp;gt;. There is an oracle B such that P&amp;lt;sup&amp;gt;&#039;&#039;B&#039;&#039;&amp;lt;/sup&amp;gt; is not equal to NP&amp;lt;sup&amp;gt;&#039;&#039;B&#039;&#039;&amp;lt;/sup&amp;gt;. || [https://www.dropbox.com/s/bvfrar2p5w3fcie/prob_08.pdf?dl=0 Problem set 8]&lt;br /&gt;
|-&lt;br /&gt;
 || 09.11 || Probabilistic computation. Probabilistic machines, the class BPP, invariance of the definition BPP for different thresholds, RP, coRP, PP, ZPP. BPP is in P/poly. Most of it is also [https://www.youtube.com/watch?v=YSMgVbOqB-8&amp;amp;list=PLm3J0oaFux3YL5vLXpzOyJiLtqLp6dCW2&amp;amp;index=23 here]|| [https://www.dropbox.com/s/dciqvmire4ze4n2/prob_09.pdf?dl=0 Problem set 9]&lt;br /&gt;
|-&lt;br /&gt;
 || [https://youtu.be/ToxNJ9p32Ec 16.11] ||  Streaming algorithms: finding the majority element, computation of the number of different elements &amp;lt;!-- &#039;&#039;F&#039;&#039;&amp;lt;sub&amp;gt;2&amp;lt;/sub&amp;gt;--&amp;gt; in logarithmic space. See Chapts 6.1-6.2 in [https://home.ttic.edu/~avrim/book.pdf foundations of datascience] by Avrim Blum and others. Another nice chapter in [http://theory.stanford.edu/~tim/w15/l/l1.pdf Tim Roughgarden&#039;s lecture notes] || [https://www.dropbox.com/s/ztg8wxuhbkhzh9e/prob_10.pdf?dl=0 Problem set 10]&lt;br /&gt;
|-&lt;br /&gt;
 || [https://drive.google.com/file/d/1mDd3HjabwwzNPMa7oPcnAeHRSymVmsvE/view?usp=sharing 23.11] || Finding the frequent items in streams of data: SpaceSaving and Count-Min Sketch. [https://www.dropbox.com/s/6u27au11u00n59p/tc-11-streaming.pdf?dl=0 Slides] || [https://www.dropbox.com/s/8fvpntf1n4hjoyu/prob_11.pdf?dl=0 Problem set 11]&lt;br /&gt;
|-&lt;br /&gt;
 || [https://youtu.be/H7hF07mMPzk 30.11] || Approximation algorithms. Approximate solutions for Vertex Cover, Weighted Vertex Cover, and TSP. [https://www.dropbox.com/s/wvtcsl6crkj8zeq/tc-12-approximation.pdf?dl=0 Slides.] [https://youtu.be/6ng15Bc8Dlw Seminar.]|| [https://www.dropbox.com/s/qug480ss98pq78p/prob_12.pdf?dl=0 Problem set 12]&lt;br /&gt;
 &lt;br /&gt;
|-&lt;br /&gt;
 || 07.12 || Colloquium. ||&lt;br /&gt;
|-&lt;br /&gt;
 || 14.12 || Complexity of clustering: an exact algorithm for maximizing the inter-cluster distance and an approximate algorithm for minimizing the intra-class distance.&lt;br /&gt;
 || &lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
For interested students, there are 3 lectures in parameterized complexity. &lt;br /&gt;
&lt;br /&gt;
14 Sept: Fixed parameter tracktability and examples, [https://www.dropbox.com/s/zzzaulpmzql7x7u/parameterizedComplexity.pdf?dl=0 presentation]. &lt;br /&gt;
&lt;br /&gt;
21 Sept: Topics from chapters 1 and 2 in &amp;quot;Parameterized algorithms&amp;quot; by Cygan, Fomin and others, 2016.&lt;br /&gt;
&lt;br /&gt;
28 Sept: The W-hierarchy, chapter 13 in the same book.&lt;br /&gt;
&lt;br /&gt;
= Office hours =&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
|-&lt;br /&gt;
!  Person !! Monday !! Tuesday !! Wednesday !! Thursday !! Friday &lt;br /&gt;
|-&lt;br /&gt;
|  [https://www.hse.ru/en/org/persons/160550073 Bruno Bauwens], S834, [https://us02web.zoom.us/j/82300259484?pwd=NWxXekxBeE5yMm9UTmwvLzNNNGlnUT09 Zoom] ||  || ||  ||  || 14:00-20:00&lt;br /&gt;
|-&lt;br /&gt;
|  [https://www.hse.ru/en/staff/obiedkov Sergei Obiedkov], T915, [https://zoom.us/j/99663354582?pwd=K1B5R3NXWEhWbFozR2lqMkFWYW5Ydz09 Zoom] ||  ||  || 16:30–18:00 || 16:30–18:00 ||  &lt;br /&gt;
|}&lt;/div&gt;</summary>
		<author><name>.obj</name></author>
	</entry>
	<entry>
		<id>https://wiki.cs.hse.ru/index.php?title=Theory_of_Computation_2021&amp;diff=62394</id>
		<title>Theory of Computation 2021</title>
		<link rel="alternate" type="text/html" href="https://wiki.cs.hse.ru/index.php?title=Theory_of_Computation_2021&amp;diff=62394"/>
		<updated>2021-12-03T14:46:30Z</updated>

		<summary type="html">&lt;p&gt;.obj: /* Dates and Deadlines */&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;= Classes =&lt;br /&gt;
 &lt;br /&gt;
Tuesdays 14:40–17:40, [https://ruz.hse.ru/ruz/main ruz]&lt;br /&gt;
&lt;br /&gt;
Lectures: 14:40 [https://us02web.zoom.us/j/83533615475?pwd=WDU3cHJ5RjREOGd2YU1qdDJCVm1idz09 zoomlink]&lt;br /&gt;
&lt;br /&gt;
Seminars: 16:20 [https://us02web.zoom.us/j/84546220686?pwd=U2dISk5UaFZpdmh3WTdFT3phRVNXZz09 zoomlink]&lt;br /&gt;
&lt;br /&gt;
= Dates and Deadlines =&lt;br /&gt;
Please send your homework by e-mail to both lecturers.&amp;lt;br&amp;gt;&lt;br /&gt;
Homework 1 (problem sets 1–4), deadline: October 5, 14:00; the deadline for the extra problems is &amp;lt;s&amp;gt;November 2&amp;lt;/s&amp;gt; November 8, 14:00&amp;lt;br&amp;gt;&lt;br /&gt;
Homework 2 (problem sets 5–7), deadline: &amp;lt;s&amp;gt;November 2&amp;lt;/s&amp;gt; November 8, 14:00 &amp;lt;br&amp;gt;&lt;br /&gt;
Homework 3, deadline: December 7, 14:00 &amp;lt;br&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Colloquium: December 7, 14:40–17:40; December 8, 16:30–18:30&#039;&#039;&#039; &amp;lt;br&amp;gt;&lt;br /&gt;
[https://www.dropbox.com/s/lxyjm6b4xatl0pz/col.pdf?dl=0 Rules and questions]&amp;lt;br&amp;gt;&lt;br /&gt;
Choose your [https://docs.google.com/document/d/1OxiLVx_6LWIJlGP9qjQe1CuBH3BGjk4Q5drHc9r5CE0/ time].&lt;br /&gt;
&lt;br /&gt;
= Grading =&lt;br /&gt;
[https://docs.google.com/spreadsheets/d/1WFBuyjv_D-8EZRhMm39fI_X69daPk2VZwzBXlchW4Mk/edit?usp=sharing Grades]&lt;br /&gt;
&lt;br /&gt;
Colloquium: 35%&amp;lt;br&amp;gt;&lt;br /&gt;
Homework: 35%&amp;lt;br&amp;gt;&lt;br /&gt;
Exam: 30%&lt;br /&gt;
&lt;br /&gt;
==Homework Grading==&lt;br /&gt;
Some homework assignments contain extra problems. Let us call all other problems normal. The weight of each problem (whether normal or extra) in the overall homework grade is 8/&#039;&#039;n&#039;&#039;, where &#039;&#039;n&#039;&#039; is the total number of normal problems in all homework assignments. Partial credit is possible for some problems.&lt;br /&gt;
&lt;br /&gt;
If you score at least 8 and solve some extra problems that do not contribute to this score, we will evaluate each of these extra problems on the scale [0, 1] and will add two maximal scores to your homework grade.&lt;br /&gt;
&lt;br /&gt;
= Course Materials =&lt;br /&gt;
&lt;br /&gt;
The main reference is Sipser&#039;s book &amp;quot;Introduction to the theory of computation&amp;quot;, chapters 3, 7–10.&lt;br /&gt;
&lt;br /&gt;
If you need some background in math, consider these two sources:&amp;lt;br&amp;gt;&lt;br /&gt;
[http://www.cs.elte.hu/~lovasz/dmbook.ps Lecture notes: Discrete Mathematics], L. Lovasz, K. Vesztergombi&amp;lt;br&amp;gt;&lt;br /&gt;
[http://rubtsov.su/public/DM-HSE-Draft.pdf Лекции по дискретной математике] (черновик учебника, in Russian)&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
|-&lt;br /&gt;
! Video !! Summary !! Problem list&lt;br /&gt;
|-&lt;br /&gt;
 || 07.09 || Turing machines, multitape Turing machines, connection between them. Universal Turing machine. Examples ([https://www.dropbox.com/s/wna14b7y7nmw3cq/tm.py?dl=0 one], [https://www.dropbox.com/s/wrl3mkeqslj3xtu/wsharpw.py?dl=0 two]). Time and space complexity. Complexity classes P, PSPACE, EXP. || [https://www.dropbox.com/s/37eel2qayios6b3/prob_1.pdf?dl=0 Problem set 1]&lt;br /&gt;
|-&lt;br /&gt;
|| 14.09 ||  Time and space hierarchy theorem. Time and space constructible functions. || [https://www.dropbox.com/s/ow4m1z8u8r211qs/prob_2.pdf?dl=0 Problem set 2]&lt;br /&gt;
|-&lt;br /&gt;
 || 21.09 || Complexity class NP. Examples. Polynomial reductions. NP-hardness and NP-completeness. &lt;br /&gt;
 ||  [https://www.dropbox.com/s/bf68zicg4uh051x/prob_03.pdf?dl=0 Problem set 3]&lt;br /&gt;
|-&lt;br /&gt;
 || 28.09 ||  Non-deterministic TMs. Another definition of NP. Proving NP-hardness by reduction from an NP-complete problem. Examples of NP-complete problems.  || [https://www.dropbox.com/s/g817m6v0ygb8h4n/prob_04.pdf?dl=0 Problem set 4]&lt;br /&gt;
|-&lt;br /&gt;
 || 05.10 || Inclusions between P, NP, and PSPACE. Circuit complexity. Examples. All functions are computed by circuits. Existence of functions with exponential circuit complexity. P is in P/poly.|| [https://www.dropbox.com/s/qkc5p4795rualwn/prob_05.pdf?dl=0 Problem set 5]&lt;br /&gt;
|-&lt;br /&gt;
 || 12.10 || P is a subset of P/poly, Cook–Levin theorem, NP-completeness of: subsetsum, set-splitting, 3-colorability and exactly 1-in-3 SAT.  || [https://www.dropbox.com/s/y2y1lu29936xy9n/prob_06.pdf?dl=0 Problem set 6]&lt;br /&gt;
|-&lt;br /&gt;
 || [https://drive.google.com/drive/folders/1loJWyo9TK6ucCp8RnD3xx3DAVPDs0OiF?usp=sharing 26.10] || Space complexity. Classes L, NL, PSPACE and NPSPACE. Directed Reachability is in SPACE(log^2 n). Configuration graph. Inclusions between time and space classes. TQBF problem, its PSPACE-completeness. PSPACE = NPSPACE. NSPACE(s(n)) is in SPACE(s(n)^2) for space constructible s. || [https://www.dropbox.com/s/b6m0u5vqtutdhq1/prob_07.pdf?dl=0 Problem set 7]&lt;br /&gt;
|- &lt;br /&gt;
|| [https://drive.google.com/drive/folders/1w4W15sPS1nCIpQZQWasqPq8wSVLle5Ik?usp=sharing 02.11] || PSPACE completeness of generalized geography. Oracle computation definitions. There exists an oracle &#039;&#039;A&#039;&#039; for which P&amp;lt;sup&amp;gt;&#039;&#039;A&#039;&#039;&amp;lt;/sup&amp;gt; = NP&amp;lt;sup&amp;gt;&#039;&#039;A&#039;&#039;&amp;lt;/sup&amp;gt;. There is an oracle B such that P&amp;lt;sup&amp;gt;&#039;&#039;B&#039;&#039;&amp;lt;/sup&amp;gt; is not equal to NP&amp;lt;sup&amp;gt;&#039;&#039;B&#039;&#039;&amp;lt;/sup&amp;gt;. || [https://www.dropbox.com/s/bvfrar2p5w3fcie/prob_08.pdf?dl=0 Problem set 8]&lt;br /&gt;
|-&lt;br /&gt;
 || 09.11 || Probabilistic computation. Probabilistic machines, the class BPP, invariance of the definition BPP for different thresholds, RP, coRP, PP, ZPP. BPP is in P/poly. Most of it is also [https://www.youtube.com/watch?v=YSMgVbOqB-8&amp;amp;list=PLm3J0oaFux3YL5vLXpzOyJiLtqLp6dCW2&amp;amp;index=23 here]|| [https://www.dropbox.com/s/dciqvmire4ze4n2/prob_09.pdf?dl=0 Problem set 9]&lt;br /&gt;
|-&lt;br /&gt;
 || [https://youtu.be/ToxNJ9p32Ec 16.11] ||  Streaming algorithms: finding the majority element, computation of the number of different elements &amp;lt;!-- &#039;&#039;F&#039;&#039;&amp;lt;sub&amp;gt;2&amp;lt;/sub&amp;gt;--&amp;gt; in logarithmic space. See Chapts 6.1-6.2 in [https://home.ttic.edu/~avrim/book.pdf foundations of datascience] by Avrim Blum and others. Another nice chapter in [http://theory.stanford.edu/~tim/w15/l/l1.pdf Tim Roughgarden&#039;s lecture notes] || [https://www.dropbox.com/s/ztg8wxuhbkhzh9e/prob_10.pdf?dl=0 Problem set 10]&lt;br /&gt;
|-&lt;br /&gt;
 || [https://drive.google.com/file/d/1mDd3HjabwwzNPMa7oPcnAeHRSymVmsvE/view?usp=sharing 23.11] || Finding the frequent items in streams of data: SpaceSaving and Count-Min Sketch. [https://www.dropbox.com/s/6u27au11u00n59p/tc-11-streaming.pdf?dl=0 Slides] || [https://www.dropbox.com/s/8fvpntf1n4hjoyu/prob_11.pdf?dl=0 Problem set 11]&lt;br /&gt;
|-&lt;br /&gt;
 || [https://youtu.be/H7hF07mMPzk 30.11] || Approximation algorithms. Approximate solutions for Vertex Cover, Weighted Vertex Cover, and TSP. [https://youtu.be/6ng15Bc8Dlw Seminar.]|| [https://www.dropbox.com/s/qug480ss98pq78p/prob_12.pdf?dl=0 Problem set 12]&lt;br /&gt;
 &lt;br /&gt;
|-&lt;br /&gt;
 || 07.12 || Colloquium. ||&lt;br /&gt;
|-&lt;br /&gt;
 || 14.12 || Complexity of clustering: an exact algorithm for maximizing the inter-cluster distance and an approximate algorithm for minimizing the intra-class distance.&lt;br /&gt;
 || &lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
For interested students, there are 3 lectures in parameterized complexity. &lt;br /&gt;
&lt;br /&gt;
14 Sept: Fixed parameter tracktability and examples, [https://www.dropbox.com/s/zzzaulpmzql7x7u/parameterizedComplexity.pdf?dl=0 presentation]. &lt;br /&gt;
&lt;br /&gt;
21 Sept: Topics from chapters 1 and 2 in &amp;quot;Parameterized algorithms&amp;quot; by Cygan, Fomin and others, 2016.&lt;br /&gt;
&lt;br /&gt;
28 Sept: The W-hierarchy, chapter 13 in the same book.&lt;br /&gt;
&lt;br /&gt;
= Office hours =&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
|-&lt;br /&gt;
!  Person !! Monday !! Tuesday !! Wednesday !! Thursday !! Friday &lt;br /&gt;
|-&lt;br /&gt;
|  [https://www.hse.ru/en/org/persons/160550073 Bruno Bauwens], S834, [https://us02web.zoom.us/j/82300259484?pwd=NWxXekxBeE5yMm9UTmwvLzNNNGlnUT09 Zoom] ||  || ||  ||  || 14:00-20:00&lt;br /&gt;
|-&lt;br /&gt;
|  [https://www.hse.ru/en/staff/obiedkov Sergei Obiedkov], T915, [https://zoom.us/j/99663354582?pwd=K1B5R3NXWEhWbFozR2lqMkFWYW5Ydz09 Zoom] ||  ||  || 16:30–18:00 || 16:30–18:00 ||  &lt;br /&gt;
|}&lt;/div&gt;</summary>
		<author><name>.obj</name></author>
	</entry>
	<entry>
		<id>https://wiki.cs.hse.ru/index.php?title=Theory_of_Computation_2021&amp;diff=62393</id>
		<title>Theory of Computation 2021</title>
		<link rel="alternate" type="text/html" href="https://wiki.cs.hse.ru/index.php?title=Theory_of_Computation_2021&amp;diff=62393"/>
		<updated>2021-12-03T14:45:56Z</updated>

		<summary type="html">&lt;p&gt;.obj: /* Dates and Deadlines */&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;= Classes =&lt;br /&gt;
 &lt;br /&gt;
Tuesdays 14:40–17:40, [https://ruz.hse.ru/ruz/main ruz]&lt;br /&gt;
&lt;br /&gt;
Lectures: 14:40 [https://us02web.zoom.us/j/83533615475?pwd=WDU3cHJ5RjREOGd2YU1qdDJCVm1idz09 zoomlink]&lt;br /&gt;
&lt;br /&gt;
Seminars: 16:20 [https://us02web.zoom.us/j/84546220686?pwd=U2dISk5UaFZpdmh3WTdFT3phRVNXZz09 zoomlink]&lt;br /&gt;
&lt;br /&gt;
= Dates and Deadlines =&lt;br /&gt;
Please send your homework by e-mail to both lecturers.&amp;lt;br&amp;gt;&lt;br /&gt;
Homework 1 (problem sets 1–4), deadline: October 5, 14:00; the deadline for the extra problems is &amp;lt;s&amp;gt;November 2&amp;lt;/s&amp;gt; November 8, 14:00&amp;lt;br&amp;gt;&lt;br /&gt;
Homework 2 (problem sets 5–7), deadline: &amp;lt;s&amp;gt;November 2&amp;lt;/s&amp;gt; November 8, 14:00 &amp;lt;br&amp;gt;&lt;br /&gt;
Homework 3, deadline: December 7, 14:00 &amp;lt;br&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Colloquium: December 7, 14:40–17:40,&#039;&#039;&#039; &amp;lt;br&amp;gt;&lt;br /&gt;
[https://www.dropbox.com/s/lxyjm6b4xatl0pz/col.pdf?dl=0 Rules and questions]&amp;lt;br&amp;gt;&lt;br /&gt;
Choose your [https://docs.google.com/document/d/1OxiLVx_6LWIJlGP9qjQe1CuBH3BGjk4Q5drHc9r5CE0/ time].&lt;br /&gt;
&lt;br /&gt;
= Grading =&lt;br /&gt;
[https://docs.google.com/spreadsheets/d/1WFBuyjv_D-8EZRhMm39fI_X69daPk2VZwzBXlchW4Mk/edit?usp=sharing Grades]&lt;br /&gt;
&lt;br /&gt;
Colloquium: 35%&amp;lt;br&amp;gt;&lt;br /&gt;
Homework: 35%&amp;lt;br&amp;gt;&lt;br /&gt;
Exam: 30%&lt;br /&gt;
&lt;br /&gt;
==Homework Grading==&lt;br /&gt;
Some homework assignments contain extra problems. Let us call all other problems normal. The weight of each problem (whether normal or extra) in the overall homework grade is 8/&#039;&#039;n&#039;&#039;, where &#039;&#039;n&#039;&#039; is the total number of normal problems in all homework assignments. Partial credit is possible for some problems.&lt;br /&gt;
&lt;br /&gt;
If you score at least 8 and solve some extra problems that do not contribute to this score, we will evaluate each of these extra problems on the scale [0, 1] and will add two maximal scores to your homework grade.&lt;br /&gt;
&lt;br /&gt;
= Course Materials =&lt;br /&gt;
&lt;br /&gt;
The main reference is Sipser&#039;s book &amp;quot;Introduction to the theory of computation&amp;quot;, chapters 3, 7–10.&lt;br /&gt;
&lt;br /&gt;
If you need some background in math, consider these two sources:&amp;lt;br&amp;gt;&lt;br /&gt;
[http://www.cs.elte.hu/~lovasz/dmbook.ps Lecture notes: Discrete Mathematics], L. Lovasz, K. Vesztergombi&amp;lt;br&amp;gt;&lt;br /&gt;
[http://rubtsov.su/public/DM-HSE-Draft.pdf Лекции по дискретной математике] (черновик учебника, in Russian)&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
|-&lt;br /&gt;
! Video !! Summary !! Problem list&lt;br /&gt;
|-&lt;br /&gt;
 || 07.09 || Turing machines, multitape Turing machines, connection between them. Universal Turing machine. Examples ([https://www.dropbox.com/s/wna14b7y7nmw3cq/tm.py?dl=0 one], [https://www.dropbox.com/s/wrl3mkeqslj3xtu/wsharpw.py?dl=0 two]). Time and space complexity. Complexity classes P, PSPACE, EXP. || [https://www.dropbox.com/s/37eel2qayios6b3/prob_1.pdf?dl=0 Problem set 1]&lt;br /&gt;
|-&lt;br /&gt;
|| 14.09 ||  Time and space hierarchy theorem. Time and space constructible functions. || [https://www.dropbox.com/s/ow4m1z8u8r211qs/prob_2.pdf?dl=0 Problem set 2]&lt;br /&gt;
|-&lt;br /&gt;
 || 21.09 || Complexity class NP. Examples. Polynomial reductions. NP-hardness and NP-completeness. &lt;br /&gt;
 ||  [https://www.dropbox.com/s/bf68zicg4uh051x/prob_03.pdf?dl=0 Problem set 3]&lt;br /&gt;
|-&lt;br /&gt;
 || 28.09 ||  Non-deterministic TMs. Another definition of NP. Proving NP-hardness by reduction from an NP-complete problem. Examples of NP-complete problems.  || [https://www.dropbox.com/s/g817m6v0ygb8h4n/prob_04.pdf?dl=0 Problem set 4]&lt;br /&gt;
|-&lt;br /&gt;
 || 05.10 || Inclusions between P, NP, and PSPACE. Circuit complexity. Examples. All functions are computed by circuits. Existence of functions with exponential circuit complexity. P is in P/poly.|| [https://www.dropbox.com/s/qkc5p4795rualwn/prob_05.pdf?dl=0 Problem set 5]&lt;br /&gt;
|-&lt;br /&gt;
 || 12.10 || P is a subset of P/poly, Cook–Levin theorem, NP-completeness of: subsetsum, set-splitting, 3-colorability and exactly 1-in-3 SAT.  || [https://www.dropbox.com/s/y2y1lu29936xy9n/prob_06.pdf?dl=0 Problem set 6]&lt;br /&gt;
|-&lt;br /&gt;
 || [https://drive.google.com/drive/folders/1loJWyo9TK6ucCp8RnD3xx3DAVPDs0OiF?usp=sharing 26.10] || Space complexity. Classes L, NL, PSPACE and NPSPACE. Directed Reachability is in SPACE(log^2 n). Configuration graph. Inclusions between time and space classes. TQBF problem, its PSPACE-completeness. PSPACE = NPSPACE. NSPACE(s(n)) is in SPACE(s(n)^2) for space constructible s. || [https://www.dropbox.com/s/b6m0u5vqtutdhq1/prob_07.pdf?dl=0 Problem set 7]&lt;br /&gt;
|- &lt;br /&gt;
|| [https://drive.google.com/drive/folders/1w4W15sPS1nCIpQZQWasqPq8wSVLle5Ik?usp=sharing 02.11] || PSPACE completeness of generalized geography. Oracle computation definitions. There exists an oracle &#039;&#039;A&#039;&#039; for which P&amp;lt;sup&amp;gt;&#039;&#039;A&#039;&#039;&amp;lt;/sup&amp;gt; = NP&amp;lt;sup&amp;gt;&#039;&#039;A&#039;&#039;&amp;lt;/sup&amp;gt;. There is an oracle B such that P&amp;lt;sup&amp;gt;&#039;&#039;B&#039;&#039;&amp;lt;/sup&amp;gt; is not equal to NP&amp;lt;sup&amp;gt;&#039;&#039;B&#039;&#039;&amp;lt;/sup&amp;gt;. || [https://www.dropbox.com/s/bvfrar2p5w3fcie/prob_08.pdf?dl=0 Problem set 8]&lt;br /&gt;
|-&lt;br /&gt;
 || 09.11 || Probabilistic computation. Probabilistic machines, the class BPP, invariance of the definition BPP for different thresholds, RP, coRP, PP, ZPP. BPP is in P/poly. Most of it is also [https://www.youtube.com/watch?v=YSMgVbOqB-8&amp;amp;list=PLm3J0oaFux3YL5vLXpzOyJiLtqLp6dCW2&amp;amp;index=23 here]|| [https://www.dropbox.com/s/dciqvmire4ze4n2/prob_09.pdf?dl=0 Problem set 9]&lt;br /&gt;
|-&lt;br /&gt;
 || [https://youtu.be/ToxNJ9p32Ec 16.11] ||  Streaming algorithms: finding the majority element, computation of the number of different elements &amp;lt;!-- &#039;&#039;F&#039;&#039;&amp;lt;sub&amp;gt;2&amp;lt;/sub&amp;gt;--&amp;gt; in logarithmic space. See Chapts 6.1-6.2 in [https://home.ttic.edu/~avrim/book.pdf foundations of datascience] by Avrim Blum and others. Another nice chapter in [http://theory.stanford.edu/~tim/w15/l/l1.pdf Tim Roughgarden&#039;s lecture notes] || [https://www.dropbox.com/s/ztg8wxuhbkhzh9e/prob_10.pdf?dl=0 Problem set 10]&lt;br /&gt;
|-&lt;br /&gt;
 || [https://drive.google.com/file/d/1mDd3HjabwwzNPMa7oPcnAeHRSymVmsvE/view?usp=sharing 23.11] || Finding the frequent items in streams of data: SpaceSaving and Count-Min Sketch. [https://www.dropbox.com/s/6u27au11u00n59p/tc-11-streaming.pdf?dl=0 Slides] || [https://www.dropbox.com/s/8fvpntf1n4hjoyu/prob_11.pdf?dl=0 Problem set 11]&lt;br /&gt;
|-&lt;br /&gt;
 || [https://youtu.be/H7hF07mMPzk 30.11] || Approximation algorithms. Approximate solutions for Vertex Cover, Weighted Vertex Cover, and TSP. [https://youtu.be/6ng15Bc8Dlw Seminar.]|| [https://www.dropbox.com/s/qug480ss98pq78p/prob_12.pdf?dl=0 Problem set 12]&lt;br /&gt;
 &lt;br /&gt;
|-&lt;br /&gt;
 || 07.12 || Colloquium. ||&lt;br /&gt;
|-&lt;br /&gt;
 || 14.12 || Complexity of clustering: an exact algorithm for maximizing the inter-cluster distance and an approximate algorithm for minimizing the intra-class distance.&lt;br /&gt;
 || &lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
For interested students, there are 3 lectures in parameterized complexity. &lt;br /&gt;
&lt;br /&gt;
14 Sept: Fixed parameter tracktability and examples, [https://www.dropbox.com/s/zzzaulpmzql7x7u/parameterizedComplexity.pdf?dl=0 presentation]. &lt;br /&gt;
&lt;br /&gt;
21 Sept: Topics from chapters 1 and 2 in &amp;quot;Parameterized algorithms&amp;quot; by Cygan, Fomin and others, 2016.&lt;br /&gt;
&lt;br /&gt;
28 Sept: The W-hierarchy, chapter 13 in the same book.&lt;br /&gt;
&lt;br /&gt;
= Office hours =&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
|-&lt;br /&gt;
!  Person !! Monday !! Tuesday !! Wednesday !! Thursday !! Friday &lt;br /&gt;
|-&lt;br /&gt;
|  [https://www.hse.ru/en/org/persons/160550073 Bruno Bauwens], S834, [https://us02web.zoom.us/j/82300259484?pwd=NWxXekxBeE5yMm9UTmwvLzNNNGlnUT09 Zoom] ||  || ||  ||  || 14:00-20:00&lt;br /&gt;
|-&lt;br /&gt;
|  [https://www.hse.ru/en/staff/obiedkov Sergei Obiedkov], T915, [https://zoom.us/j/99663354582?pwd=K1B5R3NXWEhWbFozR2lqMkFWYW5Ydz09 Zoom] ||  ||  || 16:30–18:00 || 16:30–18:00 ||  &lt;br /&gt;
|}&lt;/div&gt;</summary>
		<author><name>.obj</name></author>
	</entry>
	<entry>
		<id>https://wiki.cs.hse.ru/index.php?title=Theory_of_Computation_2021&amp;diff=62392</id>
		<title>Theory of Computation 2021</title>
		<link rel="alternate" type="text/html" href="https://wiki.cs.hse.ru/index.php?title=Theory_of_Computation_2021&amp;diff=62392"/>
		<updated>2021-12-03T14:45:01Z</updated>

		<summary type="html">&lt;p&gt;.obj: /* Dates and Deadlines */&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;= Classes =&lt;br /&gt;
 &lt;br /&gt;
Tuesdays 14:40–17:40, [https://ruz.hse.ru/ruz/main ruz]&lt;br /&gt;
&lt;br /&gt;
Lectures: 14:40 [https://us02web.zoom.us/j/83533615475?pwd=WDU3cHJ5RjREOGd2YU1qdDJCVm1idz09 zoomlink]&lt;br /&gt;
&lt;br /&gt;
Seminars: 16:20 [https://us02web.zoom.us/j/84546220686?pwd=U2dISk5UaFZpdmh3WTdFT3phRVNXZz09 zoomlink]&lt;br /&gt;
&lt;br /&gt;
= Dates and Deadlines =&lt;br /&gt;
Please send your homework by e-mail to both lecturers.&amp;lt;br&amp;gt;&lt;br /&gt;
Homework 1 (problem sets 1–4), deadline: October 5, 14:00; the deadline for the extra problems is &amp;lt;s&amp;gt;November 2&amp;lt;/s&amp;gt; November 8, 14:00&amp;lt;br&amp;gt;&lt;br /&gt;
Homework 2 (problem sets 5–7), deadline: &amp;lt;s&amp;gt;November 2&amp;lt;/s&amp;gt; November 8, 14:00 &amp;lt;br&amp;gt;&lt;br /&gt;
Homework 3, deadline: December 7, 14:00 &amp;lt;br&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Colloquium: December 7, 14:40–17:40,&#039;&#039;&#039; [https://www.dropbox.com/s/lxyjm6b4xatl0pz/col.pdf?dl=0 questions] Choose your [https://docs.google.com/document/d/1OxiLVx_6LWIJlGP9qjQe1CuBH3BGjk4Q5drHc9r5CE0/ time].&lt;br /&gt;
&lt;br /&gt;
= Grading =&lt;br /&gt;
[https://docs.google.com/spreadsheets/d/1WFBuyjv_D-8EZRhMm39fI_X69daPk2VZwzBXlchW4Mk/edit?usp=sharing Grades]&lt;br /&gt;
&lt;br /&gt;
Colloquium: 35%&amp;lt;br&amp;gt;&lt;br /&gt;
Homework: 35%&amp;lt;br&amp;gt;&lt;br /&gt;
Exam: 30%&lt;br /&gt;
&lt;br /&gt;
==Homework Grading==&lt;br /&gt;
Some homework assignments contain extra problems. Let us call all other problems normal. The weight of each problem (whether normal or extra) in the overall homework grade is 8/&#039;&#039;n&#039;&#039;, where &#039;&#039;n&#039;&#039; is the total number of normal problems in all homework assignments. Partial credit is possible for some problems.&lt;br /&gt;
&lt;br /&gt;
If you score at least 8 and solve some extra problems that do not contribute to this score, we will evaluate each of these extra problems on the scale [0, 1] and will add two maximal scores to your homework grade.&lt;br /&gt;
&lt;br /&gt;
= Course Materials =&lt;br /&gt;
&lt;br /&gt;
The main reference is Sipser&#039;s book &amp;quot;Introduction to the theory of computation&amp;quot;, chapters 3, 7–10.&lt;br /&gt;
&lt;br /&gt;
If you need some background in math, consider these two sources:&amp;lt;br&amp;gt;&lt;br /&gt;
[http://www.cs.elte.hu/~lovasz/dmbook.ps Lecture notes: Discrete Mathematics], L. Lovasz, K. Vesztergombi&amp;lt;br&amp;gt;&lt;br /&gt;
[http://rubtsov.su/public/DM-HSE-Draft.pdf Лекции по дискретной математике] (черновик учебника, in Russian)&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
|-&lt;br /&gt;
! Video !! Summary !! Problem list&lt;br /&gt;
|-&lt;br /&gt;
 || 07.09 || Turing machines, multitape Turing machines, connection between them. Universal Turing machine. Examples ([https://www.dropbox.com/s/wna14b7y7nmw3cq/tm.py?dl=0 one], [https://www.dropbox.com/s/wrl3mkeqslj3xtu/wsharpw.py?dl=0 two]). Time and space complexity. Complexity classes P, PSPACE, EXP. || [https://www.dropbox.com/s/37eel2qayios6b3/prob_1.pdf?dl=0 Problem set 1]&lt;br /&gt;
|-&lt;br /&gt;
|| 14.09 ||  Time and space hierarchy theorem. Time and space constructible functions. || [https://www.dropbox.com/s/ow4m1z8u8r211qs/prob_2.pdf?dl=0 Problem set 2]&lt;br /&gt;
|-&lt;br /&gt;
 || 21.09 || Complexity class NP. Examples. Polynomial reductions. NP-hardness and NP-completeness. &lt;br /&gt;
 ||  [https://www.dropbox.com/s/bf68zicg4uh051x/prob_03.pdf?dl=0 Problem set 3]&lt;br /&gt;
|-&lt;br /&gt;
 || 28.09 ||  Non-deterministic TMs. Another definition of NP. Proving NP-hardness by reduction from an NP-complete problem. Examples of NP-complete problems.  || [https://www.dropbox.com/s/g817m6v0ygb8h4n/prob_04.pdf?dl=0 Problem set 4]&lt;br /&gt;
|-&lt;br /&gt;
 || 05.10 || Inclusions between P, NP, and PSPACE. Circuit complexity. Examples. All functions are computed by circuits. Existence of functions with exponential circuit complexity. P is in P/poly.|| [https://www.dropbox.com/s/qkc5p4795rualwn/prob_05.pdf?dl=0 Problem set 5]&lt;br /&gt;
|-&lt;br /&gt;
 || 12.10 || P is a subset of P/poly, Cook–Levin theorem, NP-completeness of: subsetsum, set-splitting, 3-colorability and exactly 1-in-3 SAT.  || [https://www.dropbox.com/s/y2y1lu29936xy9n/prob_06.pdf?dl=0 Problem set 6]&lt;br /&gt;
|-&lt;br /&gt;
 || [https://drive.google.com/drive/folders/1loJWyo9TK6ucCp8RnD3xx3DAVPDs0OiF?usp=sharing 26.10] || Space complexity. Classes L, NL, PSPACE and NPSPACE. Directed Reachability is in SPACE(log^2 n). Configuration graph. Inclusions between time and space classes. TQBF problem, its PSPACE-completeness. PSPACE = NPSPACE. NSPACE(s(n)) is in SPACE(s(n)^2) for space constructible s. || [https://www.dropbox.com/s/b6m0u5vqtutdhq1/prob_07.pdf?dl=0 Problem set 7]&lt;br /&gt;
|- &lt;br /&gt;
|| [https://drive.google.com/drive/folders/1w4W15sPS1nCIpQZQWasqPq8wSVLle5Ik?usp=sharing 02.11] || PSPACE completeness of generalized geography. Oracle computation definitions. There exists an oracle &#039;&#039;A&#039;&#039; for which P&amp;lt;sup&amp;gt;&#039;&#039;A&#039;&#039;&amp;lt;/sup&amp;gt; = NP&amp;lt;sup&amp;gt;&#039;&#039;A&#039;&#039;&amp;lt;/sup&amp;gt;. There is an oracle B such that P&amp;lt;sup&amp;gt;&#039;&#039;B&#039;&#039;&amp;lt;/sup&amp;gt; is not equal to NP&amp;lt;sup&amp;gt;&#039;&#039;B&#039;&#039;&amp;lt;/sup&amp;gt;. || [https://www.dropbox.com/s/bvfrar2p5w3fcie/prob_08.pdf?dl=0 Problem set 8]&lt;br /&gt;
|-&lt;br /&gt;
 || 09.11 || Probabilistic computation. Probabilistic machines, the class BPP, invariance of the definition BPP for different thresholds, RP, coRP, PP, ZPP. BPP is in P/poly. Most of it is also [https://www.youtube.com/watch?v=YSMgVbOqB-8&amp;amp;list=PLm3J0oaFux3YL5vLXpzOyJiLtqLp6dCW2&amp;amp;index=23 here]|| [https://www.dropbox.com/s/dciqvmire4ze4n2/prob_09.pdf?dl=0 Problem set 9]&lt;br /&gt;
|-&lt;br /&gt;
 || [https://youtu.be/ToxNJ9p32Ec 16.11] ||  Streaming algorithms: finding the majority element, computation of the number of different elements &amp;lt;!-- &#039;&#039;F&#039;&#039;&amp;lt;sub&amp;gt;2&amp;lt;/sub&amp;gt;--&amp;gt; in logarithmic space. See Chapts 6.1-6.2 in [https://home.ttic.edu/~avrim/book.pdf foundations of datascience] by Avrim Blum and others. Another nice chapter in [http://theory.stanford.edu/~tim/w15/l/l1.pdf Tim Roughgarden&#039;s lecture notes] || [https://www.dropbox.com/s/ztg8wxuhbkhzh9e/prob_10.pdf?dl=0 Problem set 10]&lt;br /&gt;
|-&lt;br /&gt;
 || [https://drive.google.com/file/d/1mDd3HjabwwzNPMa7oPcnAeHRSymVmsvE/view?usp=sharing 23.11] || Finding the frequent items in streams of data: SpaceSaving and Count-Min Sketch. [https://www.dropbox.com/s/6u27au11u00n59p/tc-11-streaming.pdf?dl=0 Slides] || [https://www.dropbox.com/s/8fvpntf1n4hjoyu/prob_11.pdf?dl=0 Problem set 11]&lt;br /&gt;
|-&lt;br /&gt;
 || [https://youtu.be/H7hF07mMPzk 30.11] || Approximation algorithms. Approximate solutions for Vertex Cover, Weighted Vertex Cover, and TSP. [https://youtu.be/6ng15Bc8Dlw Seminar.]|| [https://www.dropbox.com/s/qug480ss98pq78p/prob_12.pdf?dl=0 Problem set 12]&lt;br /&gt;
 &lt;br /&gt;
|-&lt;br /&gt;
 || 07.12 || Colloquium. ||&lt;br /&gt;
|-&lt;br /&gt;
 || 14.12 || Complexity of clustering: an exact algorithm for maximizing the inter-cluster distance and an approximate algorithm for minimizing the intra-class distance.&lt;br /&gt;
 || &lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
For interested students, there are 3 lectures in parameterized complexity. &lt;br /&gt;
&lt;br /&gt;
14 Sept: Fixed parameter tracktability and examples, [https://www.dropbox.com/s/zzzaulpmzql7x7u/parameterizedComplexity.pdf?dl=0 presentation]. &lt;br /&gt;
&lt;br /&gt;
21 Sept: Topics from chapters 1 and 2 in &amp;quot;Parameterized algorithms&amp;quot; by Cygan, Fomin and others, 2016.&lt;br /&gt;
&lt;br /&gt;
28 Sept: The W-hierarchy, chapter 13 in the same book.&lt;br /&gt;
&lt;br /&gt;
= Office hours =&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
|-&lt;br /&gt;
!  Person !! Monday !! Tuesday !! Wednesday !! Thursday !! Friday &lt;br /&gt;
|-&lt;br /&gt;
|  [https://www.hse.ru/en/org/persons/160550073 Bruno Bauwens], S834, [https://us02web.zoom.us/j/82300259484?pwd=NWxXekxBeE5yMm9UTmwvLzNNNGlnUT09 Zoom] ||  || ||  ||  || 14:00-20:00&lt;br /&gt;
|-&lt;br /&gt;
|  [https://www.hse.ru/en/staff/obiedkov Sergei Obiedkov], T915, [https://zoom.us/j/99663354582?pwd=K1B5R3NXWEhWbFozR2lqMkFWYW5Ydz09 Zoom] ||  ||  || 16:30–18:00 || 16:30–18:00 ||  &lt;br /&gt;
|}&lt;/div&gt;</summary>
		<author><name>.obj</name></author>
	</entry>
	<entry>
		<id>https://wiki.cs.hse.ru/index.php?title=Theory_of_Computation_2021&amp;diff=61878</id>
		<title>Theory of Computation 2021</title>
		<link rel="alternate" type="text/html" href="https://wiki.cs.hse.ru/index.php?title=Theory_of_Computation_2021&amp;diff=61878"/>
		<updated>2021-11-23T16:40:22Z</updated>

		<summary type="html">&lt;p&gt;.obj: /* Course Materials */&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;= Classes =&lt;br /&gt;
 &lt;br /&gt;
Tuesdays 14:40–17:40, [https://ruz.hse.ru/ruz/main ruz]&lt;br /&gt;
&lt;br /&gt;
Lectures: 14:40 [https://us02web.zoom.us/j/83533615475?pwd=WDU3cHJ5RjREOGd2YU1qdDJCVm1idz09 zoomlink]&lt;br /&gt;
&lt;br /&gt;
Seminars: 16:20 [https://us02web.zoom.us/j/84546220686?pwd=U2dISk5UaFZpdmh3WTdFT3phRVNXZz09 zoomlink]&lt;br /&gt;
&lt;br /&gt;
= Dates and Deadlines =&lt;br /&gt;
Please send your homework by e-mail to both lecturers.&amp;lt;br&amp;gt;&lt;br /&gt;
Homework 1 (problem sets 1–4), deadline: October 5, 14:00; the deadline for the extra problems is &amp;lt;s&amp;gt;November 2&amp;lt;/s&amp;gt; November 8, 14:00&amp;lt;br&amp;gt;&lt;br /&gt;
Homework 2 (problem sets 5–7), deadline: &amp;lt;s&amp;gt;November 2&amp;lt;/s&amp;gt; November 8, 14:00 &amp;lt;br&amp;gt;&lt;br /&gt;
Homework 3, deadline: December 7, 14:00 &amp;lt;br&amp;gt;&lt;br /&gt;
Colloquium: December 7, 14:40–17:40&lt;br /&gt;
&lt;br /&gt;
= Grading =&lt;br /&gt;
[https://docs.google.com/spreadsheets/d/1WFBuyjv_D-8EZRhMm39fI_X69daPk2VZwzBXlchW4Mk/edit?usp=sharing Grades]&lt;br /&gt;
&lt;br /&gt;
Colloquium: 35%&amp;lt;br&amp;gt;&lt;br /&gt;
Homework: 35%&amp;lt;br&amp;gt;&lt;br /&gt;
Exam: 30%&lt;br /&gt;
&lt;br /&gt;
==Homework Grading==&lt;br /&gt;
Some homework assignments contain extra problems. Let us call all other problems normal. The weight of each problem (whether normal or extra) in the overall homework grade is 8/&#039;&#039;n&#039;&#039;, where &#039;&#039;n&#039;&#039; is the total number of normal problems in all homework assignments. Partial credit is possible for some problems.&lt;br /&gt;
&lt;br /&gt;
If you score at least 8 and solve some extra problems that do not contribute to this score, we will evaluate each of these extra problems on the scale [0, 1] and will add two maximal scores to your homework grade.&lt;br /&gt;
&lt;br /&gt;
= Course Materials =&lt;br /&gt;
&lt;br /&gt;
The main reference is Sipser&#039;s book &amp;quot;Introduction to the theory of computation&amp;quot;, chapters 3, 7–10.&lt;br /&gt;
&lt;br /&gt;
If you need some background in math, consider these two sources:&amp;lt;br&amp;gt;&lt;br /&gt;
[http://www.cs.elte.hu/~lovasz/dmbook.ps Lecture notes: Discrete Mathematics], L. Lovasz, K. Vesztergombi&amp;lt;br&amp;gt;&lt;br /&gt;
[http://rubtsov.su/public/DM-HSE-Draft.pdf Лекции по дискретной математике] (черновик учебника, in Russian)&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
|-&lt;br /&gt;
! Video !! Summary !! Problem list&lt;br /&gt;
|-&lt;br /&gt;
 || 07.09 || Turing machines, multitape Turing machines, connection between them. Universal Turing machine. Examples ([https://www.dropbox.com/s/wna14b7y7nmw3cq/tm.py?dl=0 one], [https://www.dropbox.com/s/wrl3mkeqslj3xtu/wsharpw.py?dl=0 two]). Time and space complexity. Complexity classes P, PSPACE, EXP. || [https://www.dropbox.com/s/37eel2qayios6b3/prob_1.pdf?dl=0 Problem set 1]&lt;br /&gt;
|-&lt;br /&gt;
|| 14.09 ||  Time and space hierarchy theorem. Time and space constructible functions. || [https://www.dropbox.com/s/ow4m1z8u8r211qs/prob_2.pdf?dl=0 Problem set 2]&lt;br /&gt;
|-&lt;br /&gt;
 || 21.09 || Complexity class NP. Examples. Polynomial reductions. NP-hardness and NP-completeness. &lt;br /&gt;
 ||  [https://www.dropbox.com/s/bf68zicg4uh051x/prob_03.pdf?dl=0 Problem set 3]&lt;br /&gt;
|-&lt;br /&gt;
 || 28.09 ||  Non-deterministic TMs. Another definition of NP. Proving NP-hardness by reduction from an NP-complete problem. Examples of NP-complete problems.  || [https://www.dropbox.com/s/g817m6v0ygb8h4n/prob_04.pdf?dl=0 Problem set 4]&lt;br /&gt;
|-&lt;br /&gt;
 || 05.10 || Inclusions between P, NP, and PSPACE. Circuit complexity. Examples. All functions are computed by circuits. Existence of functions with exponential circuit complexity. P is in P/poly.|| [https://www.dropbox.com/s/qkc5p4795rualwn/prob_05.pdf?dl=0 Problem set 5]&lt;br /&gt;
|-&lt;br /&gt;
 || 12.10 || P is a subset of P/poly, Cook–Levin theorem, NP-completeness of: subsetsum, set-splitting, 3-colorability and exactly 1-in-3 SAT.  || [https://www.dropbox.com/s/y2y1lu29936xy9n/prob_06.pdf?dl=0 Problem set 6]&lt;br /&gt;
|-&lt;br /&gt;
 || [https://drive.google.com/drive/folders/1loJWyo9TK6ucCp8RnD3xx3DAVPDs0OiF?usp=sharing 26.10] || Space complexity. Classes L, NL, PSPACE and NPSPACE. Directed Reachability is in SPACE(log^2 n). Configuration graph. Inclusions between time and space classes. TQBF problem, its PSPACE-completeness. PSPACE = NPSPACE. NSPACE(s(n)) is in SPACE(s(n)^2) for space constructible s. || [https://www.dropbox.com/s/b6m0u5vqtutdhq1/prob_07.pdf?dl=0 Problem set 7]&lt;br /&gt;
|- &lt;br /&gt;
|| [https://drive.google.com/drive/folders/1w4W15sPS1nCIpQZQWasqPq8wSVLle5Ik?usp=sharing 02.11] || PSPACE completeness of generalized geography. Oracle computation definitions. There exists an oracle &#039;&#039;A&#039;&#039; for which P&amp;lt;sup&amp;gt;&#039;&#039;A&#039;&#039;&amp;lt;/sup&amp;gt; = NP&amp;lt;sup&amp;gt;&#039;&#039;A&#039;&#039;&amp;lt;/sup&amp;gt;. There is an oracle B such that P&amp;lt;sup&amp;gt;&#039;&#039;B&#039;&#039;&amp;lt;/sup&amp;gt; is not equal to NP&amp;lt;sup&amp;gt;&#039;&#039;B&#039;&#039;&amp;lt;/sup&amp;gt;. || [https://www.dropbox.com/s/bvfrar2p5w3fcie/prob_08.pdf?dl=0 Problem set 8]&lt;br /&gt;
|-&lt;br /&gt;
 || 09.11 || Probabilistic computation. Probabilistic machines, the class BPP, invariance of the definition BPP for different thresholds, RP, coRP, PP, ZPP. BPP is in P/poly. Most of it is also [https://www.youtube.com/watch?v=YSMgVbOqB-8&amp;amp;list=PLm3J0oaFux3YL5vLXpzOyJiLtqLp6dCW2&amp;amp;index=23 here]|| [https://www.dropbox.com/s/dciqvmire4ze4n2/prob_09.pdf?dl=0 Problem set 9]&lt;br /&gt;
|-&lt;br /&gt;
 || [https://youtu.be/ToxNJ9p32Ec 16.11] ||  Streaming algorithms: finding the majority element, computation of the number of different elements &amp;lt;!-- &#039;&#039;F&#039;&#039;&amp;lt;sub&amp;gt;2&amp;lt;/sub&amp;gt;--&amp;gt; in logarithmic space. See Chapts 6.1-6.2 in [https://home.ttic.edu/~avrim/book.pdf foundations of datascience] by Avrim Blum and others. Another nice chapter in [http://theory.stanford.edu/~tim/w15/l/l1.pdf Tim Roughgarden&#039;s lecture notes] || [https://www.dropbox.com/s/ztg8wxuhbkhzh9e/prob_10.pdf?dl=0 Problem set 10]&lt;br /&gt;
|-&lt;br /&gt;
 || [https://drive.google.com/file/d/1mDd3HjabwwzNPMa7oPcnAeHRSymVmsvE/view?usp=sharing 23.11] || Finding the frequent items in streams of data: SpaceSaving and Count-Min Sketch. [https://www.dropbox.com/s/6u27au11u00n59p/tc-11-streaming.pdf?dl=0 Slides] || [https://www.dropbox.com/s/8fvpntf1n4hjoyu/prob_11.pdf?dl=0 Problem set 11]&lt;br /&gt;
|-&lt;br /&gt;
 || 30.11 || Approximation algorithms. Approximate solutions for Vertex Cover, Weighted Vertex Cover, and TSP. ||&lt;br /&gt;
 &lt;br /&gt;
|-&lt;br /&gt;
 || 07.12 || Colloquium. ||&lt;br /&gt;
|-&lt;br /&gt;
 || 14.12 || Complexity of clustering: an exact algorithm for maximizing the inter-cluster distance and an approximate algorithm for minimizing the intra-class distance.&lt;br /&gt;
 || &lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
For interested students, there are 3 lectures in parameterized complexity. &lt;br /&gt;
&lt;br /&gt;
14 Sept: Fixed parameter tracktability and examples, [https://www.dropbox.com/s/zzzaulpmzql7x7u/parameterizedComplexity.pdf?dl=0 presentation]. &lt;br /&gt;
&lt;br /&gt;
21 Sept: Topics from chapters 1 and 2 in &amp;quot;Parameterized algorithms&amp;quot; by Cygan, Fomin and others, 2016.&lt;br /&gt;
&lt;br /&gt;
28 Sept: The W-hierarchy, chapter 13 in the same book.&lt;br /&gt;
&lt;br /&gt;
= Office hours =&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
|-&lt;br /&gt;
!  Person !! Monday !! Tuesday !! Wednesday !! Thursday !! Friday &lt;br /&gt;
|-&lt;br /&gt;
|  [https://www.hse.ru/en/org/persons/160550073 Bruno Bauwens], S834, [https://us02web.zoom.us/j/82300259484?pwd=NWxXekxBeE5yMm9UTmwvLzNNNGlnUT09 Zoom] ||  || ||  ||  || 14:00-20:00&lt;br /&gt;
|-&lt;br /&gt;
|  [https://www.hse.ru/en/staff/obiedkov Sergei Obiedkov], T915, [https://zoom.us/j/99663354582?pwd=K1B5R3NXWEhWbFozR2lqMkFWYW5Ydz09 Zoom] ||  ||  || 16:30–18:00 || 16:30–18:00 ||  &lt;br /&gt;
|}&lt;/div&gt;</summary>
		<author><name>.obj</name></author>
	</entry>
	<entry>
		<id>https://wiki.cs.hse.ru/index.php?title=Theory_of_Computation_2021&amp;diff=61860</id>
		<title>Theory of Computation 2021</title>
		<link rel="alternate" type="text/html" href="https://wiki.cs.hse.ru/index.php?title=Theory_of_Computation_2021&amp;diff=61860"/>
		<updated>2021-11-23T13:12:43Z</updated>

		<summary type="html">&lt;p&gt;.obj: /* Course Materials */&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;= Classes =&lt;br /&gt;
 &lt;br /&gt;
Tuesdays 14:40–17:40, [https://ruz.hse.ru/ruz/main ruz]&lt;br /&gt;
&lt;br /&gt;
Lectures: 14:40 [https://us02web.zoom.us/j/83533615475?pwd=WDU3cHJ5RjREOGd2YU1qdDJCVm1idz09 zoomlink]&lt;br /&gt;
&lt;br /&gt;
Seminars: 16:20 [https://us02web.zoom.us/j/84546220686?pwd=U2dISk5UaFZpdmh3WTdFT3phRVNXZz09 zoomlink]&lt;br /&gt;
&lt;br /&gt;
= Dates and Deadlines =&lt;br /&gt;
Please send your homework by e-mail to both lecturers.&amp;lt;br&amp;gt;&lt;br /&gt;
Homework 1 (problem sets 1–4), deadline: October 5, 14:00; the deadline for the extra problems is &amp;lt;s&amp;gt;November 2&amp;lt;/s&amp;gt; November 8, 14:00&amp;lt;br&amp;gt;&lt;br /&gt;
Homework 2 (problem sets 5–7), deadline: &amp;lt;s&amp;gt;November 2&amp;lt;/s&amp;gt; November 8, 14:00 &amp;lt;br&amp;gt;&lt;br /&gt;
Homework 3, deadline: December 7, 14:00 &amp;lt;br&amp;gt;&lt;br /&gt;
Colloquium: December 7, 14:40–17:40&lt;br /&gt;
&lt;br /&gt;
= Grading =&lt;br /&gt;
[https://docs.google.com/spreadsheets/d/1WFBuyjv_D-8EZRhMm39fI_X69daPk2VZwzBXlchW4Mk/edit?usp=sharing Grades]&lt;br /&gt;
&lt;br /&gt;
Colloquium: 35%&amp;lt;br&amp;gt;&lt;br /&gt;
Homework: 35%&amp;lt;br&amp;gt;&lt;br /&gt;
Exam: 30%&lt;br /&gt;
&lt;br /&gt;
==Homework Grading==&lt;br /&gt;
Some homework assignments contain extra problems. Let us call all other problems normal. The weight of each problem (whether normal or extra) in the overall homework grade is 8/&#039;&#039;n&#039;&#039;, where &#039;&#039;n&#039;&#039; is the total number of normal problems in all homework assignments. Partial credit is possible for some problems.&lt;br /&gt;
&lt;br /&gt;
If you score at least 8 and solve some extra problems that do not contribute to this score, we will evaluate each of these extra problems on the scale [0, 1] and will add two maximal scores to your homework grade.&lt;br /&gt;
&lt;br /&gt;
= Course Materials =&lt;br /&gt;
&lt;br /&gt;
The main reference is Sipser&#039;s book &amp;quot;Introduction to the theory of computation&amp;quot;, chapters 3, 7–10.&lt;br /&gt;
&lt;br /&gt;
If you need some background in math, consider these two sources:&amp;lt;br&amp;gt;&lt;br /&gt;
[http://www.cs.elte.hu/~lovasz/dmbook.ps Lecture notes: Discrete Mathematics], L. Lovasz, K. Vesztergombi&amp;lt;br&amp;gt;&lt;br /&gt;
[http://rubtsov.su/public/DM-HSE-Draft.pdf Лекции по дискретной математике] (черновик учебника, in Russian)&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
|-&lt;br /&gt;
! Video !! Summary !! Problem list&lt;br /&gt;
|-&lt;br /&gt;
 || 07.09 || Turing machines, multitape Turing machines, connection between them. Universal Turing machine. Examples ([https://www.dropbox.com/s/wna14b7y7nmw3cq/tm.py?dl=0 one], [https://www.dropbox.com/s/wrl3mkeqslj3xtu/wsharpw.py?dl=0 two]). Time and space complexity. Complexity classes P, PSPACE, EXP. || [https://www.dropbox.com/s/37eel2qayios6b3/prob_1.pdf?dl=0 Problem set 1]&lt;br /&gt;
|-&lt;br /&gt;
|| 14.09 ||  Time and space hierarchy theorem. Time and space constructible functions. || [https://www.dropbox.com/s/ow4m1z8u8r211qs/prob_2.pdf?dl=0 Problem set 2]&lt;br /&gt;
|-&lt;br /&gt;
 || 21.09 || Complexity class NP. Examples. Polynomial reductions. NP-hardness and NP-completeness. &lt;br /&gt;
 ||  [https://www.dropbox.com/s/bf68zicg4uh051x/prob_03.pdf?dl=0 Problem set 3]&lt;br /&gt;
|-&lt;br /&gt;
 || 28.09 ||  Non-deterministic TMs. Another definition of NP. Proving NP-hardness by reduction from an NP-complete problem. Examples of NP-complete problems.  || [https://www.dropbox.com/s/g817m6v0ygb8h4n/prob_04.pdf?dl=0 Problem set 4]&lt;br /&gt;
|-&lt;br /&gt;
 || 05.10 || Inclusions between P, NP, and PSPACE. Circuit complexity. Examples. All functions are computed by circuits. Existence of functions with exponential circuit complexity. P is in P/poly.|| [https://www.dropbox.com/s/qkc5p4795rualwn/prob_05.pdf?dl=0 Problem set 5]&lt;br /&gt;
|-&lt;br /&gt;
 || 12.10 || P is a subset of P/poly, Cook–Levin theorem, NP-completeness of: subsetsum, set-splitting, 3-colorability and exactly 1-in-3 SAT.  || [https://www.dropbox.com/s/y2y1lu29936xy9n/prob_06.pdf?dl=0 Problem set 6]&lt;br /&gt;
|-&lt;br /&gt;
 || [https://drive.google.com/drive/folders/1loJWyo9TK6ucCp8RnD3xx3DAVPDs0OiF?usp=sharing 26.10] || Space complexity. Classes L, NL, PSPACE and NPSPACE. Directed Reachability is in SPACE(log^2 n). Configuration graph. Inclusions between time and space classes. TQBF problem, its PSPACE-completeness. PSPACE = NPSPACE. NSPACE(s(n)) is in SPACE(s(n)^2) for space constructible s. || [https://www.dropbox.com/s/b6m0u5vqtutdhq1/prob_07.pdf?dl=0 Problem set 7]&lt;br /&gt;
|- &lt;br /&gt;
|| [https://drive.google.com/drive/folders/1w4W15sPS1nCIpQZQWasqPq8wSVLle5Ik?usp=sharing 02.11] || PSPACE completeness of generalized geography. Oracle computation definitions. There exists an oracle &#039;&#039;A&#039;&#039; for which P&amp;lt;sup&amp;gt;&#039;&#039;A&#039;&#039;&amp;lt;/sup&amp;gt; = NP&amp;lt;sup&amp;gt;&#039;&#039;A&#039;&#039;&amp;lt;/sup&amp;gt;. There is an oracle B such that P&amp;lt;sup&amp;gt;&#039;&#039;B&#039;&#039;&amp;lt;/sup&amp;gt; is not equal to NP&amp;lt;sup&amp;gt;&#039;&#039;B&#039;&#039;&amp;lt;/sup&amp;gt;. || [https://www.dropbox.com/s/bvfrar2p5w3fcie/prob_08.pdf?dl=0 Problem set 8]&lt;br /&gt;
|-&lt;br /&gt;
 || 09.11 || Probabilistic computation. Probabilistic machines, the class BPP, invariance of the definition BPP for different thresholds, RP, coRP, PP, ZPP. BPP is in P/poly. Most of it is also [https://www.youtube.com/watch?v=YSMgVbOqB-8&amp;amp;list=PLm3J0oaFux3YL5vLXpzOyJiLtqLp6dCW2&amp;amp;index=23 here]|| [https://www.dropbox.com/s/dciqvmire4ze4n2/prob_09.pdf?dl=0 Problem set 9]&lt;br /&gt;
|-&lt;br /&gt;
 || [https://youtu.be/ToxNJ9p32Ec 16.11] ||  Streaming algorithms: finding the majority element, computation of the number of different elements &amp;lt;!-- &#039;&#039;F&#039;&#039;&amp;lt;sub&amp;gt;2&amp;lt;/sub&amp;gt;--&amp;gt; in logarithmic space. See Chapts 6.1-6.2 in [https://home.ttic.edu/~avrim/book.pdf foundations of datascience] by Avrim Blum and others. Another nice chapter in [http://theory.stanford.edu/~tim/w15/l/l1.pdf Tim Roughgarden&#039;s lecture notes] || [https://www.dropbox.com/s/ztg8wxuhbkhzh9e/prob_10.pdf?dl=0 Problem set 10]&lt;br /&gt;
|-&lt;br /&gt;
 || 23.11 || Finding the frequent items in streams of data: SpaceSaving and Count-Min Sketch. || [https://www.dropbox.com/s/8fvpntf1n4hjoyu/prob_11.pdf?dl=0 Problem set 11]&lt;br /&gt;
|-&lt;br /&gt;
 || 30.11 || Approximation algorithms. Approximate solutions for Vertex Cover, Weighted Vertex Cover, and TSP. ||&lt;br /&gt;
 &lt;br /&gt;
|-&lt;br /&gt;
 || 07.12 || Colloquium. ||&lt;br /&gt;
|-&lt;br /&gt;
 || 14.12 || Complexity of clustering: an exact algorithm for maximizing the inter-cluster distance and an approximate algorithm for minimizing the intra-class distance.&lt;br /&gt;
 || &lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
For interested students, there are 3 lectures in parameterized complexity. &lt;br /&gt;
&lt;br /&gt;
14 Sept: Fixed parameter tracktability and examples, [https://www.dropbox.com/s/zzzaulpmzql7x7u/parameterizedComplexity.pdf?dl=0 presentation]. &lt;br /&gt;
&lt;br /&gt;
21 Sept: Topics from chapters 1 and 2 in &amp;quot;Parameterized algorithms&amp;quot; by Cygan, Fomin and others, 2016.&lt;br /&gt;
&lt;br /&gt;
28 Sept: The W-hierarchy, chapter 13 in the same book.&lt;br /&gt;
&lt;br /&gt;
= Office hours =&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
|-&lt;br /&gt;
!  Person !! Monday !! Tuesday !! Wednesday !! Thursday !! Friday &lt;br /&gt;
|-&lt;br /&gt;
|  [https://www.hse.ru/en/org/persons/160550073 Bruno Bauwens], S834, [https://us02web.zoom.us/j/82300259484?pwd=NWxXekxBeE5yMm9UTmwvLzNNNGlnUT09 Zoom] ||  || ||  ||  || 14:00-20:00&lt;br /&gt;
|-&lt;br /&gt;
|  [https://www.hse.ru/en/staff/obiedkov Sergei Obiedkov], T915, [https://zoom.us/j/99663354582?pwd=K1B5R3NXWEhWbFozR2lqMkFWYW5Ydz09 Zoom] ||  ||  || 16:30–18:00 || 16:30–18:00 ||  &lt;br /&gt;
|}&lt;/div&gt;</summary>
		<author><name>.obj</name></author>
	</entry>
	<entry>
		<id>https://wiki.cs.hse.ru/index.php?title=Theory_of_Computation_2021&amp;diff=61211</id>
		<title>Theory of Computation 2021</title>
		<link rel="alternate" type="text/html" href="https://wiki.cs.hse.ru/index.php?title=Theory_of_Computation_2021&amp;diff=61211"/>
		<updated>2021-11-10T08:24:01Z</updated>

		<summary type="html">&lt;p&gt;.obj: &lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;= Classes =&lt;br /&gt;
 &lt;br /&gt;
Tuesdays 14:40–17:40, [https://ruz.hse.ru/ruz/main ruz]&lt;br /&gt;
&lt;br /&gt;
Lectures: 14:40 [https://us02web.zoom.us/j/83533615475?pwd=WDU3cHJ5RjREOGd2YU1qdDJCVm1idz09 zoomlink]&lt;br /&gt;
&lt;br /&gt;
Seminars: 16:20 [https://us02web.zoom.us/j/84546220686?pwd=U2dISk5UaFZpdmh3WTdFT3phRVNXZz09 zoomlink]&lt;br /&gt;
&lt;br /&gt;
= Dates and Deadlines =&lt;br /&gt;
Please send your homework by e-mail to both lecturers.&amp;lt;br&amp;gt;&lt;br /&gt;
Homework 1 (problem sets 1–4), deadline: October 5, 14:00; the deadline for the extra problems is &amp;lt;s&amp;gt;November 2&amp;lt;/s&amp;gt; November 8, 14:00&amp;lt;br&amp;gt;&lt;br /&gt;
Homework 2 (problem sets 5–7), deadline: &amp;lt;s&amp;gt;November 2&amp;lt;/s&amp;gt; November 8, 14:00 &amp;lt;br&amp;gt;&lt;br /&gt;
Homework 3, deadline: December 7, 14:00 &amp;lt;br&amp;gt;&lt;br /&gt;
Colloquium: December 7, 14:40–17:40&lt;br /&gt;
&lt;br /&gt;
= Grading =&lt;br /&gt;
[https://docs.google.com/spreadsheets/d/1WFBuyjv_D-8EZRhMm39fI_X69daPk2VZwzBXlchW4Mk/edit?usp=sharing Grades]&lt;br /&gt;
&lt;br /&gt;
Colloquium: 35%&amp;lt;br&amp;gt;&lt;br /&gt;
Homework: 35%&amp;lt;br&amp;gt;&lt;br /&gt;
Exam: 30%&lt;br /&gt;
&lt;br /&gt;
==Homework Grading==&lt;br /&gt;
Some homework assignments contain extra problems. Let us call all other problems normal. The weight of each problem (whether normal or extra) in the overall homework grade is 8/&#039;&#039;n&#039;&#039;, where &#039;&#039;n&#039;&#039; is the total number of normal problems in all homework assignments. Partial credit is possible for some problems.&lt;br /&gt;
&lt;br /&gt;
If you score at least 8 and solve some extra problems that do not contribute to this score, we will evaluate each of these extra problems on the scale [0, 1] and will add two maximal scores to your homework grade.&lt;br /&gt;
&lt;br /&gt;
= Course Materials =&lt;br /&gt;
&lt;br /&gt;
The main reference is Sipser&#039;s book &amp;quot;Introduction to the theory of computation&amp;quot;, chapters 3, 7–10.&lt;br /&gt;
&lt;br /&gt;
If you need some background in math, consider these two sources:&amp;lt;br&amp;gt;&lt;br /&gt;
[http://www.cs.elte.hu/~lovasz/dmbook.ps Lecture notes: Discrete Mathematics], L. Lovasz, K. Vesztergombi&amp;lt;br&amp;gt;&lt;br /&gt;
[http://rubtsov.su/public/DM-HSE-Draft.pdf Лекции по дискретной математике] (черновик учебника, in Russian)&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
|-&lt;br /&gt;
! Video !! Summary !! Problem list&lt;br /&gt;
|-&lt;br /&gt;
 || 07.09 || Turing machines, multitape Turing machines, connection between them. Universal Turing machine. Examples ([https://www.dropbox.com/s/wna14b7y7nmw3cq/tm.py?dl=0 one], [https://www.dropbox.com/s/wrl3mkeqslj3xtu/wsharpw.py?dl=0 two]). Time and space complexity. Complexity classes P, PSPACE, EXP. || [https://www.dropbox.com/s/37eel2qayios6b3/prob_1.pdf?dl=0 Problem set 1]&lt;br /&gt;
|-&lt;br /&gt;
|| 14.09 ||  Time and space hierarchy theorem. Time and space constructible functions. || [https://www.dropbox.com/s/ow4m1z8u8r211qs/prob_2.pdf?dl=0 Problem set 2]&lt;br /&gt;
|-&lt;br /&gt;
 || 21.09 || Complexity class NP. Examples. Polynomial reductions. NP-hardness and NP-completeness. &lt;br /&gt;
 ||  [https://www.dropbox.com/s/bf68zicg4uh051x/prob_03.pdf?dl=0 Problem set 3]&lt;br /&gt;
|-&lt;br /&gt;
 || 28.09 ||  Non-deterministic TMs. Another definition of NP. Proving NP-hardness by reduction from an NP-complete problem. Examples of NP-complete problems.  || [https://www.dropbox.com/s/g817m6v0ygb8h4n/prob_04.pdf?dl=0 Problem set 4]&lt;br /&gt;
|-&lt;br /&gt;
 || 05.10 || Inclusions between P, NP, and PSPACE. Circuit complexity. Examples. All functions are computed by circuits. Existence of functions with exponential circuit complexity. P is in P/poly.|| [https://www.dropbox.com/s/qkc5p4795rualwn/prob_05.pdf?dl=0 Problem set 5]&lt;br /&gt;
|-&lt;br /&gt;
 || 12.10 || P is a subset of P/poly, Cook–Levin theorem, NP-completeness of: subsetsum, set-splitting, 3-colorability and exactly 1-in-3 SAT.  || [https://www.dropbox.com/s/y2y1lu29936xy9n/prob_06.pdf?dl=0 Problem set 6]&lt;br /&gt;
|-&lt;br /&gt;
 || [https://drive.google.com/drive/folders/1loJWyo9TK6ucCp8RnD3xx3DAVPDs0OiF?usp=sharing 26.10] || Space complexity. Classes L, NL, PSPACE and NPSPACE. Directed Reachability is in SPACE(log^2 n). Configuration graph. Inclusions between time and space classes. TQBF problem, its PSPACE-completeness. PSPACE = NPSPACE. NSPACE(s(n)) is in SPACE(s(n)^2) for space constructible s. || [https://www.dropbox.com/s/b6m0u5vqtutdhq1/prob_07.pdf?dl=0 Problem set 7]&lt;br /&gt;
|- &lt;br /&gt;
|| [https://drive.google.com/drive/folders/1w4W15sPS1nCIpQZQWasqPq8wSVLle5Ik?usp=sharing 02.11] || PSPACE completeness of generalized geography. Oracle computation definitions. There exists an oracle &#039;&#039;A&#039;&#039; for which P&amp;lt;sup&amp;gt;&#039;&#039;A&#039;&#039;&amp;lt;/sup&amp;gt; = NP&amp;lt;sup&amp;gt;&#039;&#039;A&#039;&#039;&amp;lt;/sup&amp;gt;. There is an oracle B such that P&amp;lt;sup&amp;gt;&#039;&#039;B&#039;&#039;&amp;lt;/sup&amp;gt; is not equal to NP&amp;lt;sup&amp;gt;&#039;&#039;B&#039;&#039;&amp;lt;/sup&amp;gt;. || [https://www.dropbox.com/s/bvfrar2p5w3fcie/prob_08.pdf?dl=0 Problem set 8]&lt;br /&gt;
|-&lt;br /&gt;
 || 09.11 || Probabilistic computation. Probabilistic machines, the class BPP, invariance of the definition BPP for different thresholds, RP, coRP, PP, ZPP. BPP is in P/poly. Most of it is also [https://www.youtube.com/watch?v=YSMgVbOqB-8&amp;amp;list=PLm3J0oaFux3YL5vLXpzOyJiLtqLp6dCW2&amp;amp;index=23 here]|| [https://www.dropbox.com/s/dciqvmire4ze4n2/prob_09.pdf?dl=0 Problem set 9]&lt;br /&gt;
|-&lt;br /&gt;
 || 16.11 ||  Streaming algorithms: finding the majority element, computation of the moment &#039;&#039;F&#039;&#039;&amp;lt;sub&amp;gt;2&amp;lt;/sub&amp;gt; in logarithmic space. ||&lt;br /&gt;
|-&lt;br /&gt;
 || 23.11 || Finding the frequent items in streams of data: SpaceSaving and Count-Min Sketch. ||&lt;br /&gt;
|-&lt;br /&gt;
 || 30.11 || Approximation algorithms. Approximate solutions for Vertex Cover, Weighted Vertex Cover, and TSP. ||&lt;br /&gt;
 &lt;br /&gt;
|-&lt;br /&gt;
 || 07.12 || Colloquium. ||&lt;br /&gt;
|-&lt;br /&gt;
 || 14.12 || Complexity of clustering: an exact algorithm for maximising the inter-cluster distance and an approximate algorithm for minimising the intra-class distance.&lt;br /&gt;
 || &lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
For interested students, there are 3 lectures in parameterized complexity. &lt;br /&gt;
&lt;br /&gt;
14 Sept: Fixed parameter tracktability and examples, [https://www.dropbox.com/s/zzzaulpmzql7x7u/parameterizedComplexity.pdf?dl=0 presentation]. &lt;br /&gt;
&lt;br /&gt;
21 Sept: Topics from chapters 1 and 2 in &amp;quot;Parameterized algorithms&amp;quot; by Cygan, Fomin and others, 2016.&lt;br /&gt;
&lt;br /&gt;
28 Sept: The W-hierarchy, chapter 13 in the same book.&lt;br /&gt;
&lt;br /&gt;
= Office hours =&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
|-&lt;br /&gt;
!  Person !! Monday !! Tuesday !! Wednesday !! Thursday !! Friday &lt;br /&gt;
|-&lt;br /&gt;
|  [https://www.hse.ru/en/org/persons/160550073 Bruno Bauwens], S834, [https://us02web.zoom.us/j/82300259484?pwd=NWxXekxBeE5yMm9UTmwvLzNNNGlnUT09 Zoom] ||  || ||  ||  || 14:00-20:00&lt;br /&gt;
|-&lt;br /&gt;
|  [https://www.hse.ru/en/staff/obiedkov Sergei Obiedkov], T915, [https://zoom.us/j/99663354582?pwd=K1B5R3NXWEhWbFozR2lqMkFWYW5Ydz09 Zoom] ||  ||  || 16:30–18:00 || 16:30–18:00 ||  &lt;br /&gt;
|}&lt;/div&gt;</summary>
		<author><name>.obj</name></author>
	</entry>
	<entry>
		<id>https://wiki.cs.hse.ru/index.php?title=Theory_of_Computation_2021&amp;diff=61210</id>
		<title>Theory of Computation 2021</title>
		<link rel="alternate" type="text/html" href="https://wiki.cs.hse.ru/index.php?title=Theory_of_Computation_2021&amp;diff=61210"/>
		<updated>2021-11-10T08:23:36Z</updated>

		<summary type="html">&lt;p&gt;.obj: /* Grading */&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;= Classes =&lt;br /&gt;
 &lt;br /&gt;
Tuesdays 14:40–17:40, [https://ruz.hse.ru/ruz/main ruz]&lt;br /&gt;
&lt;br /&gt;
Lectures: 14:40 [https://us02web.zoom.us/j/83533615475?pwd=WDU3cHJ5RjREOGd2YU1qdDJCVm1idz09 zoomlink]&lt;br /&gt;
&lt;br /&gt;
Seminars: 16:20 [https://us02web.zoom.us/j/84546220686?pwd=U2dISk5UaFZpdmh3WTdFT3phRVNXZz09 zoomlink]&lt;br /&gt;
&lt;br /&gt;
= Dates and Deadlines =&lt;br /&gt;
Please send your homework by e-mail to both lecturers.&amp;lt;br&amp;gt;&lt;br /&gt;
Homework 1 (problem sets 1–4), deadline: October 5, 14:00; the deadline for the extra problems is &amp;lt;s&amp;gt;November 2&amp;lt;/s&amp;gt; November 8, 14:00&amp;lt;br&amp;gt;&lt;br /&gt;
Homework 2 (problem sets 5–7), deadline: &amp;lt;s&amp;gt;November 2&amp;lt;/s&amp;gt; November 8, 14:00 &amp;lt;br&amp;gt;&lt;br /&gt;
Homework 3, deadline: December 7, 14:00 &amp;lt;br&amp;gt;&lt;br /&gt;
Colloquium: December 7, 14:40–17:40&lt;br /&gt;
&lt;br /&gt;
= Grading =&lt;br /&gt;
Colloquium: 35%&amp;lt;br&amp;gt;&lt;br /&gt;
Homework: 35%&amp;lt;br&amp;gt;&lt;br /&gt;
Exam: 30%&lt;br /&gt;
&lt;br /&gt;
[https://docs.google.com/spreadsheets/d/1WFBuyjv_D-8EZRhMm39fI_X69daPk2VZwzBXlchW4Mk/edit?usp=sharing Grades]&lt;br /&gt;
&lt;br /&gt;
==Homework Grading==&lt;br /&gt;
Some homework assignments contain extra problems. Let us call all other problems normal. The weight of each problem (whether normal or extra) in the overall homework grade is 8/&#039;&#039;n&#039;&#039;, where &#039;&#039;n&#039;&#039; is the total number of normal problems in all homework assignments. Partial credit is possible for some problems.&lt;br /&gt;
&lt;br /&gt;
If you score at least 8 and solve some extra problems that do not contribute to this score, we will evaluate each of these extra problems on the scale [0, 1] and will add two maximal scores to your homework grade.&lt;br /&gt;
&lt;br /&gt;
= Course Materials =&lt;br /&gt;
&lt;br /&gt;
The main reference is Sipser&#039;s book &amp;quot;Introduction to the theory of computation&amp;quot;, chapters 3, 7–10.&lt;br /&gt;
&lt;br /&gt;
If you need some background in math, consider these two sources:&amp;lt;br&amp;gt;&lt;br /&gt;
[http://www.cs.elte.hu/~lovasz/dmbook.ps Lecture notes: Discrete Mathematics], L. Lovasz, K. Vesztergombi&amp;lt;br&amp;gt;&lt;br /&gt;
[http://rubtsov.su/public/DM-HSE-Draft.pdf Лекции по дискретной математике] (черновик учебника, in Russian)&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
|-&lt;br /&gt;
! Video !! Summary !! Problem list&lt;br /&gt;
|-&lt;br /&gt;
 || 07.09 || Turing machines, multitape Turing machines, connection between them. Universal Turing machine. Examples ([https://www.dropbox.com/s/wna14b7y7nmw3cq/tm.py?dl=0 one], [https://www.dropbox.com/s/wrl3mkeqslj3xtu/wsharpw.py?dl=0 two]). Time and space complexity. Complexity classes P, PSPACE, EXP. || [https://www.dropbox.com/s/37eel2qayios6b3/prob_1.pdf?dl=0 Problem set 1]&lt;br /&gt;
|-&lt;br /&gt;
|| 14.09 ||  Time and space hierarchy theorem. Time and space constructible functions. || [https://www.dropbox.com/s/ow4m1z8u8r211qs/prob_2.pdf?dl=0 Problem set 2]&lt;br /&gt;
|-&lt;br /&gt;
 || 21.09 || Complexity class NP. Examples. Polynomial reductions. NP-hardness and NP-completeness. &lt;br /&gt;
 ||  [https://www.dropbox.com/s/bf68zicg4uh051x/prob_03.pdf?dl=0 Problem set 3]&lt;br /&gt;
|-&lt;br /&gt;
 || 28.09 ||  Non-deterministic TMs. Another definition of NP. Proving NP-hardness by reduction from an NP-complete problem. Examples of NP-complete problems.  || [https://www.dropbox.com/s/g817m6v0ygb8h4n/prob_04.pdf?dl=0 Problem set 4]&lt;br /&gt;
|-&lt;br /&gt;
 || 05.10 || Inclusions between P, NP, and PSPACE. Circuit complexity. Examples. All functions are computed by circuits. Existence of functions with exponential circuit complexity. P is in P/poly.|| [https://www.dropbox.com/s/qkc5p4795rualwn/prob_05.pdf?dl=0 Problem set 5]&lt;br /&gt;
|-&lt;br /&gt;
 || 12.10 || P is a subset of P/poly, Cook–Levin theorem, NP-completeness of: subsetsum, set-splitting, 3-colorability and exactly 1-in-3 SAT.  || [https://www.dropbox.com/s/y2y1lu29936xy9n/prob_06.pdf?dl=0 Problem set 6]&lt;br /&gt;
|-&lt;br /&gt;
 || [https://drive.google.com/drive/folders/1loJWyo9TK6ucCp8RnD3xx3DAVPDs0OiF?usp=sharing 26.10] || Space complexity. Classes L, NL, PSPACE and NPSPACE. Directed Reachability is in SPACE(log^2 n). Configuration graph. Inclusions between time and space classes. TQBF problem, its PSPACE-completeness. PSPACE = NPSPACE. NSPACE(s(n)) is in SPACE(s(n)^2) for space constructible s. || [https://www.dropbox.com/s/b6m0u5vqtutdhq1/prob_07.pdf?dl=0 Problem set 7]&lt;br /&gt;
|- &lt;br /&gt;
|| [https://drive.google.com/drive/folders/1w4W15sPS1nCIpQZQWasqPq8wSVLle5Ik?usp=sharing 02.11] || PSPACE completeness of generalized geography. Oracle computation definitions. There exists an oracle &#039;&#039;A&#039;&#039; for which P&amp;lt;sup&amp;gt;&#039;&#039;A&#039;&#039;&amp;lt;/sup&amp;gt; = NP&amp;lt;sup&amp;gt;&#039;&#039;A&#039;&#039;&amp;lt;/sup&amp;gt;. There is an oracle B such that P&amp;lt;sup&amp;gt;&#039;&#039;B&#039;&#039;&amp;lt;/sup&amp;gt; is not equal to NP&amp;lt;sup&amp;gt;&#039;&#039;B&#039;&#039;&amp;lt;/sup&amp;gt;. || [https://www.dropbox.com/s/bvfrar2p5w3fcie/prob_08.pdf?dl=0 Problem set 8]&lt;br /&gt;
|-&lt;br /&gt;
 || 09.11 || Probabilistic computation. Probabilistic machines, the class BPP, invariance of the definition BPP for different thresholds, RP, coRP, PP, ZPP. BPP is in P/poly. Most of it is also [https://www.youtube.com/watch?v=YSMgVbOqB-8&amp;amp;list=PLm3J0oaFux3YL5vLXpzOyJiLtqLp6dCW2&amp;amp;index=23 here]|| [https://www.dropbox.com/s/dciqvmire4ze4n2/prob_09.pdf?dl=0 Problem set 9]&lt;br /&gt;
|-&lt;br /&gt;
 || 16.11 ||  Streaming algorithms: finding the majority element, computation of the moment &#039;&#039;F&#039;&#039;&amp;lt;sub&amp;gt;2&amp;lt;/sub&amp;gt; in logarithmic space. ||&lt;br /&gt;
|-&lt;br /&gt;
 || 23.11 || Finding the frequent items in streams of data: SpaceSaving and Count-Min Sketch. ||&lt;br /&gt;
|-&lt;br /&gt;
 || 30.11 || Approximation algorithms. Approximate solutions for Vertex Cover, Weighted Vertex Cover, and TSP. ||&lt;br /&gt;
 &lt;br /&gt;
|-&lt;br /&gt;
 || 07.12 || Colloquium. ||&lt;br /&gt;
|-&lt;br /&gt;
 || 14.12 || Complexity of clustering: an exact algorithm for maximising the inter-cluster distance and an approximate algorithm for minimising the intra-class distance.&lt;br /&gt;
 || &lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
For interested students, there are 3 lectures in parameterized complexity. &lt;br /&gt;
&lt;br /&gt;
14 Sept: Fixed parameter tracktability and examples, [https://www.dropbox.com/s/zzzaulpmzql7x7u/parameterizedComplexity.pdf?dl=0 presentation]. &lt;br /&gt;
&lt;br /&gt;
21 Sept: Topics from chapters 1 and 2 in &amp;quot;Parameterized algorithms&amp;quot; by Cygan, Fomin and others, 2016.&lt;br /&gt;
&lt;br /&gt;
28 Sept: The W-hierarchy, chapter 13 in the same book.&lt;br /&gt;
&lt;br /&gt;
= Office hours =&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
|-&lt;br /&gt;
!  Person !! Monday !! Tuesday !! Wednesday !! Thursday !! Friday &lt;br /&gt;
|-&lt;br /&gt;
|  [https://www.hse.ru/en/org/persons/160550073 Bruno Bauwens], S834, [https://us02web.zoom.us/j/82300259484?pwd=NWxXekxBeE5yMm9UTmwvLzNNNGlnUT09 Zoom] ||  || ||  ||  || 14:00-20:00&lt;br /&gt;
|-&lt;br /&gt;
|  [https://www.hse.ru/en/staff/obiedkov Sergei Obiedkov], T915, [https://zoom.us/j/99663354582?pwd=K1B5R3NXWEhWbFozR2lqMkFWYW5Ydz09 Zoom] ||  ||  || 16:30–18:00 || 16:30–18:00 ||  &lt;br /&gt;
|}&lt;/div&gt;</summary>
		<author><name>.obj</name></author>
	</entry>
	<entry>
		<id>https://wiki.cs.hse.ru/index.php?title=Theory_of_Computation_2021&amp;diff=60662</id>
		<title>Theory of Computation 2021</title>
		<link rel="alternate" type="text/html" href="https://wiki.cs.hse.ru/index.php?title=Theory_of_Computation_2021&amp;diff=60662"/>
		<updated>2021-10-30T16:42:13Z</updated>

		<summary type="html">&lt;p&gt;.obj: /* Dates and Deadlines */&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;= Classes =&lt;br /&gt;
 &lt;br /&gt;
Tuesdays 14:40–17:40, [https://ruz.hse.ru/ruz/main ruz]&lt;br /&gt;
&lt;br /&gt;
Lectures: 14:40 in room M303  [https://us02web.zoom.us/j/83533615475?pwd=WDU3cHJ5RjREOGd2YU1qdDJCVm1idz09 zoomlink 26/10]&lt;br /&gt;
&lt;br /&gt;
Seminars: 16:20 in room M302  [https://us02web.zoom.us/j/84546220686?pwd=U2dISk5UaFZpdmh3WTdFT3phRVNXZz09 zoomlink 26/10]&lt;br /&gt;
&lt;br /&gt;
= Dates and Deadlines =&lt;br /&gt;
Please send your homework by e-mail to both lecturers.&amp;lt;br&amp;gt;&lt;br /&gt;
Homework 1 (problem sets 1–4), deadline: October 5, 14:00; the deadline for the extra problems is &amp;lt;s&amp;gt;November 2&amp;lt;/s&amp;gt; November 8, 14:00&amp;lt;br&amp;gt;&lt;br /&gt;
Homework 2 (problem sets 5–7), deadline: &amp;lt;s&amp;gt;November 2&amp;lt;/s&amp;gt; November 8, 14:00 &amp;lt;br&amp;gt;&lt;br /&gt;
Homework 3, deadline: December 7, 14:00 &amp;lt;br&amp;gt;&lt;br /&gt;
Colloquium: December 7, 14:40–17:40&lt;br /&gt;
&lt;br /&gt;
= Grading =&lt;br /&gt;
Colloquium: 35%&amp;lt;br&amp;gt;&lt;br /&gt;
Homework: 35%&amp;lt;br&amp;gt;&lt;br /&gt;
Exam: 30%&lt;br /&gt;
&lt;br /&gt;
==Homework Grading==&lt;br /&gt;
Some homework assignments contain extra problems. Let us call all other problems normal. The weight of each problem (whether normal or extra) in the overall homework grade is 8/&#039;&#039;n&#039;&#039;, where &#039;&#039;n&#039;&#039; is the total number of normal problems in all homework assignments. Partial credit is possible for some problems.&lt;br /&gt;
&lt;br /&gt;
If you score at least 8 and solve some extra problems that do not contribute to this score, we will evaluate each of these extra problems on the scale [0, 1] and will add two maximal scores to your homework grade.&lt;br /&gt;
&lt;br /&gt;
= Course Materials =&lt;br /&gt;
&lt;br /&gt;
The main reference is Sipser&#039;s book &amp;quot;Introduction to the theory of computation&amp;quot;, chapters 3, 7–10.&lt;br /&gt;
&lt;br /&gt;
If you need some background in math, consider these two sources:&amp;lt;br&amp;gt;&lt;br /&gt;
[http://www.cs.elte.hu/~lovasz/dmbook.ps Lecture notes: Discrete Mathematics], L. Lovasz, K. Vesztergombi&amp;lt;br&amp;gt;&lt;br /&gt;
[http://rubtsov.su/public/DM-HSE-Draft.pdf Лекции по дискретной математике] (черновик учебника, in Russian)&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
|-&lt;br /&gt;
! Video !! Summary !! Problem list&lt;br /&gt;
|-&lt;br /&gt;
 || 07.09 || Turing machines, multitape Turing machines, connection between them. Universal Turing machine. Examples ([https://www.dropbox.com/s/wna14b7y7nmw3cq/tm.py?dl=0 one], [https://www.dropbox.com/s/wrl3mkeqslj3xtu/wsharpw.py?dl=0 two]). Time and space complexity. Complexity classes P, PSPACE, EXP. || [https://www.dropbox.com/s/37eel2qayios6b3/prob_1.pdf?dl=0 Problem set 1]&lt;br /&gt;
|-&lt;br /&gt;
|| 14.09 ||  Time and space hierarchy theorem. Time and space constructible functions. || [https://www.dropbox.com/s/ow4m1z8u8r211qs/prob_2.pdf?dl=0 Problem set 2]&lt;br /&gt;
|-&lt;br /&gt;
 || 21.09 || Complexity class NP. Examples. Polynomial reductions. NP-hardness and NP-completeness. &lt;br /&gt;
 ||  [https://www.dropbox.com/s/bf68zicg4uh051x/prob_03.pdf?dl=0 Problem set 3]&lt;br /&gt;
|-&lt;br /&gt;
 || 28.09 ||  Non-deterministic TMs. Another definition of NP. Proving NP-hardness by reduction from an NP-complete problem. Examples of NP-complete problems.  || [https://www.dropbox.com/s/g817m6v0ygb8h4n/prob_04.pdf?dl=0 Problem set 4]&lt;br /&gt;
|-&lt;br /&gt;
 || 05.10 || Inclusions between P, NP, and PSPACE. Circuit complexity. Examples. All functions are computed by circuits. Existence of functions with exponential circuit complexity. P is in P/poly.|| [https://www.dropbox.com/s/qkc5p4795rualwn/prob_05.pdf?dl=0 Problem set 5]&lt;br /&gt;
|-&lt;br /&gt;
 || 12.10 || P is a subset of P/poly, Cook–Levin theorem, NP-completeness of: subsetsum, set-splitting, 3-colorability and exactly 1-in-3 SAT.  || [https://www.dropbox.com/s/y2y1lu29936xy9n/prob_06.pdf?dl=0 Problem set 6]&lt;br /&gt;
|-&lt;br /&gt;
 || [https://drive.google.com/drive/folders/1loJWyo9TK6ucCp8RnD3xx3DAVPDs0OiF?usp=sharing 26.10] || Space complexity. Classes L, NL, PSPACE and NPSPACE. Directed Reachability is in SPACE(log^2 n). Configuration graph. Inclusions between time and space classes. TQBF problem, its PSPACE-completeness. PSPACE = NPSPACE. NSPACE(s(n)) is in SPACE(s(n)^2) for space constructible s. || [https://www.dropbox.com/s/b6m0u5vqtutdhq1/prob_07.pdf?dl=0 Problem set 7]&lt;br /&gt;
|- &lt;br /&gt;
|| 02.11 || Oracle computation definitions. There exists an oracle &#039;&#039;A&#039;&#039; for which P&amp;lt;sup&amp;gt;&#039;&#039;A&#039;&#039;&amp;lt;/sup&amp;gt; = NP&amp;lt;sup&amp;gt;&#039;&#039;A&#039;&#039;&amp;lt;/sup&amp;gt;. There is an oracle B such that P&amp;lt;sup&amp;gt;&#039;&#039;B&#039;&#039;&amp;lt;/sup&amp;gt; is not equal to NP&amp;lt;sup&amp;gt;&#039;&#039;B&#039;&#039;&amp;lt;/sup&amp;gt;. ||&lt;br /&gt;
|-&lt;br /&gt;
 || 09.11 || Probabilistic computation. Probabilistic machines, the class BPP, invariance of the definition BPP for different thresholds, RP, coRP, PP, ZPP. BPP is in P/poly. || &lt;br /&gt;
|-&lt;br /&gt;
 || 16.11 ||  Streaming algorithms: finding the majority element, computation of the moment &#039;&#039;F&#039;&#039;&amp;lt;sub&amp;gt;2&amp;lt;/sub&amp;gt; in logarithmic space. ||&lt;br /&gt;
|-&lt;br /&gt;
 || 23.11 || Finding the frequent items in streams of data: SpaceSaving and Count-Min Sketch. ||&lt;br /&gt;
|-&lt;br /&gt;
 || 30.11 || Approximation algorithms. Approximate solutions for Vertex Cover, Weighted Vertex Cover, and TSP. ||&lt;br /&gt;
 &lt;br /&gt;
|-&lt;br /&gt;
 || 07.12 || Colloquium. ||&lt;br /&gt;
|-&lt;br /&gt;
 || 14.12 || Complexity of clustering: an exact algorithm for maximising the inter-cluster distance and an approximate algorithm for minimising the intra-class distance.&lt;br /&gt;
 || &lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
For interested students, there are 3 lectures in parameterized complexity. &lt;br /&gt;
&lt;br /&gt;
14 Sept: Fixed parameter tracktability and examples, [https://www.dropbox.com/s/zzzaulpmzql7x7u/parameterizedComplexity.pdf?dl=0 presentation]. &lt;br /&gt;
&lt;br /&gt;
21 Sept: Topics from chapters 1 and 2 in &amp;quot;Parameterized algorithms&amp;quot; by Cygan, Fomin and others, 2016.&lt;br /&gt;
&lt;br /&gt;
28 Sept: The W-hierarchy, chapter 13 in the same book.&lt;br /&gt;
&lt;br /&gt;
= Office hours =&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
|-&lt;br /&gt;
!  Person !! Monday !! Tuesday !! Wednesday !! Thursday !! Friday &lt;br /&gt;
|-&lt;br /&gt;
|  [https://www.hse.ru/en/org/persons/160550073 Bruno Bauwens], S834, [https://us02web.zoom.us/j/82300259484?pwd=NWxXekxBeE5yMm9UTmwvLzNNNGlnUT09 Zoom] ||  || ||  ||  || 14:00-20:00&lt;br /&gt;
|-&lt;br /&gt;
|  [https://www.hse.ru/en/staff/obiedkov Sergei Obiedkov], T915, [https://zoom.us/j/99663354582?pwd=K1B5R3NXWEhWbFozR2lqMkFWYW5Ydz09 Zoom] ||  ||  || 16:30–18:00 || 16:30–18:00 ||  &lt;br /&gt;
|}&lt;/div&gt;</summary>
		<author><name>.obj</name></author>
	</entry>
	<entry>
		<id>https://wiki.cs.hse.ru/index.php?title=Theory_of_Computation_2021&amp;diff=60661</id>
		<title>Theory of Computation 2021</title>
		<link rel="alternate" type="text/html" href="https://wiki.cs.hse.ru/index.php?title=Theory_of_Computation_2021&amp;diff=60661"/>
		<updated>2021-10-30T16:40:43Z</updated>

		<summary type="html">&lt;p&gt;.obj: /* Dates and Deadlines */&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;= Classes =&lt;br /&gt;
 &lt;br /&gt;
Tuesdays 14:40–17:40, [https://ruz.hse.ru/ruz/main ruz]&lt;br /&gt;
&lt;br /&gt;
Lectures: 14:40 in room M303  [https://us02web.zoom.us/j/83533615475?pwd=WDU3cHJ5RjREOGd2YU1qdDJCVm1idz09 zoomlink 26/10]&lt;br /&gt;
&lt;br /&gt;
Seminars: 16:20 in room M302  [https://us02web.zoom.us/j/84546220686?pwd=U2dISk5UaFZpdmh3WTdFT3phRVNXZz09 zoomlink 26/10]&lt;br /&gt;
&lt;br /&gt;
= Dates and Deadlines =&lt;br /&gt;
Please send your homework by e-mail to both lecturers.&amp;lt;br&amp;gt;&lt;br /&gt;
Homework 1, deadline: October 5, 14:00; the deadline for the extra problems is &amp;lt;s&amp;gt;November 2&amp;lt;/s&amp;gt; November 8, 14:00&amp;lt;br&amp;gt;&lt;br /&gt;
Homework 2, deadline: &amp;lt;s&amp;gt;November 2&amp;lt;/s&amp;gt; November 8, 14:00 &amp;lt;br&amp;gt;&lt;br /&gt;
Homework 3, deadline: December 7, 14:00 &amp;lt;br&amp;gt;&lt;br /&gt;
Colloquium: December 7, 14:40–17:40&lt;br /&gt;
&lt;br /&gt;
= Grading =&lt;br /&gt;
Colloquium: 35%&amp;lt;br&amp;gt;&lt;br /&gt;
Homework: 35%&amp;lt;br&amp;gt;&lt;br /&gt;
Exam: 30%&lt;br /&gt;
&lt;br /&gt;
==Homework Grading==&lt;br /&gt;
Some homework assignments contain extra problems. Let us call all other problems normal. The weight of each problem (whether normal or extra) in the overall homework grade is 8/&#039;&#039;n&#039;&#039;, where &#039;&#039;n&#039;&#039; is the total number of normal problems in all homework assignments. Partial credit is possible for some problems.&lt;br /&gt;
&lt;br /&gt;
If you score at least 8 and solve some extra problems that do not contribute to this score, we will evaluate each of these extra problems on the scale [0, 1] and will add two maximal scores to your homework grade.&lt;br /&gt;
&lt;br /&gt;
= Course Materials =&lt;br /&gt;
&lt;br /&gt;
The main reference is Sipser&#039;s book &amp;quot;Introduction to the theory of computation&amp;quot;, chapters 3, 7–10.&lt;br /&gt;
&lt;br /&gt;
If you need some background in math, consider these two sources:&amp;lt;br&amp;gt;&lt;br /&gt;
[http://www.cs.elte.hu/~lovasz/dmbook.ps Lecture notes: Discrete Mathematics], L. Lovasz, K. Vesztergombi&amp;lt;br&amp;gt;&lt;br /&gt;
[http://rubtsov.su/public/DM-HSE-Draft.pdf Лекции по дискретной математике] (черновик учебника, in Russian)&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
|-&lt;br /&gt;
! Video !! Summary !! Problem list&lt;br /&gt;
|-&lt;br /&gt;
 || 07.09 || Turing machines, multitape Turing machines, connection between them. Universal Turing machine. Examples ([https://www.dropbox.com/s/wna14b7y7nmw3cq/tm.py?dl=0 one], [https://www.dropbox.com/s/wrl3mkeqslj3xtu/wsharpw.py?dl=0 two]). Time and space complexity. Complexity classes P, PSPACE, EXP. || [https://www.dropbox.com/s/37eel2qayios6b3/prob_1.pdf?dl=0 Problem set 1]&lt;br /&gt;
|-&lt;br /&gt;
|| 14.09 ||  Time and space hierarchy theorem. Time and space constructible functions. || [https://www.dropbox.com/s/ow4m1z8u8r211qs/prob_2.pdf?dl=0 Problem set 2]&lt;br /&gt;
|-&lt;br /&gt;
 || 21.09 || Complexity class NP. Examples. Polynomial reductions. NP-hardness and NP-completeness. &lt;br /&gt;
 ||  [https://www.dropbox.com/s/bf68zicg4uh051x/prob_03.pdf?dl=0 Problem set 3]&lt;br /&gt;
|-&lt;br /&gt;
 || 28.09 ||  Non-deterministic TMs. Another definition of NP. Proving NP-hardness by reduction from an NP-complete problem. Examples of NP-complete problems.  || [https://www.dropbox.com/s/g817m6v0ygb8h4n/prob_04.pdf?dl=0 Problem set 4]&lt;br /&gt;
|-&lt;br /&gt;
 || 05.10 || Inclusions between P, NP, and PSPACE. Circuit complexity. Examples. All functions are computed by circuits. Existence of functions with exponential circuit complexity. P is in P/poly.|| [https://www.dropbox.com/s/qkc5p4795rualwn/prob_05.pdf?dl=0 Problem set 5]&lt;br /&gt;
|-&lt;br /&gt;
 || 12.10 || P is a subset of P/poly, Cook–Levin theorem, NP-completeness of: subsetsum, set-splitting, 3-colorability and exactly 1-in-3 SAT.  || [https://www.dropbox.com/s/y2y1lu29936xy9n/prob_06.pdf?dl=0 Problem set 6]&lt;br /&gt;
|-&lt;br /&gt;
 || [https://drive.google.com/drive/folders/1loJWyo9TK6ucCp8RnD3xx3DAVPDs0OiF?usp=sharing 26.10] || Space complexity. Classes L, NL, PSPACE and NPSPACE. Directed Reachability is in SPACE(log^2 n). Configuration graph. Inclusions between time and space classes. TQBF problem, its PSPACE-completeness. PSPACE = NPSPACE. NSPACE(s(n)) is in SPACE(s(n)^2) for space constructible s. || [https://www.dropbox.com/s/b6m0u5vqtutdhq1/prob_07.pdf?dl=0 Problem set 7]&lt;br /&gt;
|- &lt;br /&gt;
|| 02.11 || Oracle computation definitions. There exists an oracle &#039;&#039;A&#039;&#039; for which P&amp;lt;sup&amp;gt;&#039;&#039;A&#039;&#039;&amp;lt;/sup&amp;gt; = NP&amp;lt;sup&amp;gt;&#039;&#039;A&#039;&#039;&amp;lt;/sup&amp;gt;. There is an oracle B such that P&amp;lt;sup&amp;gt;&#039;&#039;B&#039;&#039;&amp;lt;/sup&amp;gt; is not equal to NP&amp;lt;sup&amp;gt;&#039;&#039;B&#039;&#039;&amp;lt;/sup&amp;gt;. ||&lt;br /&gt;
|-&lt;br /&gt;
 || 09.11 || Probabilistic computation. Probabilistic machines, the class BPP, invariance of the definition BPP for different thresholds, RP, coRP, PP, ZPP. BPP is in P/poly. || &lt;br /&gt;
|-&lt;br /&gt;
 || 16.11 ||  Streaming algorithms: finding the majority element, computation of the moment &#039;&#039;F&#039;&#039;&amp;lt;sub&amp;gt;2&amp;lt;/sub&amp;gt; in logarithmic space. ||&lt;br /&gt;
|-&lt;br /&gt;
 || 23.11 || Finding the frequent items in streams of data: SpaceSaving and Count-Min Sketch. ||&lt;br /&gt;
|-&lt;br /&gt;
 || 30.11 || Approximation algorithms. Approximate solutions for Vertex Cover, Weighted Vertex Cover, and TSP. ||&lt;br /&gt;
 &lt;br /&gt;
|-&lt;br /&gt;
 || 07.12 || Colloquium. ||&lt;br /&gt;
|-&lt;br /&gt;
 || 14.12 || Complexity of clustering: an exact algorithm for maximising the inter-cluster distance and an approximate algorithm for minimising the intra-class distance.&lt;br /&gt;
 || &lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
For interested students, there are 3 lectures in parameterized complexity. &lt;br /&gt;
&lt;br /&gt;
14 Sept: Fixed parameter tracktability and examples, [https://www.dropbox.com/s/zzzaulpmzql7x7u/parameterizedComplexity.pdf?dl=0 presentation]. &lt;br /&gt;
&lt;br /&gt;
21 Sept: Topics from chapters 1 and 2 in &amp;quot;Parameterized algorithms&amp;quot; by Cygan, Fomin and others, 2016.&lt;br /&gt;
&lt;br /&gt;
28 Sept: The W-hierarchy, chapter 13 in the same book.&lt;br /&gt;
&lt;br /&gt;
= Office hours =&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
|-&lt;br /&gt;
!  Person !! Monday !! Tuesday !! Wednesday !! Thursday !! Friday &lt;br /&gt;
|-&lt;br /&gt;
|  [https://www.hse.ru/en/org/persons/160550073 Bruno Bauwens], S834, [https://us02web.zoom.us/j/82300259484?pwd=NWxXekxBeE5yMm9UTmwvLzNNNGlnUT09 Zoom] ||  || ||  ||  || 14:00-20:00&lt;br /&gt;
|-&lt;br /&gt;
|  [https://www.hse.ru/en/staff/obiedkov Sergei Obiedkov], T915, [https://zoom.us/j/99663354582?pwd=K1B5R3NXWEhWbFozR2lqMkFWYW5Ydz09 Zoom] ||  ||  || 16:30–18:00 || 16:30–18:00 ||  &lt;br /&gt;
|}&lt;/div&gt;</summary>
		<author><name>.obj</name></author>
	</entry>
	<entry>
		<id>https://wiki.cs.hse.ru/index.php?title=Theory_of_Computation_2021&amp;diff=59865</id>
		<title>Theory of Computation 2021</title>
		<link rel="alternate" type="text/html" href="https://wiki.cs.hse.ru/index.php?title=Theory_of_Computation_2021&amp;diff=59865"/>
		<updated>2021-10-12T13:17:56Z</updated>

		<summary type="html">&lt;p&gt;.obj: &lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;= Classes =&lt;br /&gt;
 &lt;br /&gt;
Tuesdays 14:40–17:40, [https://ruz.hse.ru/ruz/main ruz]&lt;br /&gt;
&lt;br /&gt;
Lectures: 14:40 in room M303&lt;br /&gt;
&lt;br /&gt;
Seminars: 16:20 in room M302&lt;br /&gt;
&lt;br /&gt;
= Dates and Deadlines =&lt;br /&gt;
Please send your homework by e-mail to both lecturers.&amp;lt;br&amp;gt;&lt;br /&gt;
Homework 1, deadline: October 5, 14:00; the deadline for the extra problems is November 2, 14:00&amp;lt;br&amp;gt;&lt;br /&gt;
Homework 2, deadline: November 2, 14:00 &amp;lt;br&amp;gt;&lt;br /&gt;
Homework 3, deadline: December 7, 14:00 &amp;lt;br&amp;gt;&lt;br /&gt;
Colloquium: December 7, 14:40–17:40&lt;br /&gt;
&lt;br /&gt;
= Grading =&lt;br /&gt;
Colloquium: 35%&amp;lt;br&amp;gt;&lt;br /&gt;
Homework: 35%&amp;lt;br&amp;gt;&lt;br /&gt;
Exam: 30%&lt;br /&gt;
&lt;br /&gt;
==Homework Grading==&lt;br /&gt;
Some homework assignments contain extra problems. Let us call all other problems normal. The weight of each problem (whether normal or extra) in the overall homework grade is 8/&#039;&#039;n&#039;&#039;, where &#039;&#039;n&#039;&#039; is the total number of normal problems in all homework assignments. Partial credit is possible for some problems.&lt;br /&gt;
&lt;br /&gt;
If you score at least 8 and solve some extra problems that do not contribute to this score, we will evaluate each of these extra problems on the scale [0, 1] and will add two maximal scores to your homework grade.&lt;br /&gt;
&lt;br /&gt;
= Course Materials =&lt;br /&gt;
&lt;br /&gt;
The main reference is Sipser&#039;s book &amp;quot;Introduction to the theory of computation&amp;quot;, chapters 3, 7–10.&lt;br /&gt;
&lt;br /&gt;
If you need some background in math, consider these two sources:&amp;lt;br&amp;gt;&lt;br /&gt;
[http://www.cs.elte.hu/~lovasz/dmbook.ps Lecture notes: Discrete Mathematics], L. Lovasz, K. Vesztergombi&amp;lt;br&amp;gt;&lt;br /&gt;
[http://rubtsov.su/public/DM-HSE-Draft.pdf Лекции по дискретной математике] (черновик учебника, in Russian)&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
|-&lt;br /&gt;
! Date !! Summary !! Problem list&lt;br /&gt;
|-&lt;br /&gt;
 || 07.09 || Turing machines, multitape Turing machines, connection between them. Universal Turing machine. Examples ([https://www.dropbox.com/s/wna14b7y7nmw3cq/tm.py?dl=0 one], [https://www.dropbox.com/s/wrl3mkeqslj3xtu/wsharpw.py?dl=0 two]). Time and space complexity. Complexity classes P, PSPACE, EXP. || [https://www.dropbox.com/s/37eel2qayios6b3/prob_1.pdf?dl=0 Problem set 1]&lt;br /&gt;
|-&lt;br /&gt;
|| 14.09 ||  Time and space hierarchy theorem. Time and space constructible functions. || [https://www.dropbox.com/s/ow4m1z8u8r211qs/prob_2.pdf?dl=0 Problem set 2]&lt;br /&gt;
|-&lt;br /&gt;
 || 21.09 || Complexity class NP. Examples. Polynomial reductions. NP-hardness and NP-completeness. &lt;br /&gt;
 ||  [https://www.dropbox.com/s/bf68zicg4uh051x/prob_03.pdf?dl=0 Problem set 3]&lt;br /&gt;
|-&lt;br /&gt;
 || 28.09 ||  Non-deterministic TMs. Another definition of NP. Proving NP-hardness by reduction from an NP-complete problem. Examples of NP-complete problems.  || [https://www.dropbox.com/s/g817m6v0ygb8h4n/prob_04.pdf?dl=0 Problem set 4]&lt;br /&gt;
|-&lt;br /&gt;
 || 05.10 || Inclusions between P, NP, and PSPACE. Circuit complexity. Examples. All functions are computed by circuits. Existence of functions with exponential circuit complexity. P is in P/poly.|| [https://www.dropbox.com/s/qkc5p4795rualwn/prob_05.pdf?dl=0 Problem set 5]&lt;br /&gt;
|-&lt;br /&gt;
 || 12.10 || Cook–Levin theorem. ||&lt;br /&gt;
|-&lt;br /&gt;
 || 26.10 || Space complexity. ||&lt;br /&gt;
|- &lt;br /&gt;
|| 02.11 || Oracle computation definitions. There exists an oracle &#039;&#039;A&#039;&#039; for which P&amp;lt;sup&amp;gt;&#039;&#039;A&#039;&#039;&amp;lt;/sup&amp;gt; = NP&amp;lt;sup&amp;gt;&#039;&#039;A&#039;&#039;&amp;lt;/sup&amp;gt;. There is an oracle B such that P&amp;lt;sup&amp;gt;&#039;&#039;B&#039;&#039;&amp;lt;/sup&amp;gt; is not equal to NP&amp;lt;sup&amp;gt;&#039;&#039;B&#039;&#039;&amp;lt;/sup&amp;gt;. ||&lt;br /&gt;
|-&lt;br /&gt;
 || 09.11 || Probabilistic computation. Probabilistic machines, the class BPP, invariance of the definition BPP for different thresholds, RP, coRP, PP, ZPP. BPP is in P/poly. || &lt;br /&gt;
|-&lt;br /&gt;
 || 16.11 ||  Streaming algorithms: finding the majority element, computation of the moment &#039;&#039;F&#039;&#039;&amp;lt;sub&amp;gt;2&amp;lt;/sub&amp;gt; in logarithmic space. ||&lt;br /&gt;
|-&lt;br /&gt;
 || 23.11 || Finding the frequent items in streams of data: SpaceSaving and Count-Min Sketch. ||&lt;br /&gt;
|-&lt;br /&gt;
 || 30.11 || Approximation algorithms. Approximate solutions for Vertex Cover, Weighted Vertex Cover, and TSP. ||&lt;br /&gt;
 &lt;br /&gt;
|-&lt;br /&gt;
 || 07.12 || Colloquium. ||&lt;br /&gt;
|-&lt;br /&gt;
 || 14.12 || Complexity of clustering: an exact algorithm for maximising the inter-cluster distance and an approximate algorithm for minimising the intra-class distance.&lt;br /&gt;
 || &lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
For interested students, there are 3 lectures in parameterized complexity. &lt;br /&gt;
&lt;br /&gt;
14 Sept: Fixed parameter tracktability and examples, [https://www.dropbox.com/s/zzzaulpmzql7x7u/parameterizedComplexity.pdf?dl=0 presentation]. &lt;br /&gt;
&lt;br /&gt;
21 Sept: Topics from chapters 1 and 2 in &amp;quot;Parameterized algorithms&amp;quot; by Cygan, Fomin and others, 2016.&lt;br /&gt;
&lt;br /&gt;
28 Sept: The W-hierarchy, chapter 13 in the same book.&lt;br /&gt;
&lt;br /&gt;
= Office hours =&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
|-&lt;br /&gt;
!  Person !! Monday !! Tuesday !! Wednesday !! Thursday !! Friday &lt;br /&gt;
|-&lt;br /&gt;
|  [https://www.hse.ru/en/org/persons/160550073 Bruno Bauwens], S834, [https://us02web.zoom.us/j/82300259484?pwd=NWxXekxBeE5yMm9UTmwvLzNNNGlnUT09 Zoom] ||  || ||  ||  || 14:00-20:00&lt;br /&gt;
|-&lt;br /&gt;
|  [https://www.hse.ru/en/staff/obiedkov Sergei Obiedkov], T915, [https://zoom.us/j/99663354582?pwd=K1B5R3NXWEhWbFozR2lqMkFWYW5Ydz09 Zoom] ||  ||  || 16:30–18:00 || 16:30–18:00 ||  &lt;br /&gt;
|}&lt;/div&gt;</summary>
		<author><name>.obj</name></author>
	</entry>
	<entry>
		<id>https://wiki.cs.hse.ru/index.php?title=Theory_of_Computation_2021&amp;diff=59864</id>
		<title>Theory of Computation 2021</title>
		<link rel="alternate" type="text/html" href="https://wiki.cs.hse.ru/index.php?title=Theory_of_Computation_2021&amp;diff=59864"/>
		<updated>2021-10-12T13:16:45Z</updated>

		<summary type="html">&lt;p&gt;.obj: /* Dates and Deadlines */&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;= Classes =&lt;br /&gt;
 &lt;br /&gt;
Tuesdays 14:40–17:40, [https://ruz.hse.ru/ruz/main ruz]&lt;br /&gt;
&lt;br /&gt;
Lectures: 14:40 in room M303, parallel [https://zoom.us/j/92154456703?pwd=aFZ0eWVoZnFVbm03ckNvTDFNS3dIdz09 session]&lt;br /&gt;
&lt;br /&gt;
Seminars: 16:20 in room M203&lt;br /&gt;
&lt;br /&gt;
= Dates and Deadlines =&lt;br /&gt;
Please send your homework by e-mail to both lecturers.&amp;lt;br&amp;gt;&lt;br /&gt;
Homework 1, deadline: October 5, 14:00; the deadline for the extra problems is November 2, 14:00&amp;lt;br&amp;gt;&lt;br /&gt;
Homework 2, deadline: November 2, 14:00 &amp;lt;br&amp;gt;&lt;br /&gt;
Homework 3, deadline: December 7, 14:00 &amp;lt;br&amp;gt;&lt;br /&gt;
Colloquium: December 7, 14:40–17:40&lt;br /&gt;
&lt;br /&gt;
= Grading =&lt;br /&gt;
Colloquium: 35%&amp;lt;br&amp;gt;&lt;br /&gt;
Homework: 35%&amp;lt;br&amp;gt;&lt;br /&gt;
Exam: 30%&lt;br /&gt;
&lt;br /&gt;
==Homework Grading==&lt;br /&gt;
Some homework assignments contain extra problems. Let us call all other problems normal. The weight of each problem (whether normal or extra) in the overall homework grade is 8/&#039;&#039;n&#039;&#039;, where &#039;&#039;n&#039;&#039; is the total number of normal problems in all homework assignments. Partial credit is possible for some problems.&lt;br /&gt;
&lt;br /&gt;
If you score at least 8 and solve some extra problems that do not contribute to this score, we will evaluate each of these extra problems on the scale [0, 1] and will add two maximal scores to your homework grade.&lt;br /&gt;
&lt;br /&gt;
= Course Materials =&lt;br /&gt;
&lt;br /&gt;
The main reference is Sipser&#039;s book &amp;quot;Introduction to the theory of computation&amp;quot;, chapters 3, 7–10.&lt;br /&gt;
&lt;br /&gt;
If you need some background in math, consider these two sources:&amp;lt;br&amp;gt;&lt;br /&gt;
[http://www.cs.elte.hu/~lovasz/dmbook.ps Lecture notes: Discrete Mathematics], L. Lovasz, K. Vesztergombi&amp;lt;br&amp;gt;&lt;br /&gt;
[http://rubtsov.su/public/DM-HSE-Draft.pdf Лекции по дискретной математике] (черновик учебника, in Russian)&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
|-&lt;br /&gt;
! Date !! Summary !! Problem list&lt;br /&gt;
|-&lt;br /&gt;
 || 07.09 || Turing machines, multitape Turing machines, connection between them. Universal Turing machine. Examples ([https://www.dropbox.com/s/wna14b7y7nmw3cq/tm.py?dl=0 one], [https://www.dropbox.com/s/wrl3mkeqslj3xtu/wsharpw.py?dl=0 two]). Time and space complexity. Complexity classes P, PSPACE, EXP. || [https://www.dropbox.com/s/37eel2qayios6b3/prob_1.pdf?dl=0 Problem set 1]&lt;br /&gt;
|-&lt;br /&gt;
|| 14.09 ||  Time and space hierarchy theorem. Time and space constructible functions. || [https://www.dropbox.com/s/ow4m1z8u8r211qs/prob_2.pdf?dl=0 Problem set 2]&lt;br /&gt;
|-&lt;br /&gt;
 || 21.09 || Complexity class NP. Examples. Polynomial reductions. NP-hardness and NP-completeness. &lt;br /&gt;
 ||  [https://www.dropbox.com/s/bf68zicg4uh051x/prob_03.pdf?dl=0 Problem set 3]&lt;br /&gt;
|-&lt;br /&gt;
 || 28.09 ||  Non-deterministic TMs. Another definition of NP. Proving NP-hardness by reduction from an NP-complete problem. Examples of NP-complete problems.  || [https://www.dropbox.com/s/g817m6v0ygb8h4n/prob_04.pdf?dl=0 Problem set 4]&lt;br /&gt;
|-&lt;br /&gt;
 || 05.10 || Inclusions between P, NP, and PSPACE. Circuit complexity. Examples. All functions are computed by circuits. Existence of functions with exponential circuit complexity. P is in P/poly.|| [https://www.dropbox.com/s/qkc5p4795rualwn/prob_05.pdf?dl=0 Problem set 5]&lt;br /&gt;
|-&lt;br /&gt;
 || 12.10 || Cook–Levin theorem. ||&lt;br /&gt;
|-&lt;br /&gt;
 || 26.10 || Space complexity. ||&lt;br /&gt;
|- &lt;br /&gt;
|| 02.11 || Oracle computation definitions. There exists an oracle &#039;&#039;A&#039;&#039; for which P&amp;lt;sup&amp;gt;&#039;&#039;A&#039;&#039;&amp;lt;/sup&amp;gt; = NP&amp;lt;sup&amp;gt;&#039;&#039;A&#039;&#039;&amp;lt;/sup&amp;gt;. There is an oracle B such that P&amp;lt;sup&amp;gt;&#039;&#039;B&#039;&#039;&amp;lt;/sup&amp;gt; is not equal to NP&amp;lt;sup&amp;gt;&#039;&#039;B&#039;&#039;&amp;lt;/sup&amp;gt;. ||&lt;br /&gt;
|-&lt;br /&gt;
 || 09.11 || Probabilistic computation. Probabilistic machines, the class BPP, invariance of the definition BPP for different thresholds, RP, coRP, PP, ZPP. BPP is in P/poly. || &lt;br /&gt;
|-&lt;br /&gt;
 || 16.11 ||  Streaming algorithms: finding the majority element, computation of the moment &#039;&#039;F&#039;&#039;&amp;lt;sub&amp;gt;2&amp;lt;/sub&amp;gt; in logarithmic space. ||&lt;br /&gt;
|-&lt;br /&gt;
 || 23.11 || Finding the frequent items in streams of data: SpaceSaving and Count-Min Sketch. ||&lt;br /&gt;
|-&lt;br /&gt;
 || 30.11 || Approximation algorithms. Approximate solutions for Vertex Cover, Weighted Vertex Cover, and TSP. ||&lt;br /&gt;
 &lt;br /&gt;
|-&lt;br /&gt;
 || 07.12 || Colloquium. ||&lt;br /&gt;
|-&lt;br /&gt;
 || 14.12 || Complexity of clustering: an exact algorithm for maximising the inter-cluster distance and an approximate algorithm for minimising the intra-class distance.&lt;br /&gt;
 || &lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
For interested students, there are 3 lectures in parameterized complexity. &lt;br /&gt;
&lt;br /&gt;
14 Sept: Fixed parameter tracktability and examples, [https://www.dropbox.com/s/zzzaulpmzql7x7u/parameterizedComplexity.pdf?dl=0 presentation]. &lt;br /&gt;
&lt;br /&gt;
21 Sept: Topics from chapters 1 and 2 in &amp;quot;Parameterized algorithms&amp;quot; by Cygan, Fomin and others, 2016.&lt;br /&gt;
&lt;br /&gt;
28 Sept: The W-hierarchy, chapter 13 in the same book.&lt;br /&gt;
&lt;br /&gt;
= Office hours =&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
|-&lt;br /&gt;
!  Person !! Monday !! Tuesday !! Wednesday !! Thursday !! Friday &lt;br /&gt;
|-&lt;br /&gt;
|  [https://www.hse.ru/en/org/persons/160550073 Bruno Bauwens], S834, [https://us02web.zoom.us/j/82300259484?pwd=NWxXekxBeE5yMm9UTmwvLzNNNGlnUT09 Zoom] ||  || ||  ||  || 14:00-20:00&lt;br /&gt;
|-&lt;br /&gt;
|  [https://www.hse.ru/en/staff/obiedkov Sergei Obiedkov], T915, [https://zoom.us/j/99663354582?pwd=K1B5R3NXWEhWbFozR2lqMkFWYW5Ydz09 Zoom] ||  ||  || 16:30–18:00 || 16:30–18:00 ||  &lt;br /&gt;
|}&lt;/div&gt;</summary>
		<author><name>.obj</name></author>
	</entry>
	<entry>
		<id>https://wiki.cs.hse.ru/index.php?title=Theory_of_Computation_2021&amp;diff=59863</id>
		<title>Theory of Computation 2021</title>
		<link rel="alternate" type="text/html" href="https://wiki.cs.hse.ru/index.php?title=Theory_of_Computation_2021&amp;diff=59863"/>
		<updated>2021-10-12T13:15:49Z</updated>

		<summary type="html">&lt;p&gt;.obj: /* Homework Grading */&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;= Classes =&lt;br /&gt;
 &lt;br /&gt;
Tuesdays 14:40–17:40, [https://ruz.hse.ru/ruz/main ruz]&lt;br /&gt;
&lt;br /&gt;
Lectures: 14:40 in room M303, parallel [https://zoom.us/j/92154456703?pwd=aFZ0eWVoZnFVbm03ckNvTDFNS3dIdz09 session]&lt;br /&gt;
&lt;br /&gt;
Seminars: 16:20 in room M203&lt;br /&gt;
&lt;br /&gt;
= Dates and Deadlines =&lt;br /&gt;
Please send your homework by e-mail to both lecturers.&amp;lt;br&amp;gt;&lt;br /&gt;
Homework 1, deadline: October 5, 14:00 &amp;lt;br&amp;gt;&lt;br /&gt;
Homework 2, deadline: November 2, 14:00 &amp;lt;br&amp;gt;&lt;br /&gt;
Homework 3, deadline: December 7, 14:00 &amp;lt;br&amp;gt;&lt;br /&gt;
Colloquium: December 7, 14:40–17:40&lt;br /&gt;
&lt;br /&gt;
= Grading =&lt;br /&gt;
Colloquium: 35%&amp;lt;br&amp;gt;&lt;br /&gt;
Homework: 35%&amp;lt;br&amp;gt;&lt;br /&gt;
Exam: 30%&lt;br /&gt;
&lt;br /&gt;
==Homework Grading==&lt;br /&gt;
Some homework assignments contain extra problems. Let us call all other problems normal. The weight of each problem (whether normal or extra) in the overall homework grade is 8/&#039;&#039;n&#039;&#039;, where &#039;&#039;n&#039;&#039; is the total number of normal problems in all homework assignments. Partial credit is possible for some problems.&lt;br /&gt;
&lt;br /&gt;
If you score at least 8 and solve some extra problems that do not contribute to this score, we will evaluate each of these extra problems on the scale [0, 1] and will add two maximal scores to your homework grade.&lt;br /&gt;
&lt;br /&gt;
= Course Materials =&lt;br /&gt;
&lt;br /&gt;
The main reference is Sipser&#039;s book &amp;quot;Introduction to the theory of computation&amp;quot;, chapters 3, 7–10.&lt;br /&gt;
&lt;br /&gt;
If you need some background in math, consider these two sources:&amp;lt;br&amp;gt;&lt;br /&gt;
[http://www.cs.elte.hu/~lovasz/dmbook.ps Lecture notes: Discrete Mathematics], L. Lovasz, K. Vesztergombi&amp;lt;br&amp;gt;&lt;br /&gt;
[http://rubtsov.su/public/DM-HSE-Draft.pdf Лекции по дискретной математике] (черновик учебника, in Russian)&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
|-&lt;br /&gt;
! Date !! Summary !! Problem list&lt;br /&gt;
|-&lt;br /&gt;
 || 07.09 || Turing machines, multitape Turing machines, connection between them. Universal Turing machine. Examples ([https://www.dropbox.com/s/wna14b7y7nmw3cq/tm.py?dl=0 one], [https://www.dropbox.com/s/wrl3mkeqslj3xtu/wsharpw.py?dl=0 two]). Time and space complexity. Complexity classes P, PSPACE, EXP. || [https://www.dropbox.com/s/37eel2qayios6b3/prob_1.pdf?dl=0 Problem set 1]&lt;br /&gt;
|-&lt;br /&gt;
|| 14.09 ||  Time and space hierarchy theorem. Time and space constructible functions. || [https://www.dropbox.com/s/ow4m1z8u8r211qs/prob_2.pdf?dl=0 Problem set 2]&lt;br /&gt;
|-&lt;br /&gt;
 || 21.09 || Complexity class NP. Examples. Polynomial reductions. NP-hardness and NP-completeness. &lt;br /&gt;
 ||  [https://www.dropbox.com/s/bf68zicg4uh051x/prob_03.pdf?dl=0 Problem set 3]&lt;br /&gt;
|-&lt;br /&gt;
 || 28.09 ||  Non-deterministic TMs. Another definition of NP. Proving NP-hardness by reduction from an NP-complete problem. Examples of NP-complete problems.  || [https://www.dropbox.com/s/g817m6v0ygb8h4n/prob_04.pdf?dl=0 Problem set 4]&lt;br /&gt;
|-&lt;br /&gt;
 || 05.10 || Inclusions between P, NP, and PSPACE. Circuit complexity. Examples. All functions are computed by circuits. Existence of functions with exponential circuit complexity. P is in P/poly.|| [https://www.dropbox.com/s/qkc5p4795rualwn/prob_05.pdf?dl=0 Problem set 5]&lt;br /&gt;
|-&lt;br /&gt;
 || 12.10 || Cook–Levin theorem. ||&lt;br /&gt;
|-&lt;br /&gt;
 || 26.10 || Space complexity. ||&lt;br /&gt;
|- &lt;br /&gt;
|| 02.11 || Oracle computation definitions. There exists an oracle &#039;&#039;A&#039;&#039; for which P&amp;lt;sup&amp;gt;&#039;&#039;A&#039;&#039;&amp;lt;/sup&amp;gt; = NP&amp;lt;sup&amp;gt;&#039;&#039;A&#039;&#039;&amp;lt;/sup&amp;gt;. There is an oracle B such that P&amp;lt;sup&amp;gt;&#039;&#039;B&#039;&#039;&amp;lt;/sup&amp;gt; is not equal to NP&amp;lt;sup&amp;gt;&#039;&#039;B&#039;&#039;&amp;lt;/sup&amp;gt;. ||&lt;br /&gt;
|-&lt;br /&gt;
 || 09.11 || Probabilistic computation. Probabilistic machines, the class BPP, invariance of the definition BPP for different thresholds, RP, coRP, PP, ZPP. BPP is in P/poly. || &lt;br /&gt;
|-&lt;br /&gt;
 || 16.11 ||  Streaming algorithms: finding the majority element, computation of the moment &#039;&#039;F&#039;&#039;&amp;lt;sub&amp;gt;2&amp;lt;/sub&amp;gt; in logarithmic space. ||&lt;br /&gt;
|-&lt;br /&gt;
 || 23.11 || Finding the frequent items in streams of data: SpaceSaving and Count-Min Sketch. ||&lt;br /&gt;
|-&lt;br /&gt;
 || 30.11 || Approximation algorithms. Approximate solutions for Vertex Cover, Weighted Vertex Cover, and TSP. ||&lt;br /&gt;
 &lt;br /&gt;
|-&lt;br /&gt;
 || 07.12 || Colloquium. ||&lt;br /&gt;
|-&lt;br /&gt;
 || 14.12 || Complexity of clustering: an exact algorithm for maximising the inter-cluster distance and an approximate algorithm for minimising the intra-class distance.&lt;br /&gt;
 || &lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
For interested students, there are 3 lectures in parameterized complexity. &lt;br /&gt;
&lt;br /&gt;
14 Sept: Fixed parameter tracktability and examples, [https://www.dropbox.com/s/zzzaulpmzql7x7u/parameterizedComplexity.pdf?dl=0 presentation]. &lt;br /&gt;
&lt;br /&gt;
21 Sept: Topics from chapters 1 and 2 in &amp;quot;Parameterized algorithms&amp;quot; by Cygan, Fomin and others, 2016.&lt;br /&gt;
&lt;br /&gt;
28 Sept: The W-hierarchy, chapter 13 in the same book.&lt;br /&gt;
&lt;br /&gt;
= Office hours =&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
|-&lt;br /&gt;
!  Person !! Monday !! Tuesday !! Wednesday !! Thursday !! Friday &lt;br /&gt;
|-&lt;br /&gt;
|  [https://www.hse.ru/en/org/persons/160550073 Bruno Bauwens], S834, [https://us02web.zoom.us/j/82300259484?pwd=NWxXekxBeE5yMm9UTmwvLzNNNGlnUT09 Zoom] ||  || ||  ||  || 14:00-20:00&lt;br /&gt;
|-&lt;br /&gt;
|  [https://www.hse.ru/en/staff/obiedkov Sergei Obiedkov], T915, [https://zoom.us/j/99663354582?pwd=K1B5R3NXWEhWbFozR2lqMkFWYW5Ydz09 Zoom] ||  ||  || 16:30–18:00 || 16:30–18:00 ||  &lt;br /&gt;
|}&lt;/div&gt;</summary>
		<author><name>.obj</name></author>
	</entry>
	<entry>
		<id>https://wiki.cs.hse.ru/index.php?title=Theory_of_Computation_2021&amp;diff=59862</id>
		<title>Theory of Computation 2021</title>
		<link rel="alternate" type="text/html" href="https://wiki.cs.hse.ru/index.php?title=Theory_of_Computation_2021&amp;diff=59862"/>
		<updated>2021-10-12T13:15:01Z</updated>

		<summary type="html">&lt;p&gt;.obj: /* Homework Grading */&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;= Classes =&lt;br /&gt;
 &lt;br /&gt;
Tuesdays 14:40–17:40, [https://ruz.hse.ru/ruz/main ruz]&lt;br /&gt;
&lt;br /&gt;
Lectures: 14:40 in room M303, parallel [https://zoom.us/j/92154456703?pwd=aFZ0eWVoZnFVbm03ckNvTDFNS3dIdz09 session]&lt;br /&gt;
&lt;br /&gt;
Seminars: 16:20 in room M203&lt;br /&gt;
&lt;br /&gt;
= Dates and Deadlines =&lt;br /&gt;
Please send your homework by e-mail to both lecturers.&amp;lt;br&amp;gt;&lt;br /&gt;
Homework 1, deadline: October 5, 14:00 &amp;lt;br&amp;gt;&lt;br /&gt;
Homework 2, deadline: November 2, 14:00 &amp;lt;br&amp;gt;&lt;br /&gt;
Homework 3, deadline: December 7, 14:00 &amp;lt;br&amp;gt;&lt;br /&gt;
Colloquium: December 7, 14:40–17:40&lt;br /&gt;
&lt;br /&gt;
= Grading =&lt;br /&gt;
Colloquium: 35%&amp;lt;br&amp;gt;&lt;br /&gt;
Homework: 35%&amp;lt;br&amp;gt;&lt;br /&gt;
Exam: 30%&lt;br /&gt;
&lt;br /&gt;
==Homework Grading==&lt;br /&gt;
Some homework assignments contain extra problems. Let us call all other problems normal. The weight of each problem (whether normal or extra) in the overall homework grade is 8/&#039;&#039;n&#039;&#039;, where &#039;&#039;n&#039;&#039; is the total number of normal problems in all homework assignments. Partial credit is possible for some problems.&lt;br /&gt;
&lt;br /&gt;
If you score at least 8 and solve some extra problems that do not contribute to this score, we will evaluate each problem on the scale [0, 1] and will add two maximal scores to your homework grade.&lt;br /&gt;
&lt;br /&gt;
= Course Materials =&lt;br /&gt;
&lt;br /&gt;
The main reference is Sipser&#039;s book &amp;quot;Introduction to the theory of computation&amp;quot;, chapters 3, 7–10.&lt;br /&gt;
&lt;br /&gt;
If you need some background in math, consider these two sources:&amp;lt;br&amp;gt;&lt;br /&gt;
[http://www.cs.elte.hu/~lovasz/dmbook.ps Lecture notes: Discrete Mathematics], L. Lovasz, K. Vesztergombi&amp;lt;br&amp;gt;&lt;br /&gt;
[http://rubtsov.su/public/DM-HSE-Draft.pdf Лекции по дискретной математике] (черновик учебника, in Russian)&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
|-&lt;br /&gt;
! Date !! Summary !! Problem list&lt;br /&gt;
|-&lt;br /&gt;
 || 07.09 || Turing machines, multitape Turing machines, connection between them. Universal Turing machine. Examples ([https://www.dropbox.com/s/wna14b7y7nmw3cq/tm.py?dl=0 one], [https://www.dropbox.com/s/wrl3mkeqslj3xtu/wsharpw.py?dl=0 two]). Time and space complexity. Complexity classes P, PSPACE, EXP. || [https://www.dropbox.com/s/37eel2qayios6b3/prob_1.pdf?dl=0 Problem set 1]&lt;br /&gt;
|-&lt;br /&gt;
|| 14.09 ||  Time and space hierarchy theorem. Time and space constructible functions. || [https://www.dropbox.com/s/ow4m1z8u8r211qs/prob_2.pdf?dl=0 Problem set 2]&lt;br /&gt;
|-&lt;br /&gt;
 || 21.09 || Complexity class NP. Examples. Polynomial reductions. NP-hardness and NP-completeness. &lt;br /&gt;
 ||  [https://www.dropbox.com/s/bf68zicg4uh051x/prob_03.pdf?dl=0 Problem set 3]&lt;br /&gt;
|-&lt;br /&gt;
 || 28.09 ||  Non-deterministic TMs. Another definition of NP. Proving NP-hardness by reduction from an NP-complete problem. Examples of NP-complete problems.  || [https://www.dropbox.com/s/g817m6v0ygb8h4n/prob_04.pdf?dl=0 Problem set 4]&lt;br /&gt;
|-&lt;br /&gt;
 || 05.10 || Inclusions between P, NP, and PSPACE. Circuit complexity. Examples. All functions are computed by circuits. Existence of functions with exponential circuit complexity. P is in P/poly.|| [https://www.dropbox.com/s/qkc5p4795rualwn/prob_05.pdf?dl=0 Problem set 5]&lt;br /&gt;
|-&lt;br /&gt;
 || 12.10 || Cook–Levin theorem. ||&lt;br /&gt;
|-&lt;br /&gt;
 || 26.10 || Space complexity. ||&lt;br /&gt;
|- &lt;br /&gt;
|| 02.11 || Oracle computation definitions. There exists an oracle &#039;&#039;A&#039;&#039; for which P&amp;lt;sup&amp;gt;&#039;&#039;A&#039;&#039;&amp;lt;/sup&amp;gt; = NP&amp;lt;sup&amp;gt;&#039;&#039;A&#039;&#039;&amp;lt;/sup&amp;gt;. There is an oracle B such that P&amp;lt;sup&amp;gt;&#039;&#039;B&#039;&#039;&amp;lt;/sup&amp;gt; is not equal to NP&amp;lt;sup&amp;gt;&#039;&#039;B&#039;&#039;&amp;lt;/sup&amp;gt;. ||&lt;br /&gt;
|-&lt;br /&gt;
 || 09.11 || Probabilistic computation. Probabilistic machines, the class BPP, invariance of the definition BPP for different thresholds, RP, coRP, PP, ZPP. BPP is in P/poly. || &lt;br /&gt;
|-&lt;br /&gt;
 || 16.11 ||  Streaming algorithms: finding the majority element, computation of the moment &#039;&#039;F&#039;&#039;&amp;lt;sub&amp;gt;2&amp;lt;/sub&amp;gt; in logarithmic space. ||&lt;br /&gt;
|-&lt;br /&gt;
 || 23.11 || Finding the frequent items in streams of data: SpaceSaving and Count-Min Sketch. ||&lt;br /&gt;
|-&lt;br /&gt;
 || 30.11 || Approximation algorithms. Approximate solutions for Vertex Cover, Weighted Vertex Cover, and TSP. ||&lt;br /&gt;
 &lt;br /&gt;
|-&lt;br /&gt;
 || 07.12 || Colloquium. ||&lt;br /&gt;
|-&lt;br /&gt;
 || 14.12 || Complexity of clustering: an exact algorithm for maximising the inter-cluster distance and an approximate algorithm for minimising the intra-class distance.&lt;br /&gt;
 || &lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
For interested students, there are 3 lectures in parameterized complexity. &lt;br /&gt;
&lt;br /&gt;
14 Sept: Fixed parameter tracktability and examples, [https://www.dropbox.com/s/zzzaulpmzql7x7u/parameterizedComplexity.pdf?dl=0 presentation]. &lt;br /&gt;
&lt;br /&gt;
21 Sept: Topics from chapters 1 and 2 in &amp;quot;Parameterized algorithms&amp;quot; by Cygan, Fomin and others, 2016.&lt;br /&gt;
&lt;br /&gt;
28 Sept: The W-hierarchy, chapter 13 in the same book.&lt;br /&gt;
&lt;br /&gt;
= Office hours =&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
|-&lt;br /&gt;
!  Person !! Monday !! Tuesday !! Wednesday !! Thursday !! Friday &lt;br /&gt;
|-&lt;br /&gt;
|  [https://www.hse.ru/en/org/persons/160550073 Bruno Bauwens], S834, [https://us02web.zoom.us/j/82300259484?pwd=NWxXekxBeE5yMm9UTmwvLzNNNGlnUT09 Zoom] ||  || ||  ||  || 14:00-20:00&lt;br /&gt;
|-&lt;br /&gt;
|  [https://www.hse.ru/en/staff/obiedkov Sergei Obiedkov], T915, [https://zoom.us/j/99663354582?pwd=K1B5R3NXWEhWbFozR2lqMkFWYW5Ydz09 Zoom] ||  ||  || 16:30–18:00 || 16:30–18:00 ||  &lt;br /&gt;
|}&lt;/div&gt;</summary>
		<author><name>.obj</name></author>
	</entry>
	<entry>
		<id>https://wiki.cs.hse.ru/index.php?title=Theory_of_Computation_2021&amp;diff=59861</id>
		<title>Theory of Computation 2021</title>
		<link rel="alternate" type="text/html" href="https://wiki.cs.hse.ru/index.php?title=Theory_of_Computation_2021&amp;diff=59861"/>
		<updated>2021-10-12T13:14:38Z</updated>

		<summary type="html">&lt;p&gt;.obj: /* Grading */&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;= Classes =&lt;br /&gt;
 &lt;br /&gt;
Tuesdays 14:40–17:40, [https://ruz.hse.ru/ruz/main ruz]&lt;br /&gt;
&lt;br /&gt;
Lectures: 14:40 in room M303, parallel [https://zoom.us/j/92154456703?pwd=aFZ0eWVoZnFVbm03ckNvTDFNS3dIdz09 session]&lt;br /&gt;
&lt;br /&gt;
Seminars: 16:20 in room M203&lt;br /&gt;
&lt;br /&gt;
= Dates and Deadlines =&lt;br /&gt;
Please send your homework by e-mail to both lecturers.&amp;lt;br&amp;gt;&lt;br /&gt;
Homework 1, deadline: October 5, 14:00 &amp;lt;br&amp;gt;&lt;br /&gt;
Homework 2, deadline: November 2, 14:00 &amp;lt;br&amp;gt;&lt;br /&gt;
Homework 3, deadline: December 7, 14:00 &amp;lt;br&amp;gt;&lt;br /&gt;
Colloquium: December 7, 14:40–17:40&lt;br /&gt;
&lt;br /&gt;
= Grading =&lt;br /&gt;
Colloquium: 35%&amp;lt;br&amp;gt;&lt;br /&gt;
Homework: 35%&amp;lt;br&amp;gt;&lt;br /&gt;
Exam: 30%&lt;br /&gt;
&lt;br /&gt;
==Homework Grading==&lt;br /&gt;
Some homework assignments contain extra problems. Let us call all other problems normal. The weight of each problem (whether normal or extra) in the overall homework grade is 8/n, where n is the total number of normal problems in all homework assignments. Partial credit is possible for some problems.&lt;br /&gt;
&lt;br /&gt;
If you score at least 8 and solve some extra problems that do not contribute to this score, we will evaluate each problem on the scale [0, 1] and will add two maximal scores to your homework grade.&lt;br /&gt;
&lt;br /&gt;
= Course Materials =&lt;br /&gt;
&lt;br /&gt;
The main reference is Sipser&#039;s book &amp;quot;Introduction to the theory of computation&amp;quot;, chapters 3, 7–10.&lt;br /&gt;
&lt;br /&gt;
If you need some background in math, consider these two sources:&amp;lt;br&amp;gt;&lt;br /&gt;
[http://www.cs.elte.hu/~lovasz/dmbook.ps Lecture notes: Discrete Mathematics], L. Lovasz, K. Vesztergombi&amp;lt;br&amp;gt;&lt;br /&gt;
[http://rubtsov.su/public/DM-HSE-Draft.pdf Лекции по дискретной математике] (черновик учебника, in Russian)&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
|-&lt;br /&gt;
! Date !! Summary !! Problem list&lt;br /&gt;
|-&lt;br /&gt;
 || 07.09 || Turing machines, multitape Turing machines, connection between them. Universal Turing machine. Examples ([https://www.dropbox.com/s/wna14b7y7nmw3cq/tm.py?dl=0 one], [https://www.dropbox.com/s/wrl3mkeqslj3xtu/wsharpw.py?dl=0 two]). Time and space complexity. Complexity classes P, PSPACE, EXP. || [https://www.dropbox.com/s/37eel2qayios6b3/prob_1.pdf?dl=0 Problem set 1]&lt;br /&gt;
|-&lt;br /&gt;
|| 14.09 ||  Time and space hierarchy theorem. Time and space constructible functions. || [https://www.dropbox.com/s/ow4m1z8u8r211qs/prob_2.pdf?dl=0 Problem set 2]&lt;br /&gt;
|-&lt;br /&gt;
 || 21.09 || Complexity class NP. Examples. Polynomial reductions. NP-hardness and NP-completeness. &lt;br /&gt;
 ||  [https://www.dropbox.com/s/bf68zicg4uh051x/prob_03.pdf?dl=0 Problem set 3]&lt;br /&gt;
|-&lt;br /&gt;
 || 28.09 ||  Non-deterministic TMs. Another definition of NP. Proving NP-hardness by reduction from an NP-complete problem. Examples of NP-complete problems.  || [https://www.dropbox.com/s/g817m6v0ygb8h4n/prob_04.pdf?dl=0 Problem set 4]&lt;br /&gt;
|-&lt;br /&gt;
 || 05.10 || Inclusions between P, NP, and PSPACE. Circuit complexity. Examples. All functions are computed by circuits. Existence of functions with exponential circuit complexity. P is in P/poly.|| [https://www.dropbox.com/s/qkc5p4795rualwn/prob_05.pdf?dl=0 Problem set 5]&lt;br /&gt;
|-&lt;br /&gt;
 || 12.10 || Cook–Levin theorem. ||&lt;br /&gt;
|-&lt;br /&gt;
 || 26.10 || Space complexity. ||&lt;br /&gt;
|- &lt;br /&gt;
|| 02.11 || Oracle computation definitions. There exists an oracle &#039;&#039;A&#039;&#039; for which P&amp;lt;sup&amp;gt;&#039;&#039;A&#039;&#039;&amp;lt;/sup&amp;gt; = NP&amp;lt;sup&amp;gt;&#039;&#039;A&#039;&#039;&amp;lt;/sup&amp;gt;. There is an oracle B such that P&amp;lt;sup&amp;gt;&#039;&#039;B&#039;&#039;&amp;lt;/sup&amp;gt; is not equal to NP&amp;lt;sup&amp;gt;&#039;&#039;B&#039;&#039;&amp;lt;/sup&amp;gt;. ||&lt;br /&gt;
|-&lt;br /&gt;
 || 09.11 || Probabilistic computation. Probabilistic machines, the class BPP, invariance of the definition BPP for different thresholds, RP, coRP, PP, ZPP. BPP is in P/poly. || &lt;br /&gt;
|-&lt;br /&gt;
 || 16.11 ||  Streaming algorithms: finding the majority element, computation of the moment &#039;&#039;F&#039;&#039;&amp;lt;sub&amp;gt;2&amp;lt;/sub&amp;gt; in logarithmic space. ||&lt;br /&gt;
|-&lt;br /&gt;
 || 23.11 || Finding the frequent items in streams of data: SpaceSaving and Count-Min Sketch. ||&lt;br /&gt;
|-&lt;br /&gt;
 || 30.11 || Approximation algorithms. Approximate solutions for Vertex Cover, Weighted Vertex Cover, and TSP. ||&lt;br /&gt;
 &lt;br /&gt;
|-&lt;br /&gt;
 || 07.12 || Colloquium. ||&lt;br /&gt;
|-&lt;br /&gt;
 || 14.12 || Complexity of clustering: an exact algorithm for maximising the inter-cluster distance and an approximate algorithm for minimising the intra-class distance.&lt;br /&gt;
 || &lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
For interested students, there are 3 lectures in parameterized complexity. &lt;br /&gt;
&lt;br /&gt;
14 Sept: Fixed parameter tracktability and examples, [https://www.dropbox.com/s/zzzaulpmzql7x7u/parameterizedComplexity.pdf?dl=0 presentation]. &lt;br /&gt;
&lt;br /&gt;
21 Sept: Topics from chapters 1 and 2 in &amp;quot;Parameterized algorithms&amp;quot; by Cygan, Fomin and others, 2016.&lt;br /&gt;
&lt;br /&gt;
28 Sept: The W-hierarchy, chapter 13 in the same book.&lt;br /&gt;
&lt;br /&gt;
= Office hours =&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
|-&lt;br /&gt;
!  Person !! Monday !! Tuesday !! Wednesday !! Thursday !! Friday &lt;br /&gt;
|-&lt;br /&gt;
|  [https://www.hse.ru/en/org/persons/160550073 Bruno Bauwens], S834, [https://us02web.zoom.us/j/82300259484?pwd=NWxXekxBeE5yMm9UTmwvLzNNNGlnUT09 Zoom] ||  || ||  ||  || 14:00-20:00&lt;br /&gt;
|-&lt;br /&gt;
|  [https://www.hse.ru/en/staff/obiedkov Sergei Obiedkov], T915, [https://zoom.us/j/99663354582?pwd=K1B5R3NXWEhWbFozR2lqMkFWYW5Ydz09 Zoom] ||  ||  || 16:30–18:00 || 16:30–18:00 ||  &lt;br /&gt;
|}&lt;/div&gt;</summary>
		<author><name>.obj</name></author>
	</entry>
	<entry>
		<id>https://wiki.cs.hse.ru/index.php?title=Theory_of_Computation_2021&amp;diff=59465</id>
		<title>Theory of Computation 2021</title>
		<link rel="alternate" type="text/html" href="https://wiki.cs.hse.ru/index.php?title=Theory_of_Computation_2021&amp;diff=59465"/>
		<updated>2021-10-05T13:19:34Z</updated>

		<summary type="html">&lt;p&gt;.obj: /* Course Materials */&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;= Classes =&lt;br /&gt;
 &lt;br /&gt;
Tuesdays 14:40–17:40, [https://ruz.hse.ru/ruz/main ruz]&lt;br /&gt;
&lt;br /&gt;
Lectures: 14:40 in room M303, parallel [https://zoom.us/j/92154456703?pwd=aFZ0eWVoZnFVbm03ckNvTDFNS3dIdz09 session]&lt;br /&gt;
&lt;br /&gt;
Seminars: 16:20 in room M203&lt;br /&gt;
&lt;br /&gt;
= Dates and Deadlines =&lt;br /&gt;
Please send your homework by e-mail to both lecturers.&amp;lt;br&amp;gt;&lt;br /&gt;
Homework 1, deadline: October 5, 14:00 &amp;lt;br&amp;gt;&lt;br /&gt;
Homework 2, deadline: November 2, 14:00 &amp;lt;br&amp;gt;&lt;br /&gt;
Homework 3, deadline: December 7, 14:00 &amp;lt;br&amp;gt;&lt;br /&gt;
Colloquium: December 7, 14:40–17:40&lt;br /&gt;
&lt;br /&gt;
= Grading =&lt;br /&gt;
Colloquium: 35%&amp;lt;br&amp;gt;&lt;br /&gt;
Homework: 35%&amp;lt;br&amp;gt;&lt;br /&gt;
Exam: 30%&lt;br /&gt;
&lt;br /&gt;
= Course Materials =&lt;br /&gt;
&lt;br /&gt;
The main reference is Sipser&#039;s book &amp;quot;Introduction to the theory of computation&amp;quot;, chapters 3, 7–10.&lt;br /&gt;
&lt;br /&gt;
If you need some background in math, consider these two sources:&amp;lt;br&amp;gt;&lt;br /&gt;
[http://www.cs.elte.hu/~lovasz/dmbook.ps Lecture notes: Discrete Mathematics], L. Lovasz, K. Vesztergombi&amp;lt;br&amp;gt;&lt;br /&gt;
[http://rubtsov.su/public/DM-HSE-Draft.pdf Лекции по дискретной математике] (черновик учебника, in Russian)&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
|-&lt;br /&gt;
! Date !! Summary !! Problem list&lt;br /&gt;
|-&lt;br /&gt;
 || 07.09 || Turing machines, multitape Turing machines, connection between them. Universal Turing machine. Examples ([https://www.dropbox.com/s/wna14b7y7nmw3cq/tm.py?dl=0 one], [https://www.dropbox.com/s/wrl3mkeqslj3xtu/wsharpw.py?dl=0 two]). Time and space complexity. Complexity classes P, PSPACE, EXP. || [https://www.dropbox.com/s/37eel2qayios6b3/prob_1.pdf?dl=0 Problem set 1]&lt;br /&gt;
|-&lt;br /&gt;
|| 14.09 ||  Time and space hierarchy theorem. Time and space constructible functions. || [https://www.dropbox.com/s/ow4m1z8u8r211qs/prob_2.pdf?dl=0 Problem set 2]&lt;br /&gt;
|-&lt;br /&gt;
 || 21.09 || Complexity class NP. Examples. Polynomial reductions. NP-hardness and NP-completeness. &lt;br /&gt;
 ||  [https://www.dropbox.com/s/bf68zicg4uh051x/prob_03.pdf?dl=0 Problem set 3]&lt;br /&gt;
|-&lt;br /&gt;
 || 28.09 ||  Non-deterministic TMs. Another definition of NP. Proving NP-hardness by reduction from an NP-complete problem. Examples of NP-complete problems.  || [https://www.dropbox.com/s/g817m6v0ygb8h4n/prob_04.pdf?dl=0 Problem set 4]&lt;br /&gt;
|-&lt;br /&gt;
 || 05.10 || Inclusions between P, NP, and PSPACE. Circuit complexity. Examples. All functions are computed by circuits. Existence of functions with exponential circuit complexity. P is in P/poly.|| [https://www.dropbox.com/s/qkc5p4795rualwn/prob_05.pdf?dl=0 Problem set 5]&lt;br /&gt;
|-&lt;br /&gt;
 || 12.10 || Cook–Levin theorem. ||&lt;br /&gt;
|-&lt;br /&gt;
 || 26.10 || Space complexity. ||&lt;br /&gt;
|- &lt;br /&gt;
|| 02.11 || Oracle computation definitions. There exists an oracle &#039;&#039;A&#039;&#039; for which P&amp;lt;sup&amp;gt;&#039;&#039;A&#039;&#039;&amp;lt;/sup&amp;gt; = NP&amp;lt;sup&amp;gt;&#039;&#039;A&#039;&#039;&amp;lt;/sup&amp;gt;. There is an oracle B such that P&amp;lt;sup&amp;gt;&#039;&#039;B&#039;&#039;&amp;lt;/sup&amp;gt; is not equal to NP&amp;lt;sup&amp;gt;&#039;&#039;B&#039;&#039;&amp;lt;/sup&amp;gt;. ||&lt;br /&gt;
|-&lt;br /&gt;
 || 09.11 || Probabilistic computation. Probabilistic machines, the class BPP, invariance of the definition BPP for different thresholds, RP, coRP, PP, ZPP. BPP is in P/poly. || &lt;br /&gt;
|-&lt;br /&gt;
 || 16.11 ||  Streaming algorithms: finding the majority element, computation of the moment &#039;&#039;F&#039;&#039;&amp;lt;sub&amp;gt;2&amp;lt;/sub&amp;gt; in logarithmic space. ||&lt;br /&gt;
|-&lt;br /&gt;
 || 23.11 || Finding the frequent items in streams of data: SpaceSaving and Count-Min Sketch. ||&lt;br /&gt;
|-&lt;br /&gt;
 || 30.11 || Approximation algorithms. Approximate solutions for Vertex Cover, Weighted Vertex Cover, and TSP. ||&lt;br /&gt;
 &lt;br /&gt;
|-&lt;br /&gt;
 || 07.12 || Colloquium. ||&lt;br /&gt;
|-&lt;br /&gt;
 || 14.12 || Complexity of clustering: an exact algorithm for maximising the inter-cluster distance and an approximate algorithm for minimising the intra-class distance.&lt;br /&gt;
 || &lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
For interested students, there are 3 lectures in parameterized complexity. &lt;br /&gt;
&lt;br /&gt;
14 Sept: Fixed parameter tracktability and examples, [https://www.dropbox.com/s/zzzaulpmzql7x7u/parameterizedComplexity.pdf?dl=0 presentation]. &lt;br /&gt;
&lt;br /&gt;
21 Sept: Topics from chapters 1 and 2 in &amp;quot;Parameterized algorithms&amp;quot; by Cygan, Fomin and others, 2016.&lt;br /&gt;
&lt;br /&gt;
28 Sept: The W-hierarchy, chapter 13 in the same book.&lt;br /&gt;
&lt;br /&gt;
= Office hours =&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
|-&lt;br /&gt;
!  Person !! Monday !! Tuesday !! Wednesday !! Thursday !! Friday &lt;br /&gt;
|-&lt;br /&gt;
|  [https://www.hse.ru/en/org/persons/160550073 Bruno Bauwens], S834, [https://us02web.zoom.us/j/82300259484?pwd=NWxXekxBeE5yMm9UTmwvLzNNNGlnUT09 Zoom] ||  || ||  ||  || 14:00-20:00&lt;br /&gt;
|-&lt;br /&gt;
|  [https://www.hse.ru/en/staff/obiedkov Sergei Obiedkov], T915, [https://zoom.us/j/99663354582?pwd=K1B5R3NXWEhWbFozR2lqMkFWYW5Ydz09 Zoom] ||  ||  || 16:30–18:00 || 16:30–18:00 ||  &lt;br /&gt;
|}&lt;/div&gt;</summary>
		<author><name>.obj</name></author>
	</entry>
	<entry>
		<id>https://wiki.cs.hse.ru/index.php?title=Theory_of_Computation_2021&amp;diff=59100</id>
		<title>Theory of Computation 2021</title>
		<link rel="alternate" type="text/html" href="https://wiki.cs.hse.ru/index.php?title=Theory_of_Computation_2021&amp;diff=59100"/>
		<updated>2021-09-28T16:22:25Z</updated>

		<summary type="html">&lt;p&gt;.obj: /* Course Materials */&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;= Classes =&lt;br /&gt;
 &lt;br /&gt;
Tuesdays 14:40–17:40, [https://ruz.hse.ru/ruz/main ruz]&lt;br /&gt;
&lt;br /&gt;
Lectures: 14:40 in room M303, parallel [https://zoom.us/j/92154456703?pwd=aFZ0eWVoZnFVbm03ckNvTDFNS3dIdz09 session]&lt;br /&gt;
&lt;br /&gt;
Seminars: 16:20 in room M203&lt;br /&gt;
&lt;br /&gt;
= Dates and Deadlines =&lt;br /&gt;
Please send your homework by e-mail to both lecturers.&amp;lt;br&amp;gt;&lt;br /&gt;
Homework 1, deadline: October 5, 14:00 &amp;lt;br&amp;gt;&lt;br /&gt;
Homework 2, deadline: November 2, 14:00 &amp;lt;br&amp;gt;&lt;br /&gt;
Homework 3, deadline: December 7, 14:00 &amp;lt;br&amp;gt;&lt;br /&gt;
Colloquium: December 7, 14:40–17:40&lt;br /&gt;
&lt;br /&gt;
= Grading =&lt;br /&gt;
Colloquium: 35%&amp;lt;br&amp;gt;&lt;br /&gt;
Homework: 35%&amp;lt;br&amp;gt;&lt;br /&gt;
Exam: 30%&lt;br /&gt;
&lt;br /&gt;
= Course Materials =&lt;br /&gt;
&lt;br /&gt;
The main reference is Sipser&#039;s book &amp;quot;Introduction to the theory of computation&amp;quot;, chapters 3, 7–10.&lt;br /&gt;
&lt;br /&gt;
If you need some background in math, consider these two sources:&amp;lt;br&amp;gt;&lt;br /&gt;
[http://www.cs.elte.hu/~lovasz/dmbook.ps Lecture notes: Discrete Mathematics], L. Lovasz, K. Vesztergombi&amp;lt;br&amp;gt;&lt;br /&gt;
[http://rubtsov.su/public/DM-HSE-Draft.pdf Лекции по дискретной математике] (черновик учебника, in Russian)&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
|-&lt;br /&gt;
! Date !! Summary !! Problem list&lt;br /&gt;
|-&lt;br /&gt;
 || 07.09 || Turing machines, multitape Turing machines, connection between them. Universal Turing machine. Examples ([https://www.dropbox.com/s/wna14b7y7nmw3cq/tm.py?dl=0 one], [https://www.dropbox.com/s/wrl3mkeqslj3xtu/wsharpw.py?dl=0 two]). Time and space complexity. Complexity classes P, PSPACE, EXP. || [https://www.dropbox.com/s/37eel2qayios6b3/prob_1.pdf?dl=0 Problem set 1]&lt;br /&gt;
|-&lt;br /&gt;
|| 14.09 ||  Time and space hierarchy theorem. Time and space constructible functions. || [https://www.dropbox.com/s/ow4m1z8u8r211qs/prob_2.pdf?dl=0 Problem set 2]&lt;br /&gt;
|-&lt;br /&gt;
 || 21.09 || Complexity class NP. Examples. Polynomial reductions. NP-hardness and NP-completeness. &lt;br /&gt;
 ||  [https://www.dropbox.com/s/bf68zicg4uh051x/prob_03.pdf?dl=0 Problem set 3]&lt;br /&gt;
|-&lt;br /&gt;
 || 28.09 ||  Non-deterministic TMs. Another definition of NP. Proving NP-hardness by reduction from an NP-complete problem. Examples of NP-complete problems.  || [https://www.dropbox.com/s/g817m6v0ygb8h4n/prob_04.pdf?dl=0 Problem set 4]&lt;br /&gt;
|-&lt;br /&gt;
 || 05.10 || Inclusions between P, NP, and PSPACE. Circuit complexity. Examples. All functions are computed by circuits. Existence of functions with exponential circuit complexity. P is in P/poly.|| &lt;br /&gt;
|-&lt;br /&gt;
 || 12.10 || Cook–Levin theorem. ||&lt;br /&gt;
|-&lt;br /&gt;
 || 26.10 || Space complexity. ||&lt;br /&gt;
|- &lt;br /&gt;
|| 02.11 || Oracle computation definitions. There exists an oracle &#039;&#039;A&#039;&#039; for which P&amp;lt;sup&amp;gt;&#039;&#039;A&#039;&#039;&amp;lt;/sup&amp;gt; = NP&amp;lt;sup&amp;gt;&#039;&#039;A&#039;&#039;&amp;lt;/sup&amp;gt;. There is an oracle B such that P&amp;lt;sup&amp;gt;&#039;&#039;B&#039;&#039;&amp;lt;/sup&amp;gt; is not equal to NP&amp;lt;sup&amp;gt;&#039;&#039;B&#039;&#039;&amp;lt;/sup&amp;gt;. ||&lt;br /&gt;
|-&lt;br /&gt;
 || 09.11 || Probabilistic computation. Probabilistic machines, the class BPP, invariance of the definition BPP for different thresholds, RP, coRP, PP, ZPP. BPP is in P/poly. || &lt;br /&gt;
|-&lt;br /&gt;
 || 16.11 ||  Streaming algorithms: finding the majority element, computation of the moment &#039;&#039;F&#039;&#039;&amp;lt;sub&amp;gt;2&amp;lt;/sub&amp;gt; in logarithmic space. ||&lt;br /&gt;
|-&lt;br /&gt;
 || 23.11 || Finding the frequent items in streams of data: SpaceSaving and Count-Min Sketch. ||&lt;br /&gt;
|-&lt;br /&gt;
 || 30.11 || Approximation algorithms. Approximate solutions for Vertex Cover, Weighted Vertex Cover, and TSP. ||&lt;br /&gt;
 &lt;br /&gt;
|-&lt;br /&gt;
 || 07.12 || Colloquium. ||&lt;br /&gt;
|-&lt;br /&gt;
 || 14.12 || Complexity of clustering: an exact algorithm for maximising the inter-cluster distance and an approximate algorithm for minimising the intra-class distance.&lt;br /&gt;
 || &lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
For interested students, there are 3 lectures in parameterized complexity. &lt;br /&gt;
&lt;br /&gt;
14 Sept: Fixed parameter tracktability and examples, [https://www.dropbox.com/s/zzzaulpmzql7x7u/parameterizedComplexity.pdf?dl=0 presentation]. &lt;br /&gt;
&lt;br /&gt;
21 Sept: Topics from chapters 1 and 2 in &amp;quot;Parameterized algorithms&amp;quot; by Cygan, Fomin and others, 2016.&lt;br /&gt;
&lt;br /&gt;
28 Sept: The W-hierarchy, chapter 13 in the same book.&lt;br /&gt;
&lt;br /&gt;
= Office hours =&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
|-&lt;br /&gt;
!  Person !! Monday !! Tuesday !! Wednesday !! Thursday !! Friday &lt;br /&gt;
|-&lt;br /&gt;
|  [https://www.hse.ru/en/org/persons/160550073 Bruno Bauwens], S834, [https://us02web.zoom.us/j/82300259484?pwd=NWxXekxBeE5yMm9UTmwvLzNNNGlnUT09 Zoom] ||  || ||  ||  || 14:00-20:00&lt;br /&gt;
|-&lt;br /&gt;
|  [https://www.hse.ru/en/staff/obiedkov Sergei Obiedkov], T915, [https://zoom.us/j/99663354582?pwd=K1B5R3NXWEhWbFozR2lqMkFWYW5Ydz09 Zoom] ||  ||  || 16:30–18:00 || 16:30–18:00 ||  &lt;br /&gt;
|}&lt;/div&gt;</summary>
		<author><name>.obj</name></author>
	</entry>
	<entry>
		<id>https://wiki.cs.hse.ru/index.php?title=Theory_of_Computation_2021&amp;diff=59063</id>
		<title>Theory of Computation 2021</title>
		<link rel="alternate" type="text/html" href="https://wiki.cs.hse.ru/index.php?title=Theory_of_Computation_2021&amp;diff=59063"/>
		<updated>2021-09-28T10:29:36Z</updated>

		<summary type="html">&lt;p&gt;.obj: /* Classes */&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;= Classes =&lt;br /&gt;
 &lt;br /&gt;
Tuesdays 14:40–17:40, [https://ruz.hse.ru/ruz/main ruz]&lt;br /&gt;
&lt;br /&gt;
Lectures: 14:40 in room M303, parallel [https://zoom.us/j/92154456703?pwd=aFZ0eWVoZnFVbm03ckNvTDFNS3dIdz09 session]&lt;br /&gt;
&lt;br /&gt;
Seminars: 16:20 in room M203&lt;br /&gt;
&lt;br /&gt;
= Dates and Deadlines =&lt;br /&gt;
Please send your homework by e-mail to both lecturers.&amp;lt;br&amp;gt;&lt;br /&gt;
Homework 1, deadline: October 5, 14:00 &amp;lt;br&amp;gt;&lt;br /&gt;
Homework 2, deadline: November 2, 14:00 &amp;lt;br&amp;gt;&lt;br /&gt;
Homework 3, deadline: December 7, 14:00 &amp;lt;br&amp;gt;&lt;br /&gt;
Colloquium: December 7, 14:40–17:40&lt;br /&gt;
&lt;br /&gt;
= Grading =&lt;br /&gt;
Colloquium: 35%&amp;lt;br&amp;gt;&lt;br /&gt;
Homework: 35%&amp;lt;br&amp;gt;&lt;br /&gt;
Exam: 30%&lt;br /&gt;
&lt;br /&gt;
= Course Materials =&lt;br /&gt;
&lt;br /&gt;
The main reference is Sipser&#039;s book &amp;quot;Introduction to the theory of computation&amp;quot;, chapters 3, 7–10.&lt;br /&gt;
&lt;br /&gt;
If you need some background in math, consider these two sources:&amp;lt;br&amp;gt;&lt;br /&gt;
[http://www.cs.elte.hu/~lovasz/dmbook.ps Lecture notes: Discrete Mathematics], L. Lovasz, K. Vesztergombi&amp;lt;br&amp;gt;&lt;br /&gt;
[http://rubtsov.su/public/DM-HSE-Draft.pdf Лекции по дискретной математике] (черновик учебника, in Russian)&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
|-&lt;br /&gt;
! Date !! Summary !! Problem list&lt;br /&gt;
|-&lt;br /&gt;
 || 07.09 || Turing machines, multitape Turing machines, connection between them. Universal Turing machine. Examples ([https://www.dropbox.com/s/wna14b7y7nmw3cq/tm.py?dl=0 one], [https://www.dropbox.com/s/wrl3mkeqslj3xtu/wsharpw.py?dl=0 two]). Time and space complexity. Complexity classes P, PSPACE, EXP. || [https://www.dropbox.com/s/37eel2qayios6b3/prob_1.pdf?dl=0 Problem set 1]&lt;br /&gt;
|-&lt;br /&gt;
|| 14.09 ||  Time and space hierarchy theorem. Time and space constructible functions. || [https://www.dropbox.com/s/ow4m1z8u8r211qs/prob_2.pdf?dl=0 Problem set 2]&lt;br /&gt;
|-&lt;br /&gt;
 || 21.09 || Complexity class NP. Examples. Polynomial reductions. NP-hardness and NP-completeness. &lt;br /&gt;
 ||  [https://www.dropbox.com/s/bf68zicg4uh051x/prob_03.pdf?dl=0 Problem set 3]&lt;br /&gt;
|-&lt;br /&gt;
 || 28.09 ||  Inclusions between P, NP, and PSPACE. Non-deterministic TMs. Another definition of NP. Proving NP-hardness by reduction from an NP-complete problem. Examples of NP-complete problems.  ||&lt;br /&gt;
|-&lt;br /&gt;
 || 05.10 || Circuit complexity. Examples. All functions are computed by circuits. Existence of functions with exponential circuit complexity. P is in P/poly.|| &lt;br /&gt;
|-&lt;br /&gt;
 || 12.10 || Cook–Levin theorem. ||&lt;br /&gt;
|-&lt;br /&gt;
 || 26.10 || Space complexity. ||&lt;br /&gt;
|- &lt;br /&gt;
|| 02.11 || Oracle computation definitions. There exists an oracle &#039;&#039;A&#039;&#039; for which P&amp;lt;sup&amp;gt;&#039;&#039;A&#039;&#039;&amp;lt;/sup&amp;gt; = NP&amp;lt;sup&amp;gt;&#039;&#039;A&#039;&#039;&amp;lt;/sup&amp;gt;. There is an oracle B such that P&amp;lt;sup&amp;gt;&#039;&#039;B&#039;&#039;&amp;lt;/sup&amp;gt; is not equal to NP&amp;lt;sup&amp;gt;&#039;&#039;B&#039;&#039;&amp;lt;/sup&amp;gt;. ||&lt;br /&gt;
|-&lt;br /&gt;
 || 09.11 || Probabilistic computation. Probabilistic machines, the class BPP, invariance of the definition BPP for different thresholds, RP, coRP, PP, ZPP. BPP is in P/poly. || &lt;br /&gt;
|-&lt;br /&gt;
 || 16.11 ||  Streaming algorithms: finding the majority element, computation of the moment &#039;&#039;F&#039;&#039;&amp;lt;sub&amp;gt;2&amp;lt;/sub&amp;gt; in logarithmic space. ||&lt;br /&gt;
|-&lt;br /&gt;
 || 23.11 || Finding the frequent items in streams of data: SpaceSaving and Count-Min Sketch. ||&lt;br /&gt;
|-&lt;br /&gt;
 || 30.11 || Approximation algorithms. Approximate solutions for Vertex Cover, Weighted Vertex Cover, and TSP. ||&lt;br /&gt;
 &lt;br /&gt;
|-&lt;br /&gt;
 || 07.12 || Colloquium. ||&lt;br /&gt;
|-&lt;br /&gt;
 || 14.12 || Complexity of clustering: an exact algorithm for maximising the inter-cluster distance and an approximate algorithm for minimising the intra-class distance.&lt;br /&gt;
 || &lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
For interested students, there are 3 lectures in parameterized complexity. &lt;br /&gt;
&lt;br /&gt;
14 Sept: Fixed parameter tracktability and examples, [https://www.dropbox.com/s/zzzaulpmzql7x7u/parameterizedComplexity.pdf?dl=0 presentation]. &lt;br /&gt;
&lt;br /&gt;
21 Sept: Topics from chapters 1 and 2 in &amp;quot;Parameterized algorithms&amp;quot; by Cygan, Fomin and others, 2016.&lt;br /&gt;
&lt;br /&gt;
28 Sept: The W-hierarchy, chapter 13 in the same book.&lt;br /&gt;
&lt;br /&gt;
= Office hours =&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
|-&lt;br /&gt;
!  Person !! Monday !! Tuesday !! Wednesday !! Thursday !! Friday &lt;br /&gt;
|-&lt;br /&gt;
|  [https://www.hse.ru/en/org/persons/160550073 Bruno Bauwens], S834, [https://us02web.zoom.us/j/82300259484?pwd=NWxXekxBeE5yMm9UTmwvLzNNNGlnUT09 Zoom] ||  || ||  ||  || 14:00-20:00&lt;br /&gt;
|-&lt;br /&gt;
|  [https://www.hse.ru/en/staff/obiedkov Sergei Obiedkov], T915, [https://zoom.us/j/99663354582?pwd=K1B5R3NXWEhWbFozR2lqMkFWYW5Ydz09 Zoom] ||  ||  || 16:30–18:00 || 16:30–18:00 ||  &lt;br /&gt;
|}&lt;/div&gt;</summary>
		<author><name>.obj</name></author>
	</entry>
	<entry>
		<id>https://wiki.cs.hse.ru/index.php?title=Theory_of_Computation_2021&amp;diff=58682</id>
		<title>Theory of Computation 2021</title>
		<link rel="alternate" type="text/html" href="https://wiki.cs.hse.ru/index.php?title=Theory_of_Computation_2021&amp;diff=58682"/>
		<updated>2021-09-21T15:54:53Z</updated>

		<summary type="html">&lt;p&gt;.obj: /* Course Materials */&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;= Classes =&lt;br /&gt;
 &lt;br /&gt;
Tuesdays 14:40–17:40, [https://ruz.hse.ru/ruz/main ruz]&lt;br /&gt;
&lt;br /&gt;
Lectures: 14:40 in room M303, also streamed [https://us02web.zoom.us/j/83533615475?pwd=WDU3cHJ5RjREOGd2YU1qdDJCVm1idz09 here] parallel [https://zoom.us/j/92154456703?pwd=aFZ0eWVoZnFVbm03ckNvTDFNS3dIdz09 session]&lt;br /&gt;
&lt;br /&gt;
Seminars: 16:20 in room M203, also streamed [https://us02web.zoom.us/j/84546220686?pwd=U2dISk5UaFZpdmh3WTdFT3phRVNXZz09 here]&lt;br /&gt;
&lt;br /&gt;
= Dates and Deadlines =&lt;br /&gt;
Please send your homework by e-mail to both lecturers.&amp;lt;br&amp;gt;&lt;br /&gt;
Homework 1, deadline: October 5, 14:00 &amp;lt;br&amp;gt;&lt;br /&gt;
Homework 2, deadline: November 2, 14:00 &amp;lt;br&amp;gt;&lt;br /&gt;
Homework 3, deadline: December 7, 14:00 &amp;lt;br&amp;gt;&lt;br /&gt;
Colloquium: December 7, 14:40–17:40&lt;br /&gt;
&lt;br /&gt;
= Grading =&lt;br /&gt;
Colloquium: 35%&amp;lt;br&amp;gt;&lt;br /&gt;
Homework: 35%&amp;lt;br&amp;gt;&lt;br /&gt;
Exam: 30%&lt;br /&gt;
&lt;br /&gt;
= Course Materials =&lt;br /&gt;
&lt;br /&gt;
The main reference is Sipser&#039;s book &amp;quot;Introduction to the theory of computation&amp;quot;, chapters 3, 7–10.&lt;br /&gt;
&lt;br /&gt;
If you need some background in math, consider these two sources:&amp;lt;br&amp;gt;&lt;br /&gt;
[http://www.cs.elte.hu/~lovasz/dmbook.ps Lecture notes: Discrete Mathematics], L. Lovasz, K. Vesztergombi&amp;lt;br&amp;gt;&lt;br /&gt;
[http://rubtsov.su/public/DM-HSE-Draft.pdf Лекции по дискретной математике] (черновик учебника, in Russian)&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
|-&lt;br /&gt;
! Date !! Summary !! Problem list&lt;br /&gt;
|-&lt;br /&gt;
 || 07.09 || Turing machines, multitape Turing machines, connection between them. Universal Turing machine. Examples ([https://www.dropbox.com/s/wna14b7y7nmw3cq/tm.py?dl=0 one], [https://www.dropbox.com/s/wrl3mkeqslj3xtu/wsharpw.py?dl=0 two]). Time and space complexity. Complexity classes P, PSPACE, EXP. || [https://www.dropbox.com/s/37eel2qayios6b3/prob_1.pdf?dl=0 Problem set 1]&lt;br /&gt;
|-&lt;br /&gt;
|| 14.09 ||  Time and space hierarchy theorem. Time and space constructible functions. || [https://www.dropbox.com/s/ow4m1z8u8r211qs/prob_2.pdf?dl=0 Problem set 2]&lt;br /&gt;
|-&lt;br /&gt;
 || 21.09 || Complexity class NP. Examples. Polynomial reductions. NP-hardness and NP-completeness. &lt;br /&gt;
 ||  [https://www.dropbox.com/s/bf68zicg4uh051x/prob_03.pdf?dl=0 Problem set 3]&lt;br /&gt;
|-&lt;br /&gt;
 || 28.09 ||  Inclusions between P, NP, and PSPACE. Non-deterministic TMs. Another definition of NP. Proving NP-hardness by reduction from an NP-complete problem. Examples of NP-complete problems.  ||&lt;br /&gt;
|-&lt;br /&gt;
 || 05.10 || Circuit complexity. Examples. All functions are computed by circuits. Existence of functions with exponential circuit complexity. P is in P/poly.|| &lt;br /&gt;
|-&lt;br /&gt;
 || 12.10 || Cook–Levin theorem. ||&lt;br /&gt;
|-&lt;br /&gt;
 || 26.10 || Space complexity. ||&lt;br /&gt;
|- &lt;br /&gt;
|| 02.11 || Oracle computation definitions. There exists an oracle &#039;&#039;A&#039;&#039; for which P&amp;lt;sup&amp;gt;&#039;&#039;A&#039;&#039;&amp;lt;/sup&amp;gt; = NP&amp;lt;sup&amp;gt;&#039;&#039;A&#039;&#039;&amp;lt;/sup&amp;gt;. There is an oracle B such that P&amp;lt;sup&amp;gt;&#039;&#039;B&#039;&#039;&amp;lt;/sup&amp;gt; is not equal to NP&amp;lt;sup&amp;gt;&#039;&#039;B&#039;&#039;&amp;lt;/sup&amp;gt;. ||&lt;br /&gt;
|-&lt;br /&gt;
 || 09.11 || Probabilistic computation. Probabilistic machines, the class BPP, invariance of the definition BPP for different thresholds, RP, coRP, PP, ZPP. BPP is in P/poly. || &lt;br /&gt;
|-&lt;br /&gt;
 || 16.11 ||  Streaming algorithms: finding the majority element, computation of the moment &#039;&#039;F&#039;&#039;&amp;lt;sub&amp;gt;2&amp;lt;/sub&amp;gt; in logarithmic space. ||&lt;br /&gt;
|-&lt;br /&gt;
 || 23.11 || Finding the frequent items in streams of data: SpaceSaving and Count-Min Sketch. ||&lt;br /&gt;
|-&lt;br /&gt;
 || 30.11 || Approximation algorithms. Approximate solutions for Vertex Cover, Weighted Vertex Cover, and TSP. ||&lt;br /&gt;
 &lt;br /&gt;
|-&lt;br /&gt;
 || 07.12 || Colloquium. ||&lt;br /&gt;
|-&lt;br /&gt;
 || 14.12 || Complexity of clustering: an exact algorithm for maximising the inter-cluster distance and an approximate algorithm for minimising the intra-class distance.&lt;br /&gt;
 || &lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
For interested students, there are 3 lectures in parameterized complexity. &lt;br /&gt;
&lt;br /&gt;
14 Sept: Fixed parameter tracktability and examples, [https://www.dropbox.com/s/zzzaulpmzql7x7u/parameterizedComplexity.pdf?dl=0 presentation]. &lt;br /&gt;
&lt;br /&gt;
21 Sept: Topics from chapters 1 and 2 in &amp;quot;Parameterized algorithms&amp;quot; by Cygan, Fomin and others, 2016.&lt;br /&gt;
&lt;br /&gt;
28 Sept: The W-hierarchy, chapter 13 in the same book.&lt;br /&gt;
&lt;br /&gt;
= Office hours =&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
|-&lt;br /&gt;
!  Person !! Monday !! Tuesday !! Wednesday !! Thursday !! Friday &lt;br /&gt;
|-&lt;br /&gt;
|  [https://www.hse.ru/en/org/persons/160550073 Bruno Bauwens], S834, [https://us02web.zoom.us/j/82300259484?pwd=NWxXekxBeE5yMm9UTmwvLzNNNGlnUT09 Zoom] ||  || ||  ||  || 14:00-20:00&lt;br /&gt;
|-&lt;br /&gt;
|  [https://www.hse.ru/en/staff/obiedkov Sergei Obiedkov], T915, [https://zoom.us/j/99663354582?pwd=K1B5R3NXWEhWbFozR2lqMkFWYW5Ydz09 Zoom] ||  ||  || 16:30–18:00 || 16:30–18:00 ||  &lt;br /&gt;
|}&lt;/div&gt;</summary>
		<author><name>.obj</name></author>
	</entry>
	<entry>
		<id>https://wiki.cs.hse.ru/index.php?title=Theory_of_Computation_2021&amp;diff=58681</id>
		<title>Theory of Computation 2021</title>
		<link rel="alternate" type="text/html" href="https://wiki.cs.hse.ru/index.php?title=Theory_of_Computation_2021&amp;diff=58681"/>
		<updated>2021-09-21T15:54:33Z</updated>

		<summary type="html">&lt;p&gt;.obj: /* Course Materials */&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;= Classes =&lt;br /&gt;
 &lt;br /&gt;
Tuesdays 14:40–17:40, [https://ruz.hse.ru/ruz/main ruz]&lt;br /&gt;
&lt;br /&gt;
Lectures: 14:40 in room M303, also streamed [https://us02web.zoom.us/j/83533615475?pwd=WDU3cHJ5RjREOGd2YU1qdDJCVm1idz09 here] parallel [https://zoom.us/j/92154456703?pwd=aFZ0eWVoZnFVbm03ckNvTDFNS3dIdz09 session]&lt;br /&gt;
&lt;br /&gt;
Seminars: 16:20 in room M203, also streamed [https://us02web.zoom.us/j/84546220686?pwd=U2dISk5UaFZpdmh3WTdFT3phRVNXZz09 here]&lt;br /&gt;
&lt;br /&gt;
= Dates and Deadlines =&lt;br /&gt;
Please send your homework by e-mail to both lecturers.&amp;lt;br&amp;gt;&lt;br /&gt;
Homework 1, deadline: October 5, 14:00 &amp;lt;br&amp;gt;&lt;br /&gt;
Homework 2, deadline: November 2, 14:00 &amp;lt;br&amp;gt;&lt;br /&gt;
Homework 3, deadline: December 7, 14:00 &amp;lt;br&amp;gt;&lt;br /&gt;
Colloquium: December 7, 14:40–17:40&lt;br /&gt;
&lt;br /&gt;
= Grading =&lt;br /&gt;
Colloquium: 35%&amp;lt;br&amp;gt;&lt;br /&gt;
Homework: 35%&amp;lt;br&amp;gt;&lt;br /&gt;
Exam: 30%&lt;br /&gt;
&lt;br /&gt;
= Course Materials =&lt;br /&gt;
&lt;br /&gt;
The main reference is Sipser&#039;s book &amp;quot;Introduction to the theory of computation&amp;quot;, chapters 3, 7–10.&lt;br /&gt;
&lt;br /&gt;
If you need some background in math, consider these two sources:&amp;lt;br&amp;gt;&lt;br /&gt;
[http://www.cs.elte.hu/~lovasz/dmbook.ps Lecture notes: Discrete Mathematics], L. Lovasz, K. Vesztergombi&amp;lt;br&amp;gt;&lt;br /&gt;
[http://rubtsov.su/public/DM-HSE-Draft.pdf Лекции по дискретной математике] (черновик учебника, in Russian)&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
|-&lt;br /&gt;
! Date !! Summary !! Problem list&lt;br /&gt;
|-&lt;br /&gt;
 || 07.09 || Turing machines, multitape Turing machines, connection between them. Universal Turing machine. Examples ([https://www.dropbox.com/s/wna14b7y7nmw3cq/tm.py?dl=0 one], [https://www.dropbox.com/s/wrl3mkeqslj3xtu/wsharpw.py?dl=0 two]). Time and space complexity. Complexity classes P, PSPACE, EXP. || [https://www.dropbox.com/s/37eel2qayios6b3/prob_1.pdf?dl=0 Problem set 1]&lt;br /&gt;
|-&lt;br /&gt;
|| 14.09 ||  Time and space hierarchy theorem. Time and space constructible functions. || [https://www.dropbox.com/s/ow4m1z8u8r211qs/prob_2.pdf?dl=0 Problem set 2]&lt;br /&gt;
|-&lt;br /&gt;
 || 21.09 || Complexity class NP. Examples. Polynomial reductions. NP-hardness and NP-completeness. &lt;br /&gt;
 ||  [https://www.dropbox.com/s/bf68zicg4uh051x/prob_03.pdf?dl=0 Problem set 3]&lt;br /&gt;
|-&lt;br /&gt;
 || 28.09 ||  Inclusions between P, NP and PSPACE. Non-deterministic TMs. Another definition of NP. Proving NP-hardness by reduction from an NP-complete problem. Examples of NP-complete problems.  ||&lt;br /&gt;
|-&lt;br /&gt;
 || 05.10 || Circuit complexity. Examples. All functions are computed by circuits. Existence of functions with exponential circuit complexity. P is in P/poly.|| &lt;br /&gt;
|-&lt;br /&gt;
 || 12.10 || Cook–Levin theorem. ||&lt;br /&gt;
|-&lt;br /&gt;
 || 26.10 || Space complexity. ||&lt;br /&gt;
|- &lt;br /&gt;
|| 02.11 || Oracle computation definitions. There exists an oracle &#039;&#039;A&#039;&#039; for which P&amp;lt;sup&amp;gt;&#039;&#039;A&#039;&#039;&amp;lt;/sup&amp;gt; = NP&amp;lt;sup&amp;gt;&#039;&#039;A&#039;&#039;&amp;lt;/sup&amp;gt;. There is an oracle B such that P&amp;lt;sup&amp;gt;&#039;&#039;B&#039;&#039;&amp;lt;/sup&amp;gt; is not equal to NP&amp;lt;sup&amp;gt;&#039;&#039;B&#039;&#039;&amp;lt;/sup&amp;gt;. ||&lt;br /&gt;
|-&lt;br /&gt;
 || 09.11 || Probabilistic computation. Probabilistic machines, the class BPP, invariance of the definition BPP for different thresholds, RP, coRP, PP, ZPP. BPP is in P/poly. || &lt;br /&gt;
|-&lt;br /&gt;
 || 16.11 ||  Streaming algorithms: finding the majority element, computation of the moment &#039;&#039;F&#039;&#039;&amp;lt;sub&amp;gt;2&amp;lt;/sub&amp;gt; in logarithmic space. ||&lt;br /&gt;
|-&lt;br /&gt;
 || 23.11 || Finding the frequent items in streams of data: SpaceSaving and Count-Min Sketch. ||&lt;br /&gt;
|-&lt;br /&gt;
 || 30.11 || Approximation algorithms. Approximate solutions for Vertex Cover, Weighted Vertex Cover, and TSP. ||&lt;br /&gt;
 &lt;br /&gt;
|-&lt;br /&gt;
 || 07.12 || Colloquium. ||&lt;br /&gt;
|-&lt;br /&gt;
 || 14.12 || Complexity of clustering: an exact algorithm for maximising the inter-cluster distance and an approximate algorithm for minimising the intra-class distance.&lt;br /&gt;
 || &lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
For interested students, there are 3 lectures in parameterized complexity. &lt;br /&gt;
&lt;br /&gt;
14 Sept: Fixed parameter tracktability and examples, [https://www.dropbox.com/s/zzzaulpmzql7x7u/parameterizedComplexity.pdf?dl=0 presentation]. &lt;br /&gt;
&lt;br /&gt;
21 Sept: Topics from chapters 1 and 2 in &amp;quot;Parameterized algorithms&amp;quot; by Cygan, Fomin and others, 2016.&lt;br /&gt;
&lt;br /&gt;
28 Sept: The W-hierarchy, chapter 13 in the same book.&lt;br /&gt;
&lt;br /&gt;
= Office hours =&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
|-&lt;br /&gt;
!  Person !! Monday !! Tuesday !! Wednesday !! Thursday !! Friday &lt;br /&gt;
|-&lt;br /&gt;
|  [https://www.hse.ru/en/org/persons/160550073 Bruno Bauwens], S834, [https://us02web.zoom.us/j/82300259484?pwd=NWxXekxBeE5yMm9UTmwvLzNNNGlnUT09 Zoom] ||  || ||  ||  || 14:00-20:00&lt;br /&gt;
|-&lt;br /&gt;
|  [https://www.hse.ru/en/staff/obiedkov Sergei Obiedkov], T915, [https://zoom.us/j/99663354582?pwd=K1B5R3NXWEhWbFozR2lqMkFWYW5Ydz09 Zoom] ||  ||  || 16:30–18:00 || 16:30–18:00 ||  &lt;br /&gt;
|}&lt;/div&gt;</summary>
		<author><name>.obj</name></author>
	</entry>
	<entry>
		<id>https://wiki.cs.hse.ru/index.php?title=Theory_of_Computation_2021&amp;diff=58674</id>
		<title>Theory of Computation 2021</title>
		<link rel="alternate" type="text/html" href="https://wiki.cs.hse.ru/index.php?title=Theory_of_Computation_2021&amp;diff=58674"/>
		<updated>2021-09-21T13:16:28Z</updated>

		<summary type="html">&lt;p&gt;.obj: /* Course Materials */&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;= Classes =&lt;br /&gt;
 &lt;br /&gt;
Tuesdays 14:40–17:40, [https://ruz.hse.ru/ruz/main ruz]&lt;br /&gt;
&lt;br /&gt;
Lectures: 14:40 in room M303, also streamed [https://us02web.zoom.us/j/83533615475?pwd=WDU3cHJ5RjREOGd2YU1qdDJCVm1idz09 here] parallel [https://zoom.us/j/92154456703?pwd=aFZ0eWVoZnFVbm03ckNvTDFNS3dIdz09 session]&lt;br /&gt;
&lt;br /&gt;
Seminars: 16:20 in room M203, also streamed [https://us02web.zoom.us/j/84546220686?pwd=U2dISk5UaFZpdmh3WTdFT3phRVNXZz09 here]&lt;br /&gt;
&lt;br /&gt;
= Dates and Deadlines =&lt;br /&gt;
Please send your homework by e-mail to both lecturers.&amp;lt;br&amp;gt;&lt;br /&gt;
Homework 1, deadline: October 5, 14:00 &amp;lt;br&amp;gt;&lt;br /&gt;
Homework 2, deadline: November 2, 14:00 &amp;lt;br&amp;gt;&lt;br /&gt;
Homework 3, deadline: December 7, 14:00 &amp;lt;br&amp;gt;&lt;br /&gt;
Colloquium: December 7, 14:40–17:40&lt;br /&gt;
&lt;br /&gt;
= Grading =&lt;br /&gt;
Colloquium: 35%&amp;lt;br&amp;gt;&lt;br /&gt;
Homework: 35%&amp;lt;br&amp;gt;&lt;br /&gt;
Exam: 30%&lt;br /&gt;
&lt;br /&gt;
= Course Materials =&lt;br /&gt;
&lt;br /&gt;
The main reference is Sipser&#039;s book &amp;quot;Introduction to the theory of computation&amp;quot;, chapters 3, 7–10.&lt;br /&gt;
&lt;br /&gt;
If you need some background in math, consider these two sources:&amp;lt;br&amp;gt;&lt;br /&gt;
[http://www.cs.elte.hu/~lovasz/dmbook.ps Lecture notes: Discrete Mathematics], L. Lovasz, K. Vesztergombi&amp;lt;br&amp;gt;&lt;br /&gt;
[http://rubtsov.su/public/DM-HSE-Draft.pdf Лекции по дискретной математике] (черновик учебника, in Russian)&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
|-&lt;br /&gt;
! Date !! Summary !! Problem list&lt;br /&gt;
|-&lt;br /&gt;
 || 07.09 || Turing machines, multitape Turing machines, connection between them. Universal Turing machine. Examples ([https://www.dropbox.com/s/wna14b7y7nmw3cq/tm.py?dl=0 one], [https://www.dropbox.com/s/wrl3mkeqslj3xtu/wsharpw.py?dl=0 two]). Time and space complexity. Complexity classes P, PSPACE, EXP. || [https://www.dropbox.com/s/37eel2qayios6b3/prob_1.pdf?dl=0 Problem set 1]&lt;br /&gt;
|-&lt;br /&gt;
|| 14.09 ||  Time and space hierarchy theorem. Time and space constructible functions. || [https://www.dropbox.com/s/ow4m1z8u8r211qs/prob_2.pdf?dl=0 Problem set 2]&lt;br /&gt;
|-&lt;br /&gt;
 || 21.09 || Complexity class NP. Examples. Inclusions between P, NP and PSPACE. Non-deterministic TMs. Another definition of NP. Polynomial reductions, their properties. NP-hardness and NP-completeness, their properties. &lt;br /&gt;
 ||  [https://www.dropbox.com/s/bf68zicg4uh051x/prob_03.pdf?dl=0 Problem set 3]&lt;br /&gt;
|-&lt;br /&gt;
 || 28.09 ||  Proving NP-hardness by reduction from an NP-complete problem. Examples of NP-complete problems.  ||&lt;br /&gt;
|-&lt;br /&gt;
 || 05.10 || Circuit complexity. Examples. All functions are computed by circuits. Existence of functions with exponential circuit complexity. P is in P/poly.|| &lt;br /&gt;
|-&lt;br /&gt;
 || 12.10 || Cook–Levin theorem. ||&lt;br /&gt;
|-&lt;br /&gt;
 || 26.10 || Space complexity. ||&lt;br /&gt;
|- &lt;br /&gt;
|| 02.11 || Oracle computation definitions. There exists an oracle &#039;&#039;A&#039;&#039; for which P&amp;lt;sup&amp;gt;&#039;&#039;A&#039;&#039;&amp;lt;/sup&amp;gt; = NP&amp;lt;sup&amp;gt;&#039;&#039;A&#039;&#039;&amp;lt;/sup&amp;gt;. There is an oracle B such that P&amp;lt;sup&amp;gt;&#039;&#039;B&#039;&#039;&amp;lt;/sup&amp;gt; is not equal to NP&amp;lt;sup&amp;gt;&#039;&#039;B&#039;&#039;&amp;lt;/sup&amp;gt;. ||&lt;br /&gt;
|-&lt;br /&gt;
 || 09.11 || Probabilistic computation. Probabilistic machines, the class BPP, invariance of the definition BPP for different thresholds, RP, coRP, PP, ZPP. BPP is in P/poly. || &lt;br /&gt;
|-&lt;br /&gt;
 || 16.11 ||  Streaming algorithms: finding the majority element, computation of the moment &#039;&#039;F&#039;&#039;&amp;lt;sub&amp;gt;2&amp;lt;/sub&amp;gt; in logarithmic space. ||&lt;br /&gt;
|-&lt;br /&gt;
 || 23.11 || Finding the frequent items in streams of data: SpaceSaving and Count-Min Sketch. ||&lt;br /&gt;
|-&lt;br /&gt;
 || 30.11 || Approximation algorithms. Approximate solutions for Vertex Cover, Weighted Vertex Cover, and TSP. ||&lt;br /&gt;
 &lt;br /&gt;
|-&lt;br /&gt;
 || 07.12 || Colloquium. ||&lt;br /&gt;
|-&lt;br /&gt;
 || 14.12 || Complexity of clustering: an exact algorithm for maximising the inter-cluster distance and an approximate algorithm for minimising the intra-class distance.&lt;br /&gt;
 || &lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
For interested students, there are 3 lectures in parameterized complexity. &lt;br /&gt;
&lt;br /&gt;
14 Sept: Fixed parameter tracktability and examples, [https://www.dropbox.com/s/zzzaulpmzql7x7u/parameterizedComplexity.pdf?dl=0 presentation]. &lt;br /&gt;
&lt;br /&gt;
21 Sept: Topics from chapters 1 and 2 in &amp;quot;Parameterized algorithms&amp;quot; by Cygan, Fomin and others, 2016.&lt;br /&gt;
&lt;br /&gt;
28 Sept: The W-hierarchy, chapter 13 in the same book.&lt;br /&gt;
&lt;br /&gt;
= Office hours =&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
|-&lt;br /&gt;
!  Person !! Monday !! Tuesday !! Wednesday !! Thursday !! Friday &lt;br /&gt;
|-&lt;br /&gt;
|  [https://www.hse.ru/en/org/persons/160550073 Bruno Bauwens], S834, [https://us02web.zoom.us/j/82300259484?pwd=NWxXekxBeE5yMm9UTmwvLzNNNGlnUT09 Zoom] ||  || ||  ||  || 14:00-20:00&lt;br /&gt;
|-&lt;br /&gt;
|  [https://www.hse.ru/en/staff/obiedkov Sergei Obiedkov], T915, [https://zoom.us/j/99663354582?pwd=K1B5R3NXWEhWbFozR2lqMkFWYW5Ydz09 Zoom] ||  ||  || 16:30–18:00 || 16:30–18:00 ||  &lt;br /&gt;
|}&lt;/div&gt;</summary>
		<author><name>.obj</name></author>
	</entry>
	<entry>
		<id>https://wiki.cs.hse.ru/index.php?title=Theory_of_Computation_2021&amp;diff=58162</id>
		<title>Theory of Computation 2021</title>
		<link rel="alternate" type="text/html" href="https://wiki.cs.hse.ru/index.php?title=Theory_of_Computation_2021&amp;diff=58162"/>
		<updated>2021-09-14T13:16:15Z</updated>

		<summary type="html">&lt;p&gt;.obj: /* Course Materials */&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;= Classes =&lt;br /&gt;
 &lt;br /&gt;
Tuesdays 14:40–17:40, [https://ruz.hse.ru/ruz/main ruz]&lt;br /&gt;
&lt;br /&gt;
Lectures: 14:40 in room M303, also streamed [https://us02web.zoom.us/j/83533615475?pwd=WDU3cHJ5RjREOGd2YU1qdDJCVm1idz09 here] parallel [https://zoom.us/j/92154456703?pwd=aFZ0eWVoZnFVbm03ckNvTDFNS3dIdz09 session]&lt;br /&gt;
&lt;br /&gt;
Seminars: 16:20 in room M203, also streamed [https://us02web.zoom.us/j/84546220686?pwd=U2dISk5UaFZpdmh3WTdFT3phRVNXZz09 here]&lt;br /&gt;
&lt;br /&gt;
= Dates and Deadlines =&lt;br /&gt;
Please send your homework by e-mail to both lecturers.&amp;lt;br&amp;gt;&lt;br /&gt;
Homework 1, deadline: October 5, 14:00 &amp;lt;br&amp;gt;&lt;br /&gt;
Homework 2, deadline: November 2, 14:00 &amp;lt;br&amp;gt;&lt;br /&gt;
Homework 3, deadline: December 7, 14:00 &amp;lt;br&amp;gt;&lt;br /&gt;
Colloquium: December 7, 14:40–17:40&lt;br /&gt;
&lt;br /&gt;
= Grading =&lt;br /&gt;
Colloquium: 35%&amp;lt;br&amp;gt;&lt;br /&gt;
Homework: 35%&amp;lt;br&amp;gt;&lt;br /&gt;
Exam: 30%&lt;br /&gt;
&lt;br /&gt;
= Course Materials =&lt;br /&gt;
&lt;br /&gt;
The main reference is Sipser&#039;s book &amp;quot;Introduction to the theory of computation&amp;quot;, chapters 3, 7–10.&lt;br /&gt;
&lt;br /&gt;
If you need some background in math, consider these two sources:&amp;lt;br&amp;gt;&lt;br /&gt;
[http://www.cs.elte.hu/~lovasz/dmbook.ps Lecture notes: Discrete Mathematics], L. Lovasz, K. Vesztergombi&amp;lt;br&amp;gt;&lt;br /&gt;
[http://rubtsov.su/public/DM-HSE-Draft.pdf Лекции по дискретной математике] (черновик учебника, in Russian)&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
|-&lt;br /&gt;
! Date !! Summary !! Problem list&lt;br /&gt;
|-&lt;br /&gt;
 || 07.09 || Turing machines, multitape Turing machines, connection between them. Universal Turing machine. Examples ([https://www.dropbox.com/s/wna14b7y7nmw3cq/tm.py?dl=0 one], [https://www.dropbox.com/s/wrl3mkeqslj3xtu/wsharpw.py?dl=0 two]). Time and space complexity. Complexity classes P, PSPACE, EXP. || [https://www.dropbox.com/s/37eel2qayios6b3/prob_1.pdf?dl=0 Problem set 1]&lt;br /&gt;
|-&lt;br /&gt;
|| 14.09 ||  Time and space hierarchy theorem. Time and space constructible functions. || [https://www.dropbox.com/s/ow4m1z8u8r211qs/prob_2.pdf?dl=0 Problem set 2]&lt;br /&gt;
|-&lt;br /&gt;
 || 21.09 || Complexity class NP. Examples. Inclusions between P, NP and PSPACE. Non-deterministic TMs. Another definition of NP. Polynomial reductions, their properties. NP-hardness and NP-completeness, their properties. &lt;br /&gt;
 || &lt;br /&gt;
|-&lt;br /&gt;
 || 28.09 ||  Proving NP-hardness by reduction from an NP-complete problem. Examples of NP-complete problems.  ||&lt;br /&gt;
|-&lt;br /&gt;
 || 05.10 || Circuit complexity. Examples. All functions are computed by circuits. Existence of functions with exponential circuit complexity. P is in P/poly.|| &lt;br /&gt;
|-&lt;br /&gt;
 || 12.10 || Cook–Levin theorem. ||&lt;br /&gt;
|-&lt;br /&gt;
 || 26.10 || Space complexity. ||&lt;br /&gt;
|- &lt;br /&gt;
|| 02.11 || Oracle computation definitions. There exists an oracle &#039;&#039;A&#039;&#039; for which P&amp;lt;sup&amp;gt;&#039;&#039;A&#039;&#039;&amp;lt;/sup&amp;gt; = NP&amp;lt;sup&amp;gt;&#039;&#039;A&#039;&#039;&amp;lt;/sup&amp;gt;. There is an oracle B such that P&amp;lt;sup&amp;gt;&#039;&#039;B&#039;&#039;&amp;lt;/sup&amp;gt; is not equal to NP&amp;lt;sup&amp;gt;&#039;&#039;B&#039;&#039;&amp;lt;/sup&amp;gt;. ||&lt;br /&gt;
|-&lt;br /&gt;
 || 09.11 || Probabilistic computation. Probabilistic machines, the class BPP, invariance of the definition BPP for different thresholds, RP, coRP, PP, ZPP. BPP is in P/poly. || &lt;br /&gt;
|-&lt;br /&gt;
 || 16.11 ||  Streaming algorithms: finding the majority element, computation of the moment &#039;&#039;F&#039;&#039;&amp;lt;sub&amp;gt;2&amp;lt;/sub&amp;gt; in logarithmic space. ||&lt;br /&gt;
|-&lt;br /&gt;
 || 23.11 || Finding the frequent items in streams of data: SpaceSaving and Count-Min Sketch. ||&lt;br /&gt;
|-&lt;br /&gt;
 || 30.11 || Approximation algorithms. Approximate solutions for Vertex Cover, Weighted Vertex Cover, and TSP. ||&lt;br /&gt;
 &lt;br /&gt;
|-&lt;br /&gt;
 || 07.12 || Colloquium. ||&lt;br /&gt;
|-&lt;br /&gt;
 || 14.12 || Complexity of clustering: an exact algorithm for maximising the inter-cluster distance and an approximate algorithm for minimising the intra-class distance.&lt;br /&gt;
 || &lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
= Office hours =&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
|-&lt;br /&gt;
!  Person !! Monday !! Tuesday !! Wednesday !! Thursday !! Friday &lt;br /&gt;
|-&lt;br /&gt;
|  [https://www.hse.ru/en/org/persons/160550073 Bruno Bauwens] ||  || ||  ||  || &lt;br /&gt;
|-&lt;br /&gt;
|  [https://www.hse.ru/en/staff/obiedkov Sergei Obiedkov], T915, [https://zoom.us/j/99663354582?pwd=K1B5R3NXWEhWbFozR2lqMkFWYW5Ydz09 Zoom] ||  ||  || 16:30–18:00 || 16:30–18:00 ||  &lt;br /&gt;
|}&lt;/div&gt;</summary>
		<author><name>.obj</name></author>
	</entry>
	<entry>
		<id>https://wiki.cs.hse.ru/index.php?title=Theory_of_Computation_2021&amp;diff=58080</id>
		<title>Theory of Computation 2021</title>
		<link rel="alternate" type="text/html" href="https://wiki.cs.hse.ru/index.php?title=Theory_of_Computation_2021&amp;diff=58080"/>
		<updated>2021-09-13T14:23:44Z</updated>

		<summary type="html">&lt;p&gt;.obj: /* Course Materials */&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;= Classes =&lt;br /&gt;
 &lt;br /&gt;
Tuesdays 14:40–17:40, [https://ruz.hse.ru/ruz/main ruz]&lt;br /&gt;
&lt;br /&gt;
Lectures: 14:40 in room M303, also streamed [https://us02web.zoom.us/j/83533615475?pwd=WDU3cHJ5RjREOGd2YU1qdDJCVm1idz09 here]&lt;br /&gt;
&lt;br /&gt;
Seminars: 16:20 in room M203, also streamed [https://us02web.zoom.us/j/84546220686?pwd=U2dISk5UaFZpdmh3WTdFT3phRVNXZz09 here]&lt;br /&gt;
&lt;br /&gt;
= Dates and Deadlines =&lt;br /&gt;
Please send your homework by e-mail to both lecturers.&amp;lt;br&amp;gt;&lt;br /&gt;
Homework 1, deadline: October 5, 14:00 &amp;lt;br&amp;gt;&lt;br /&gt;
Homework 2, deadline: November 2, 14:00 &amp;lt;br&amp;gt;&lt;br /&gt;
Homework 3, deadline: December 7, 14:00 &amp;lt;br&amp;gt;&lt;br /&gt;
Colloquium: December 7, 14:40–17:40&lt;br /&gt;
&lt;br /&gt;
= Grading =&lt;br /&gt;
Colloquium: 35%&amp;lt;br&amp;gt;&lt;br /&gt;
Homework: 35%&amp;lt;br&amp;gt;&lt;br /&gt;
Exam: 30%&lt;br /&gt;
&lt;br /&gt;
= Course Materials =&lt;br /&gt;
&lt;br /&gt;
The main reference is Sipser&#039;s book &amp;quot;Introduction to the theory of computation&amp;quot;, chapters 3, 7–10.&lt;br /&gt;
&lt;br /&gt;
If you need some background in math, consider these two sources:&amp;lt;br&amp;gt;&lt;br /&gt;
[http://www.cs.elte.hu/~lovasz/dmbook.ps Lecture notes: Discrete Mathematics], L. Lovasz, K. Vesztergombi&amp;lt;br&amp;gt;&lt;br /&gt;
[http://rubtsov.su/public/DM-HSE-Draft.pdf Лекции по дискретной математике] (черновик учебника, in Russian)&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
|-&lt;br /&gt;
! Date !! Summary !! Problem list&lt;br /&gt;
|-&lt;br /&gt;
 || 07.09 || Turing machines, multitape Turing machines, connection between them. Universal Turing machine. Examples ([https://www.dropbox.com/s/wna14b7y7nmw3cq/tm.py?dl=0 one], [https://www.dropbox.com/s/wrl3mkeqslj3xtu/wsharpw.py?dl=0 two]). Time and space complexity. Complexity classes P, PSPACE, EXP. || [https://www.dropbox.com/s/37eel2qayios6b3/prob_1.pdf?dl=0 Problem set 1]&lt;br /&gt;
|-&lt;br /&gt;
|| 14.09 ||  Time and space hierarchy theorem. Time and space constructible functions. ||&lt;br /&gt;
|-&lt;br /&gt;
 || 21.09 || Complexity class NP. Examples. Inclusions between P, NP and PSPACE. Non-deterministic TMs. Another definition of NP. Polynomial reductions, their properties. NP-hardness and NP-completeness, their properties. &lt;br /&gt;
 || &lt;br /&gt;
|-&lt;br /&gt;
 || 28.09 ||  Proving NP-hardness by reduction from an NP-complete problem. Examples of NP-complete problems.  ||&lt;br /&gt;
|-&lt;br /&gt;
 || 05.10 || Circuit complexity. Examples. All functions are computed by circuits. Existence of functions with exponential circuit complexity. P is in P/poly.|| &lt;br /&gt;
|-&lt;br /&gt;
 || 12.10 || Cook–Levin theorem. ||&lt;br /&gt;
|-&lt;br /&gt;
 || 26.10 || Space complexity. ||&lt;br /&gt;
|- &lt;br /&gt;
|| 02.11 || Oracle computation definitions. There exists an oracle &#039;&#039;A&#039;&#039; for which P&amp;lt;sup&amp;gt;&#039;&#039;A&#039;&#039;&amp;lt;/sup&amp;gt; = NP&amp;lt;sup&amp;gt;&#039;&#039;A&#039;&#039;&amp;lt;/sup&amp;gt;. There is an oracle B such that P&amp;lt;sup&amp;gt;&#039;&#039;B&#039;&#039;&amp;lt;/sup&amp;gt; is not equal to NP&amp;lt;sup&amp;gt;&#039;&#039;B&#039;&#039;&amp;lt;/sup&amp;gt;. ||&lt;br /&gt;
|-&lt;br /&gt;
 || 09.11 || Probabilistic computation. Probabilistic machines, the class BPP, invariance of the definition BPP for different thresholds, RP, coRP, PP, ZPP. BPP is in P/poly. || &lt;br /&gt;
|-&lt;br /&gt;
 || 16.11 ||  Streaming algorithms: finding the majority element, computation of the moment &#039;&#039;F&#039;&#039;&amp;lt;sub&amp;gt;2&amp;lt;/sub&amp;gt; in logarithmic space. ||&lt;br /&gt;
|-&lt;br /&gt;
 || 23.11 || Finding the frequent items in streams of data: SpaceSaving and Count-Min Sketch. ||&lt;br /&gt;
|-&lt;br /&gt;
 || 30.11 || Approximation algorithms. Approximate solutions for Vertex Cover, Weighted Vertex Cover, and TSP. ||&lt;br /&gt;
 &lt;br /&gt;
|-&lt;br /&gt;
 || 07.12 || Colloquium. ||&lt;br /&gt;
|-&lt;br /&gt;
 || 14.12 || Complexity of clustering: an exact algorithm for maximising the inter-cluster distance and an approximate algorithm for minimising the intra-class distance.&lt;br /&gt;
 || &lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
= Office hours =&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
|-&lt;br /&gt;
!  Person !! Monday !! Tuesday !! Wednesday !! Thursday !! Friday &lt;br /&gt;
|-&lt;br /&gt;
|  [https://www.hse.ru/en/org/persons/160550073 Bruno Bauwens] ||  || ||  ||  || &lt;br /&gt;
|-&lt;br /&gt;
|  [https://www.hse.ru/en/staff/obiedkov Sergei Obiedkov], T915, [https://zoom.us/j/99663354582?pwd=K1B5R3NXWEhWbFozR2lqMkFWYW5Ydz09 Zoom] ||  ||  || 16:30–18:00 || 16:30–18:00 ||  &lt;br /&gt;
|}&lt;/div&gt;</summary>
		<author><name>.obj</name></author>
	</entry>
	<entry>
		<id>https://wiki.cs.hse.ru/index.php?title=Theory_of_Computation_2021&amp;diff=58054</id>
		<title>Theory of Computation 2021</title>
		<link rel="alternate" type="text/html" href="https://wiki.cs.hse.ru/index.php?title=Theory_of_Computation_2021&amp;diff=58054"/>
		<updated>2021-09-13T10:13:50Z</updated>

		<summary type="html">&lt;p&gt;.obj: /* Dates and Deadlines */&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;= Classes =&lt;br /&gt;
 &lt;br /&gt;
Tuesdays 14:40–17:40, [https://ruz.hse.ru/ruz/main ruz]&lt;br /&gt;
&lt;br /&gt;
Lectures: 14:40 in room M303, also streamed [https://us02web.zoom.us/j/83533615475?pwd=WDU3cHJ5RjREOGd2YU1qdDJCVm1idz09 here]&lt;br /&gt;
&lt;br /&gt;
Seminars: 16:20 in room M203, also streamed [https://us02web.zoom.us/j/84546220686?pwd=U2dISk5UaFZpdmh3WTdFT3phRVNXZz09 here]&lt;br /&gt;
&lt;br /&gt;
= Dates and Deadlines =&lt;br /&gt;
Please send your homework by e-mail to both lecturers.&amp;lt;br&amp;gt;&lt;br /&gt;
Homework 1, deadline: October 5, 14:00 &amp;lt;br&amp;gt;&lt;br /&gt;
Homework 2, deadline: November 2, 14:00 &amp;lt;br&amp;gt;&lt;br /&gt;
Homework 3, deadline: December 7, 14:00 &amp;lt;br&amp;gt;&lt;br /&gt;
Colloquium: December 7, 14:40–17:40&lt;br /&gt;
&lt;br /&gt;
= Grading =&lt;br /&gt;
Colloquium: 35%&amp;lt;br&amp;gt;&lt;br /&gt;
Homework: 35%&amp;lt;br&amp;gt;&lt;br /&gt;
Exam: 30%&lt;br /&gt;
&lt;br /&gt;
= Course Materials =&lt;br /&gt;
&lt;br /&gt;
The main reference is Sipser&#039;s book &amp;quot;Introduction to the theory of computation&amp;quot;, chapters 3, 7–10.&lt;br /&gt;
&lt;br /&gt;
If you need some background in math, consider these two sources:&amp;lt;br&amp;gt;&lt;br /&gt;
[http://www.cs.elte.hu/~lovasz/dmbook.ps Lecture notes: Discrete Mathematics], L. Lovasz, K. Vesztergombi&amp;lt;br&amp;gt;&lt;br /&gt;
[http://rubtsov.su/public/DM-HSE-Draft.pdf Лекции по дискретной математике] (черновик учебника, in Russian)&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
|-&lt;br /&gt;
! Date !! Summary !! Problem list&lt;br /&gt;
|-&lt;br /&gt;
 || 07.09 || Turing machines, multitape Turing machines, connection between them. Universal Turing machine. Examples ([https://www.dropbox.com/s/wna14b7y7nmw3cq/tm.py?dl=0 one], [https://www.dropbox.com/s/wrl3mkeqslj3xtu/wsharpw.py?dl=0 two]). Time and space complexity. Complexity classes P, PSPACE, EXP. || [https://www.dropbox.com/s/37eel2qayios6b3/prob_1.pdf?dl=0 Problem set 1]&lt;br /&gt;
|-&lt;br /&gt;
|| 14.09 ||  Time and space hierarchy theorem. Time and space constructible functions. ||&lt;br /&gt;
|-&lt;br /&gt;
 || 21.09 || Circuit complexity. Examples. All functions are computed by circuits. Existence of functions with exponential circuit complexity. P is in P/poly.&lt;br /&gt;
 || &lt;br /&gt;
|-&lt;br /&gt;
 || 28.09 ||  Complexity class NP. Examples. Inclusions between P, NP and PSPACE. Non-deterministic TMs. Another definition of NP. Polynomial reductions, their properties. NP-hardness and NP-completeness, their properties.  ||&lt;br /&gt;
|-&lt;br /&gt;
 || 05.10 || Proving NP-hardness by reduction from an NP-complete problem. Examples of NP-complete problems. || &lt;br /&gt;
|-&lt;br /&gt;
 || 12.10 || Cook–Levin theorem. ||&lt;br /&gt;
|-&lt;br /&gt;
 || 26.10 || Space complexity. ||&lt;br /&gt;
|- &lt;br /&gt;
|| 02.11 || Oracle computation definitions. There exists an oracle &#039;&#039;A&#039;&#039; for which P&amp;lt;sup&amp;gt;&#039;&#039;A&#039;&#039;&amp;lt;/sup&amp;gt; = NP&amp;lt;sup&amp;gt;&#039;&#039;A&#039;&#039;&amp;lt;/sup&amp;gt;. There is an oracle B such that P&amp;lt;sup&amp;gt;&#039;&#039;B&#039;&#039;&amp;lt;/sup&amp;gt; is not equal to NP&amp;lt;sup&amp;gt;&#039;&#039;B&#039;&#039;&amp;lt;/sup&amp;gt;. ||&lt;br /&gt;
|-&lt;br /&gt;
 || 09.11 || Probabilistic computation. Probabilistic machines, the class BPP, invariance of the definition BPP for different thresholds, RP, coRP, PP, ZPP. BPP is in P/poly. || &lt;br /&gt;
|-&lt;br /&gt;
 || 16.11 ||  Streaming algorithms: finding the majority element, computation of the moment &#039;&#039;F&#039;&#039;&amp;lt;sub&amp;gt;2&amp;lt;/sub&amp;gt; in logarithmic space. ||&lt;br /&gt;
|-&lt;br /&gt;
 || 23.11 || Finding the frequent items in streams of data: SpaceSaving and Count-Min Sketch. ||&lt;br /&gt;
|-&lt;br /&gt;
 || 30.11 || Approximation algorithms. Approximate solutions for Vertex Cover, Weighted Vertex Cover, and TSP. ||&lt;br /&gt;
 &lt;br /&gt;
|-&lt;br /&gt;
 || 07.12 || Colloquium. ||&lt;br /&gt;
|-&lt;br /&gt;
 || 14.12 || Complexity of clustering: an exact algorithm for maximising the inter-cluster distance and an approximate algorithm for minimising the intra-class distance.&lt;br /&gt;
 || &lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
= Office hours =&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
|-&lt;br /&gt;
!  Person !! Monday !! Tuesday !! Wednesday !! Thursday !! Friday &lt;br /&gt;
|-&lt;br /&gt;
|  [https://www.hse.ru/en/org/persons/160550073 Bruno Bauwens] ||  || ||  ||  || &lt;br /&gt;
|-&lt;br /&gt;
|  [https://www.hse.ru/en/staff/obiedkov Sergei Obiedkov], T915, [https://zoom.us/j/99663354582?pwd=K1B5R3NXWEhWbFozR2lqMkFWYW5Ydz09 Zoom] ||  ||  || 16:30–18:00 || 16:30–18:00 ||  &lt;br /&gt;
|}&lt;/div&gt;</summary>
		<author><name>.obj</name></author>
	</entry>
	<entry>
		<id>https://wiki.cs.hse.ru/index.php?title=Theory_of_Computation_2021&amp;diff=57903</id>
		<title>Theory of Computation 2021</title>
		<link rel="alternate" type="text/html" href="https://wiki.cs.hse.ru/index.php?title=Theory_of_Computation_2021&amp;diff=57903"/>
		<updated>2021-09-10T15:49:29Z</updated>

		<summary type="html">&lt;p&gt;.obj: /* Course Materials */&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;= Classes =&lt;br /&gt;
 &lt;br /&gt;
Tuesdays 14:40–17:40, [https://ruz.hse.ru/ruz/main ruz]&lt;br /&gt;
&lt;br /&gt;
Lectures: 14:40 in room M303, also streamed [https://us02web.zoom.us/j/83533615475?pwd=WDU3cHJ5RjREOGd2YU1qdDJCVm1idz09 here]&lt;br /&gt;
&lt;br /&gt;
Seminars: 16:20 in room M203, also streamed [https://us02web.zoom.us/j/84546220686?pwd=U2dISk5UaFZpdmh3WTdFT3phRVNXZz09 here]&lt;br /&gt;
&lt;br /&gt;
= Dates and Deadlines =&lt;br /&gt;
&lt;br /&gt;
Homework 1, deadline: October 5, 14:00 &amp;lt;br&amp;gt;&lt;br /&gt;
Homework 2, deadline: November 2, 14:00 &amp;lt;br&amp;gt;&lt;br /&gt;
Homework 3, deadline: December 7, 14:00 &amp;lt;br&amp;gt;&lt;br /&gt;
Colloquium: December 7, 14:40–17:40&lt;br /&gt;
&lt;br /&gt;
= Grading =&lt;br /&gt;
Colloquium: 35%&amp;lt;br&amp;gt;&lt;br /&gt;
Homework: 35%&amp;lt;br&amp;gt;&lt;br /&gt;
Exam: 30%&lt;br /&gt;
&lt;br /&gt;
= Course Materials =&lt;br /&gt;
&lt;br /&gt;
The main reference is Sipser&#039;s book &amp;quot;Introduction to the theory of computation&amp;quot;, chapters 3, 7–10.&lt;br /&gt;
&lt;br /&gt;
If you need some background in math, consider these two sources:&amp;lt;br&amp;gt;&lt;br /&gt;
[http://www.cs.elte.hu/~lovasz/dmbook.ps Lecture notes: Discrete Mathematics], L. Lovasz, K. Vesztergombi&amp;lt;br&amp;gt;&lt;br /&gt;
[http://rubtsov.su/public/DM-HSE-Draft.pdf Лекции по дискретной математике] (черновик учебника, in Russian)&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
|-&lt;br /&gt;
! Date !! Summary !! Problem list&lt;br /&gt;
|-&lt;br /&gt;
 || 07.09 || Turing machines, multitape Turing machines, connection between them. Universal Turing machine. Examples ([https://www.dropbox.com/s/wna14b7y7nmw3cq/tm.py?dl=0 one], [https://www.dropbox.com/s/wrl3mkeqslj3xtu/wsharpw.py?dl=0 two]). Time and space complexity. Complexity classes P, PSPACE, EXP. || [https://www.dropbox.com/s/37eel2qayios6b3/prob_1.pdf?dl=0 Problem set 1]&lt;br /&gt;
|-&lt;br /&gt;
|| 14.09 ||  Time and space hierarchy theorem. Time and space constructible functions. ||&lt;br /&gt;
|-&lt;br /&gt;
 || 21.09 || Circuit complexity. Examples. All functions are computed by circuits. Existence of functions with exponential circuit complexity. P is in P/poly.&lt;br /&gt;
 || &lt;br /&gt;
|-&lt;br /&gt;
 || 28.09 ||  Complexity class NP. Examples. Inclusions between P, NP and PSPACE. Non-deterministic TMs. Another definition of NP. Polynomial reductions, their properties. NP-hardness and NP-completeness, their properties.  ||&lt;br /&gt;
|-&lt;br /&gt;
 || 05.10 || Proving NP-hardness by reduction from an NP-complete problem. Examples of NP-complete problems. || &lt;br /&gt;
|-&lt;br /&gt;
 || 12.10 || Cook–Levin theorem. ||&lt;br /&gt;
|-&lt;br /&gt;
 || 26.10 || Space complexity. ||&lt;br /&gt;
|- &lt;br /&gt;
|| 02.11 || Oracle computation definitions. There exists an oracle &#039;&#039;A&#039;&#039; for which P&amp;lt;sup&amp;gt;&#039;&#039;A&#039;&#039;&amp;lt;/sup&amp;gt; = NP&amp;lt;sup&amp;gt;&#039;&#039;A&#039;&#039;&amp;lt;/sup&amp;gt;. There is an oracle B such that P&amp;lt;sup&amp;gt;&#039;&#039;B&#039;&#039;&amp;lt;/sup&amp;gt; is not equal to NP&amp;lt;sup&amp;gt;&#039;&#039;B&#039;&#039;&amp;lt;/sup&amp;gt;. ||&lt;br /&gt;
|-&lt;br /&gt;
 || 09.11 || Probabilistic computation. Probabilistic machines, the class BPP, invariance of the definition BPP for different thresholds, RP, coRP, PP, ZPP. BPP is in P/poly. || &lt;br /&gt;
|-&lt;br /&gt;
 || 16.11 ||  Streaming algorithms: finding the majority element, computation of the moment &#039;&#039;F&#039;&#039;&amp;lt;sub&amp;gt;2&amp;lt;/sub&amp;gt; in logarithmic space. ||&lt;br /&gt;
|-&lt;br /&gt;
 || 23.11 || Finding the frequent items in streams of data: SpaceSaving and Count-Min Sketch. ||&lt;br /&gt;
|-&lt;br /&gt;
 || 30.11 || Approximation algorithms. Approximate solutions for Vertex Cover, Weighted Vertex Cover, and TSP. ||&lt;br /&gt;
 &lt;br /&gt;
|-&lt;br /&gt;
 || 07.12 || Colloquium. ||&lt;br /&gt;
|-&lt;br /&gt;
 || 14.12 || Complexity of clustering: an exact algorithm for maximising the inter-cluster distance and an approximate algorithm for minimising the intra-class distance.&lt;br /&gt;
 || &lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
= Office hours =&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
|-&lt;br /&gt;
!  Person !! Monday !! Tuesday !! Wednesday !! Thursday !! Friday &lt;br /&gt;
|-&lt;br /&gt;
|  [https://www.hse.ru/en/org/persons/160550073 Bruno Bauwens] ||  || ||  ||  || &lt;br /&gt;
|-&lt;br /&gt;
|  [https://www.hse.ru/en/staff/obiedkov Sergei Obiedkov], T915, [https://zoom.us/j/99663354582?pwd=K1B5R3NXWEhWbFozR2lqMkFWYW5Ydz09 Zoom] ||  ||  || 16:30–18:00 || 16:30–18:00 ||  &lt;br /&gt;
|}&lt;/div&gt;</summary>
		<author><name>.obj</name></author>
	</entry>
	<entry>
		<id>https://wiki.cs.hse.ru/index.php?title=Theory_of_Computation_2021&amp;diff=57552</id>
		<title>Theory of Computation 2021</title>
		<link rel="alternate" type="text/html" href="https://wiki.cs.hse.ru/index.php?title=Theory_of_Computation_2021&amp;diff=57552"/>
		<updated>2021-09-07T14:02:45Z</updated>

		<summary type="html">&lt;p&gt;.obj: /* Course Materials */&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;= Classes =&lt;br /&gt;
 &lt;br /&gt;
Tuesdays 14:40–17:40, [https://ruz.hse.ru/ruz/main ruz]&lt;br /&gt;
&lt;br /&gt;
Lectures: 14:40 in room M303, also streamed [https://us02web.zoom.us/j/83533615475?pwd=WDU3cHJ5RjREOGd2YU1qdDJCVm1idz09 here]&lt;br /&gt;
&lt;br /&gt;
Seminars: 16:20 in room M203, also streamed [https://us02web.zoom.us/j/84546220686?pwd=U2dISk5UaFZpdmh3WTdFT3phRVNXZz09 here]&lt;br /&gt;
&lt;br /&gt;
= Dates and Deadlines =&lt;br /&gt;
&lt;br /&gt;
Homework 1, deadline: October 5, 14:00 &amp;lt;br&amp;gt;&lt;br /&gt;
Homework 2, deadline: November 2, 14:00 &amp;lt;br&amp;gt;&lt;br /&gt;
Homework 3, deadline: December 7, 14:00 &amp;lt;br&amp;gt;&lt;br /&gt;
Colloquium: December 7, 14:40–17:40&lt;br /&gt;
&lt;br /&gt;
= Grading =&lt;br /&gt;
Colloquium: 35%&amp;lt;br&amp;gt;&lt;br /&gt;
Homework: 35%&amp;lt;br&amp;gt;&lt;br /&gt;
Exam: 30%&lt;br /&gt;
&lt;br /&gt;
= Course Materials =&lt;br /&gt;
&lt;br /&gt;
The main reference is Sipser&#039;s book &amp;quot;Introduction to the theory of computation&amp;quot;, chapters 3, 7–10.&lt;br /&gt;
&lt;br /&gt;
If you need some background in math, consider these two sources:&amp;lt;br&amp;gt;&lt;br /&gt;
[http://www.cs.elte.hu/~lovasz/dmbook.ps Lecture notes: Discrete Mathematics], L. Lovasz, K. Vesztergombi&amp;lt;br&amp;gt;&lt;br /&gt;
[http://rubtsov.su/public/DM-HSE-Draft.pdf Лекции по дискретной математике] (черновик учебника, in Russian)&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
|-&lt;br /&gt;
! Date !! Summary !! Problem list&lt;br /&gt;
|-&lt;br /&gt;
 || 07.09 || Turing machines, multitape Turing machines, connection between them. Universal Turing machine. Examples ([https://www.dropbox.com/s/wna14b7y7nmw3cq/tm.py?dl=0 one], [https://www.dropbox.com/s/wrl3mkeqslj3xtu/wsharpw.py?dl=0 two]. Time and space complexity. Complexity classes P, PSPACE, EXP. || [https://www.dropbox.com/s/37eel2qayios6b3/prob_1.pdf?dl=0 Problem set 1]&lt;br /&gt;
|-&lt;br /&gt;
|| 14.09 ||  Time and space hierarchy theorem. Time and space constructible functions. ||&lt;br /&gt;
|-&lt;br /&gt;
 || 21.09 || Circuit complexity. Examples. All functions are computed by circuits. Existence of functions with exponential circuit complexity. P is in P/poly.&lt;br /&gt;
 || &lt;br /&gt;
|-&lt;br /&gt;
 || 28.09 ||  Complexity class NP. Examples. Inclusions between P, NP and PSPACE. Non-deterministic TMs. Another definition of NP. Polynomial reductions, their properties. NP-hardness and NP-completeness, their properties.  ||&lt;br /&gt;
|-&lt;br /&gt;
 || 05.10 || Proving NP-hardness by reduction from an NP-complete problem. Examples of NP-complete problems. || &lt;br /&gt;
|-&lt;br /&gt;
 || 12.10 || Cook–Levin theorem. ||&lt;br /&gt;
|-&lt;br /&gt;
 || 26.10 || Space complexity. ||&lt;br /&gt;
|- &lt;br /&gt;
|| 02.11 || Oracle computation definitions. There exists an oracle &#039;&#039;A&#039;&#039; for which P&amp;lt;sup&amp;gt;&#039;&#039;A&#039;&#039;&amp;lt;/sup&amp;gt; = NP&amp;lt;sup&amp;gt;&#039;&#039;A&#039;&#039;&amp;lt;/sup&amp;gt;. There is an oracle B such that P&amp;lt;sup&amp;gt;&#039;&#039;B&#039;&#039;&amp;lt;/sup&amp;gt; is not equal to NP&amp;lt;sup&amp;gt;&#039;&#039;B&#039;&#039;&amp;lt;/sup&amp;gt;. ||&lt;br /&gt;
|-&lt;br /&gt;
 || 09.11 || Probabilistic computation. Probabilistic machines, the class BPP, invariance of the definition BPP for different thresholds, RP, coRP, PP, ZPP. BPP is in P/poly. || &lt;br /&gt;
|-&lt;br /&gt;
 || 16.11 ||  Streaming algorithms: finding the majority element, computation of the moment &#039;&#039;F&#039;&#039;&amp;lt;sub&amp;gt;2&amp;lt;/sub&amp;gt; in logarithmic space. ||&lt;br /&gt;
|-&lt;br /&gt;
 || 23.11 || Finding the frequent items in streams of data: SpaceSaving and Count-Min Sketch. ||&lt;br /&gt;
|-&lt;br /&gt;
 || 30.11 || Approximation algorithms. Approximate solutions for Vertex Cover, Weighted Vertex Cover, and TSP. ||&lt;br /&gt;
 &lt;br /&gt;
|-&lt;br /&gt;
 || 07.12 || Colloquium. ||&lt;br /&gt;
|-&lt;br /&gt;
 || 14.12 || Complexity of clustering: an exact algorithm for maximising the inter-cluster distance and an approximate algorithm for minimising the intra-class distance.&lt;br /&gt;
 || &lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
= Office hours =&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
|-&lt;br /&gt;
!  Person !! Monday !! Tuesday !! Wednesday !! Thursday !! Friday &lt;br /&gt;
|-&lt;br /&gt;
|  [https://www.hse.ru/en/org/persons/160550073 Bruno Bauwens] ||  || ||  ||  || &lt;br /&gt;
|-&lt;br /&gt;
|  [https://www.hse.ru/en/staff/obiedkov Sergei Obiedkov], T915, [https://zoom.us/j/99663354582?pwd=K1B5R3NXWEhWbFozR2lqMkFWYW5Ydz09 Zoom] ||  ||  || 16:30–18:00 || 16:30–18:00 ||  &lt;br /&gt;
|}&lt;/div&gt;</summary>
		<author><name>.obj</name></author>
	</entry>
	<entry>
		<id>https://wiki.cs.hse.ru/index.php?title=Theory_of_Computation_2021&amp;diff=57542</id>
		<title>Theory of Computation 2021</title>
		<link rel="alternate" type="text/html" href="https://wiki.cs.hse.ru/index.php?title=Theory_of_Computation_2021&amp;diff=57542"/>
		<updated>2021-09-07T13:18:20Z</updated>

		<summary type="html">&lt;p&gt;.obj: /* Course Materials */&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;= Classes =&lt;br /&gt;
 &lt;br /&gt;
Tuesdays 14:40–17:40, [https://ruz.hse.ru/ruz/main ruz]&lt;br /&gt;
&lt;br /&gt;
Lectures: 14:40 in room M303, also streamed [https://us02web.zoom.us/j/83533615475?pwd=WDU3cHJ5RjREOGd2YU1qdDJCVm1idz09 here]&lt;br /&gt;
&lt;br /&gt;
Seminars: 16:20 in room M203, also streamed [https://us02web.zoom.us/j/84546220686?pwd=U2dISk5UaFZpdmh3WTdFT3phRVNXZz09 here]&lt;br /&gt;
&lt;br /&gt;
= Dates and Deadlines =&lt;br /&gt;
&lt;br /&gt;
Homework 1, deadline: October 5, 14:00 &amp;lt;br&amp;gt;&lt;br /&gt;
Homework 2, deadline: November 2, 14:00 &amp;lt;br&amp;gt;&lt;br /&gt;
Homework 3, deadline: December 7, 14:00 &amp;lt;br&amp;gt;&lt;br /&gt;
Colloquium: December 7, 14:40–17:40&lt;br /&gt;
&lt;br /&gt;
= Grading =&lt;br /&gt;
Colloquium: 35%&amp;lt;br&amp;gt;&lt;br /&gt;
Homework: 35%&amp;lt;br&amp;gt;&lt;br /&gt;
Exam: 30%&lt;br /&gt;
&lt;br /&gt;
= Course Materials =&lt;br /&gt;
&lt;br /&gt;
The main reference is Sipser&#039;s book &amp;quot;Introduction to the theory of computation&amp;quot;, chapters 3, 7–10.&lt;br /&gt;
&lt;br /&gt;
If you need some background in math, consider these two sources:&amp;lt;br&amp;gt;&lt;br /&gt;
[http://www.cs.elte.hu/~lovasz/dmbook.ps Lecture notes: Discrete Mathematics], L. Lovasz, K. Vesztergombi&amp;lt;br&amp;gt;&lt;br /&gt;
[http://rubtsov.su/public/DM-HSE-Draft.pdf Лекции по дискретной математике] (черновик учебника, in Russian)&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
|-&lt;br /&gt;
! Date !! Summary !! Problem list&lt;br /&gt;
|-&lt;br /&gt;
 || 07.09 || Turing machines, multitape Turing machines, connection between them. Universal Turing machine. Examples. Time and space complexity. Complexity classes P, PSPACE, EXP. || [https://www.dropbox.com/s/37eel2qayios6b3/prob_1.pdf?dl=0 Problem set 1]&lt;br /&gt;
|-&lt;br /&gt;
|| 14.09 ||  Time and space hierarchy theorem. Time and space constructible functions. ||&lt;br /&gt;
|-&lt;br /&gt;
 || 21.09 || Circuit complexity. Examples. All functions are computed by circuits. Existence of functions with exponential circuit complexity. P is in P/poly.&lt;br /&gt;
 || &lt;br /&gt;
|-&lt;br /&gt;
 || 28.09 ||  Complexity class NP. Examples. Inclusions between P, NP and PSPACE. Non-deterministic TMs. Another definition of NP. Polynomial reductions, their properties. NP-hardness and NP-completeness, their properties.  ||&lt;br /&gt;
|-&lt;br /&gt;
 || 05.10 || Proving NP-hardness by reduction from an NP-complete problem. Examples of NP-complete problems. || &lt;br /&gt;
|-&lt;br /&gt;
 || 12.10 || Cook–Levin theorem. ||&lt;br /&gt;
|-&lt;br /&gt;
 || 26.10 || Space complexity. ||&lt;br /&gt;
|- &lt;br /&gt;
|| 02.11 || Oracle computation definitions. There exists an oracle &#039;&#039;A&#039;&#039; for which P&amp;lt;sup&amp;gt;&#039;&#039;A&#039;&#039;&amp;lt;/sup&amp;gt; = NP&amp;lt;sup&amp;gt;&#039;&#039;A&#039;&#039;&amp;lt;/sup&amp;gt;. There is an oracle B such that P&amp;lt;sup&amp;gt;&#039;&#039;B&#039;&#039;&amp;lt;/sup&amp;gt; is not equal to NP&amp;lt;sup&amp;gt;&#039;&#039;B&#039;&#039;&amp;lt;/sup&amp;gt;. ||&lt;br /&gt;
|-&lt;br /&gt;
 || 09.11 || Probabilistic computation. Probabilistic machines, the class BPP, invariance of the definition BPP for different thresholds, RP, coRP, PP, ZPP. BPP is in P/poly. || &lt;br /&gt;
|-&lt;br /&gt;
 || 16.11 ||  Streaming algorithms: finding the majority element, computation of the moment &#039;&#039;F&#039;&#039;&amp;lt;sub&amp;gt;2&amp;lt;/sub&amp;gt; in logarithmic space. ||&lt;br /&gt;
|-&lt;br /&gt;
 || 23.11 || Finding the frequent items in streams of data: SpaceSaving and Count-Min Sketch. ||&lt;br /&gt;
|-&lt;br /&gt;
 || 30.11 || Approximation algorithms. Approximate solutions for Vertex Cover, Weighted Vertex Cover, and TSP. ||&lt;br /&gt;
 &lt;br /&gt;
|-&lt;br /&gt;
 || 07.12 || Colloquium. ||&lt;br /&gt;
|-&lt;br /&gt;
 || 14.12 || Complexity of clustering: an exact algorithm for maximising the inter-cluster distance and an approximate algorithm for minimising the intra-class distance.&lt;br /&gt;
 || &lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
= Office hours =&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
|-&lt;br /&gt;
!  Person !! Monday !! Tuesday !! Wednesday !! Thursday !! Friday &lt;br /&gt;
|-&lt;br /&gt;
|  [https://www.hse.ru/en/org/persons/160550073 Bruno Bauwens] ||  || ||  ||  || &lt;br /&gt;
|-&lt;br /&gt;
|  [https://www.hse.ru/en/staff/obiedkov Sergei Obiedkov], T915, [https://zoom.us/j/99663354582?pwd=K1B5R3NXWEhWbFozR2lqMkFWYW5Ydz09 Zoom] ||  ||  || 16:30–18:00 || 16:30–18:00 ||  &lt;br /&gt;
|}&lt;/div&gt;</summary>
		<author><name>.obj</name></author>
	</entry>
	<entry>
		<id>https://wiki.cs.hse.ru/index.php?title=Theory_of_Computation_2021&amp;diff=57410</id>
		<title>Theory of Computation 2021</title>
		<link rel="alternate" type="text/html" href="https://wiki.cs.hse.ru/index.php?title=Theory_of_Computation_2021&amp;diff=57410"/>
		<updated>2021-09-06T14:13:27Z</updated>

		<summary type="html">&lt;p&gt;.obj: /* Classes */&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;= Classes =&lt;br /&gt;
 &lt;br /&gt;
Tuesdays 14:40–17:40, [https://ruz.hse.ru/ruz/main ruz]&lt;br /&gt;
&lt;br /&gt;
Lectures: 14:40 in room M303, also streamed [https://us02web.zoom.us/j/83533615475?pwd=WDU3cHJ5RjREOGd2YU1qdDJCVm1idz09 here]&lt;br /&gt;
&lt;br /&gt;
Seminars: 16:20 in room M203, also streamed [https://us02web.zoom.us/j/84546220686?pwd=U2dISk5UaFZpdmh3WTdFT3phRVNXZz09 here]&lt;br /&gt;
&lt;br /&gt;
= Dates and Deadlines =&lt;br /&gt;
&lt;br /&gt;
Homework 1, deadline: October 5, 14:00 &amp;lt;br&amp;gt;&lt;br /&gt;
Homework 2, deadline: November 2, 14:00 &amp;lt;br&amp;gt;&lt;br /&gt;
Homework 3, deadline: December 7, 14:00 &amp;lt;br&amp;gt;&lt;br /&gt;
Colloquium: December 7, 14:40–17:40&lt;br /&gt;
&lt;br /&gt;
= Grading =&lt;br /&gt;
Colloquium: 35%&amp;lt;br&amp;gt;&lt;br /&gt;
Homework: 35%&amp;lt;br&amp;gt;&lt;br /&gt;
Exam: 30%&lt;br /&gt;
&lt;br /&gt;
= Course Materials =&lt;br /&gt;
&lt;br /&gt;
The main reference is Sipser&#039;s book &amp;quot;Introduction to the theory of computation&amp;quot;, chapters 3, 7–10.&lt;br /&gt;
&lt;br /&gt;
If you need some background in math, consider these two sources:&amp;lt;br&amp;gt;&lt;br /&gt;
[http://www.cs.elte.hu/~lovasz/dmbook.ps Lecture notes: Discrete Mathematics], L. Lovasz, K. Vesztergombi&amp;lt;br&amp;gt;&lt;br /&gt;
[http://rubtsov.su/public/DM-HSE-Draft.pdf Лекции по дискретной математике] (черновик учебника, in Russian)&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
|-&lt;br /&gt;
! Date !! Summary !! Problem list&lt;br /&gt;
|-&lt;br /&gt;
 || 07.09 || Turing machines, multitape Turing machines, connection between them. Universal Turing machine. Examples. Time and space complexity. Complexity classes P, PSPACE, EXP. ||&lt;br /&gt;
|-&lt;br /&gt;
|| 14.09 ||  Time and space hierarchy theorem. Time and space constructible functions. ||&lt;br /&gt;
|-&lt;br /&gt;
 || 21.09 || Circuit complexity. Examples. All functions are computed by circuits. Existence of functions with exponential circuit complexity. P is in P/poly.&lt;br /&gt;
 || &lt;br /&gt;
|-&lt;br /&gt;
 || 28.09 ||  Complexity class NP. Examples. Inclusions between P, NP and PSPACE. Non-deterministic TMs. Another definition of NP. Polynomial reductions, their properties. NP-hardness and NP-completeness, their properties.  ||&lt;br /&gt;
|-&lt;br /&gt;
 || 05.10 || Proving NP-hardness by reduction from an NP-complete problem. Examples of NP-complete problems. || &lt;br /&gt;
|-&lt;br /&gt;
 || 12.10 || Cook–Levin theorem. ||&lt;br /&gt;
|-&lt;br /&gt;
 || 26.10 || Space complexity. ||&lt;br /&gt;
|- &lt;br /&gt;
|| 02.11 || Oracle computation definitions. There exists an oracle &#039;&#039;A&#039;&#039; for which P&amp;lt;sup&amp;gt;&#039;&#039;A&#039;&#039;&amp;lt;/sup&amp;gt; = NP&amp;lt;sup&amp;gt;&#039;&#039;A&#039;&#039;&amp;lt;/sup&amp;gt;. There is an oracle B such that P&amp;lt;sup&amp;gt;&#039;&#039;B&#039;&#039;&amp;lt;/sup&amp;gt; is not equal to NP&amp;lt;sup&amp;gt;&#039;&#039;B&#039;&#039;&amp;lt;/sup&amp;gt;. ||&lt;br /&gt;
|-&lt;br /&gt;
 || 09.11 || Probabilistic computation. Probabilistic machines, the class BPP, invariance of the definition BPP for different thresholds, RP, coRP, PP, ZPP. BPP is in P/poly. || &lt;br /&gt;
|-&lt;br /&gt;
 || 16.11 ||  Streaming algorithms: finding the majority element, computation of the moment &#039;&#039;F&#039;&#039;&amp;lt;sub&amp;gt;2&amp;lt;/sub&amp;gt; in logarithmic space. ||&lt;br /&gt;
|-&lt;br /&gt;
 || 23.11 || Finding the frequent items in streams of data: SpaceSaving and Count-Min Sketch. ||&lt;br /&gt;
|-&lt;br /&gt;
 || 30.11 || Approximation algorithms. Approximate solutions for Vertex Cover, Weighted Vertex Cover, and TSP. ||&lt;br /&gt;
 &lt;br /&gt;
|-&lt;br /&gt;
 || 07.12 || Colloquium. ||&lt;br /&gt;
|-&lt;br /&gt;
 || 14.12 || Complexity of clustering: an exact algorithm for maximising the inter-cluster distance and an approximate algorithm for minimising the intra-class distance.&lt;br /&gt;
 || &lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
= Office hours =&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
|-&lt;br /&gt;
!  Person !! Monday !! Tuesday !! Wednesday !! Thursday !! Friday &lt;br /&gt;
|-&lt;br /&gt;
|  [https://www.hse.ru/en/org/persons/160550073 Bruno Bauwens] ||  || ||  ||  || &lt;br /&gt;
|-&lt;br /&gt;
|  [https://www.hse.ru/en/staff/obiedkov Sergei Obiedkov], T915, [https://zoom.us/j/99663354582?pwd=K1B5R3NXWEhWbFozR2lqMkFWYW5Ydz09 Zoom] ||  ||  || 16:30–18:00 || 16:30–18:00 ||  &lt;br /&gt;
|}&lt;/div&gt;</summary>
		<author><name>.obj</name></author>
	</entry>
	<entry>
		<id>https://wiki.cs.hse.ru/index.php?title=Theory_of_Computation_2021&amp;diff=57402</id>
		<title>Theory of Computation 2021</title>
		<link rel="alternate" type="text/html" href="https://wiki.cs.hse.ru/index.php?title=Theory_of_Computation_2021&amp;diff=57402"/>
		<updated>2021-09-06T14:07:10Z</updated>

		<summary type="html">&lt;p&gt;.obj: /* Classes */&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;= Classes =&lt;br /&gt;
 &lt;br /&gt;
Tuesdays 14:40–17:40, [https://ruz.hse.ru/ruz/main ruz]&lt;br /&gt;
&lt;br /&gt;
Lectures 14:40 in room M303, also streamed [https://us02web.zoom.us/j/83533615475?pwd=WDU3cHJ5RjREOGd2YU1qdDJCVm1idz09 here]&lt;br /&gt;
&lt;br /&gt;
Seminars 16:20 in room M203, also streamed [https://us02web.zoom.us/j/84546220686?pwd=U2dISk5UaFZpdmh3WTdFT3phRVNXZz09 here]&lt;br /&gt;
&lt;br /&gt;
= Dates and Deadlines =&lt;br /&gt;
&lt;br /&gt;
Homework 1, deadline: October 5, 14:00 &amp;lt;br&amp;gt;&lt;br /&gt;
Homework 2, deadline: November 2, 14:00 &amp;lt;br&amp;gt;&lt;br /&gt;
Homework 3, deadline: December 7, 14:00 &amp;lt;br&amp;gt;&lt;br /&gt;
Colloquium: December 7, 14:40–17:40&lt;br /&gt;
&lt;br /&gt;
= Grading =&lt;br /&gt;
Colloquium: 35%&amp;lt;br&amp;gt;&lt;br /&gt;
Homework: 35%&amp;lt;br&amp;gt;&lt;br /&gt;
Exam: 30%&lt;br /&gt;
&lt;br /&gt;
= Course Materials =&lt;br /&gt;
&lt;br /&gt;
The main reference is Sipser&#039;s book &amp;quot;Introduction to the theory of computation&amp;quot;, chapters 3, 7–10.&lt;br /&gt;
&lt;br /&gt;
If you need some background in math, consider these two sources:&amp;lt;br&amp;gt;&lt;br /&gt;
[http://www.cs.elte.hu/~lovasz/dmbook.ps Lecture notes: Discrete Mathematics], L. Lovasz, K. Vesztergombi&amp;lt;br&amp;gt;&lt;br /&gt;
[http://rubtsov.su/public/DM-HSE-Draft.pdf Лекции по дискретной математике] (черновик учебника, in Russian)&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
|-&lt;br /&gt;
! Date !! Summary !! Problem list&lt;br /&gt;
|-&lt;br /&gt;
 || 07.09 || Turing machines, multitape Turing machines, connection between them. Universal Turing machine. Examples. Time and space complexity. Complexity classes P, PSPACE, EXP. ||&lt;br /&gt;
|-&lt;br /&gt;
|| 14.09 ||  Time and space hierarchy theorem. Time and space constructible functions. ||&lt;br /&gt;
|-&lt;br /&gt;
 || 21.09 || Circuit complexity. Examples. All functions are computed by circuits. Existence of functions with exponential circuit complexity. P is in P/poly.&lt;br /&gt;
 || &lt;br /&gt;
|-&lt;br /&gt;
 || 28.09 ||  Complexity class NP. Examples. Inclusions between P, NP and PSPACE. Non-deterministic TMs. Another definition of NP. Polynomial reductions, their properties. NP-hardness and NP-completeness, their properties.  ||&lt;br /&gt;
|-&lt;br /&gt;
 || 05.10 || Proving NP-hardness by reduction from an NP-complete problem. Examples of NP-complete problems. || &lt;br /&gt;
|-&lt;br /&gt;
 || 12.10 || Cook–Levin theorem. ||&lt;br /&gt;
|-&lt;br /&gt;
 || 26.10 || Space complexity. ||&lt;br /&gt;
|- &lt;br /&gt;
|| 02.11 || Oracle computation definitions. There exists an oracle &#039;&#039;A&#039;&#039; for which P&amp;lt;sup&amp;gt;&#039;&#039;A&#039;&#039;&amp;lt;/sup&amp;gt; = NP&amp;lt;sup&amp;gt;&#039;&#039;A&#039;&#039;&amp;lt;/sup&amp;gt;. There is an oracle B such that P&amp;lt;sup&amp;gt;&#039;&#039;B&#039;&#039;&amp;lt;/sup&amp;gt; is not equal to NP&amp;lt;sup&amp;gt;&#039;&#039;B&#039;&#039;&amp;lt;/sup&amp;gt;. ||&lt;br /&gt;
|-&lt;br /&gt;
 || 09.11 || Probabilistic computation. Probabilistic machines, the class BPP, invariance of the definition BPP for different thresholds, RP, coRP, PP, ZPP. BPP is in P/poly. || &lt;br /&gt;
|-&lt;br /&gt;
 || 16.11 ||  Streaming algorithms: finding the majority element, computation of the moment &#039;&#039;F&#039;&#039;&amp;lt;sub&amp;gt;2&amp;lt;/sub&amp;gt; in logarithmic space. ||&lt;br /&gt;
|-&lt;br /&gt;
 || 23.11 || Finding the frequent items in streams of data: SpaceSaving and Count-Min Sketch. ||&lt;br /&gt;
|-&lt;br /&gt;
 || 30.11 || Approximation algorithms. Approximate solutions for Vertex Cover, Weighted Vertex Cover, and TSP. ||&lt;br /&gt;
 &lt;br /&gt;
|-&lt;br /&gt;
 || 07.12 || Colloquium. ||&lt;br /&gt;
|-&lt;br /&gt;
 || 14.12 || Complexity of clustering: an exact algorithm for maximising the inter-cluster distance and an approximate algorithm for minimising the intra-class distance.&lt;br /&gt;
 || &lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
= Office hours =&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
|-&lt;br /&gt;
!  Person !! Monday !! Tuesday !! Wednesday !! Thursday !! Friday &lt;br /&gt;
|-&lt;br /&gt;
|  [https://www.hse.ru/en/org/persons/160550073 Bruno Bauwens] ||  || ||  ||  || &lt;br /&gt;
|-&lt;br /&gt;
|  [https://www.hse.ru/en/staff/obiedkov Sergei Obiedkov], T915, [https://zoom.us/j/99663354582?pwd=K1B5R3NXWEhWbFozR2lqMkFWYW5Ydz09 Zoom] ||  ||  || 16:30–18:00 || 16:30–18:00 ||  &lt;br /&gt;
|}&lt;/div&gt;</summary>
		<author><name>.obj</name></author>
	</entry>
	<entry>
		<id>https://wiki.cs.hse.ru/index.php?title=Theory_of_Computation_2021&amp;diff=57400</id>
		<title>Theory of Computation 2021</title>
		<link rel="alternate" type="text/html" href="https://wiki.cs.hse.ru/index.php?title=Theory_of_Computation_2021&amp;diff=57400"/>
		<updated>2021-09-06T14:01:50Z</updated>

		<summary type="html">&lt;p&gt;.obj: /* Grading */&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;= Classes =&lt;br /&gt;
 &lt;br /&gt;
Tuesdays 14:40–17:40, [https://ruz.hse.ru/ruz/main ruz]&lt;br /&gt;
&lt;br /&gt;
Lectures 14:40 in room M303, also streamed [https://us02web.zoom.us/j/83533615475?pwd=WDU3cHJ5RjREOGd2YU1qdDJCVm1idz09 here]&lt;br /&gt;
&lt;br /&gt;
Seminars 16:20 in room ??, also streamed [https://us02web.zoom.us/j/84546220686?pwd=U2dISk5UaFZpdmh3WTdFT3phRVNXZz09 here]&lt;br /&gt;
&lt;br /&gt;
= Dates and Deadlines =&lt;br /&gt;
&lt;br /&gt;
Homework 1, deadline: October 5, 14:00 &amp;lt;br&amp;gt;&lt;br /&gt;
Homework 2, deadline: November 2, 14:00 &amp;lt;br&amp;gt;&lt;br /&gt;
Homework 3, deadline: December 7, 14:00 &amp;lt;br&amp;gt;&lt;br /&gt;
Colloquium: December 7, 14:40–17:40&lt;br /&gt;
&lt;br /&gt;
= Grading =&lt;br /&gt;
Colloquium: 35%&amp;lt;br&amp;gt;&lt;br /&gt;
Homework: 35%&amp;lt;br&amp;gt;&lt;br /&gt;
Exam: 30%&lt;br /&gt;
&lt;br /&gt;
= Course Materials =&lt;br /&gt;
&lt;br /&gt;
The main reference is Sipser&#039;s book &amp;quot;Introduction to the theory of computation&amp;quot;, chapters 3, 7–10.&lt;br /&gt;
&lt;br /&gt;
If you need some background in math, consider these two sources:&amp;lt;br&amp;gt;&lt;br /&gt;
[http://www.cs.elte.hu/~lovasz/dmbook.ps Lecture notes: Discrete Mathematics], L. Lovasz, K. Vesztergombi&amp;lt;br&amp;gt;&lt;br /&gt;
[http://rubtsov.su/public/DM-HSE-Draft.pdf Лекции по дискретной математике] (черновик учебника, in Russian)&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
|-&lt;br /&gt;
! Date !! Summary !! Problem list&lt;br /&gt;
|-&lt;br /&gt;
 || 07.09 || Turing machines, multitape Turing machines, connection between them. Universal Turing machine. Examples. Time and space complexity. Complexity classes P, PSPACE, EXP. ||&lt;br /&gt;
|-&lt;br /&gt;
|| 14.09 ||  Time and space hierarchy theorem. Time and space constructible functions. ||&lt;br /&gt;
|-&lt;br /&gt;
 || 21.09 || Circuit complexity. Examples. All functions are computed by circuits. Existence of functions with exponential circuit complexity. P is in P/poly.&lt;br /&gt;
 || &lt;br /&gt;
|-&lt;br /&gt;
 || 28.09 ||  Complexity class NP. Examples. Inclusions between P, NP and PSPACE. Non-deterministic TMs. Another definition of NP. Polynomial reductions, their properties. NP-hardness and NP-completeness, their properties.  ||&lt;br /&gt;
|-&lt;br /&gt;
 || 05.10 || Proving NP-hardness by reduction from an NP-complete problem. Examples of NP-complete problems. || &lt;br /&gt;
|-&lt;br /&gt;
 || 12.10 || Cook–Levin theorem. ||&lt;br /&gt;
|-&lt;br /&gt;
 || 26.10 || Space complexity. ||&lt;br /&gt;
|- &lt;br /&gt;
|| 02.11 || Oracle computation definitions. There exists an oracle &#039;&#039;A&#039;&#039; for which P&amp;lt;sup&amp;gt;&#039;&#039;A&#039;&#039;&amp;lt;/sup&amp;gt; = NP&amp;lt;sup&amp;gt;&#039;&#039;A&#039;&#039;&amp;lt;/sup&amp;gt;. There is an oracle B such that P&amp;lt;sup&amp;gt;&#039;&#039;B&#039;&#039;&amp;lt;/sup&amp;gt; is not equal to NP&amp;lt;sup&amp;gt;&#039;&#039;B&#039;&#039;&amp;lt;/sup&amp;gt;. ||&lt;br /&gt;
|-&lt;br /&gt;
 || 09.11 || Probabilistic computation. Probabilistic machines, the class BPP, invariance of the definition BPP for different thresholds, RP, coRP, PP, ZPP. BPP is in P/poly. || &lt;br /&gt;
|-&lt;br /&gt;
 || 16.11 ||  Streaming algorithms: finding the majority element, computation of the moment &#039;&#039;F&#039;&#039;&amp;lt;sub&amp;gt;2&amp;lt;/sub&amp;gt; in logarithmic space. ||&lt;br /&gt;
|-&lt;br /&gt;
 || 23.11 || Finding the frequent items in streams of data: SpaceSaving and Count-Min Sketch. ||&lt;br /&gt;
|-&lt;br /&gt;
 || 30.11 || Approximation algorithms. Approximate solutions for Vertex Cover, Weighted Vertex Cover, and TSP. ||&lt;br /&gt;
 &lt;br /&gt;
|-&lt;br /&gt;
 || 07.12 || Colloquium. ||&lt;br /&gt;
|-&lt;br /&gt;
 || 14.12 || Complexity of clustering: an exact algorithm for maximising the inter-cluster distance and an approximate algorithm for minimising the intra-class distance.&lt;br /&gt;
 || &lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
= Office hours =&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
|-&lt;br /&gt;
!  Person !! Monday !! Tuesday !! Wednesday !! Thursday !! Friday &lt;br /&gt;
|-&lt;br /&gt;
|  [https://www.hse.ru/en/org/persons/160550073 Bruno Bauwens] ||  || ||  ||  || &lt;br /&gt;
|-&lt;br /&gt;
|  [https://www.hse.ru/en/staff/obiedkov Sergei Obiedkov], T915, [https://zoom.us/j/99663354582?pwd=K1B5R3NXWEhWbFozR2lqMkFWYW5Ydz09 Zoom] ||  ||  || 16:30–18:00 || 16:30–18:00 ||  &lt;br /&gt;
|}&lt;/div&gt;</summary>
		<author><name>.obj</name></author>
	</entry>
	<entry>
		<id>https://wiki.cs.hse.ru/index.php?title=Theory_of_Computation_2021&amp;diff=56663</id>
		<title>Theory of Computation 2021</title>
		<link rel="alternate" type="text/html" href="https://wiki.cs.hse.ru/index.php?title=Theory_of_Computation_2021&amp;diff=56663"/>
		<updated>2021-08-25T13:07:30Z</updated>

		<summary type="html">&lt;p&gt;.obj: /* Course Materials */&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;= Classes =&lt;br /&gt;
&lt;br /&gt;
Tuesdays, 14:40–17:40.&lt;br /&gt;
&lt;br /&gt;
= Dates and Deadlines =&lt;br /&gt;
&lt;br /&gt;
Homework 1, deadline: October 5, 14:00 &amp;lt;br&amp;gt;&lt;br /&gt;
Homework 2, deadline: November 2, 14:00 &amp;lt;br&amp;gt;&lt;br /&gt;
Homework 3, deadline: December 7, 14:00 &amp;lt;br&amp;gt;&lt;br /&gt;
Colloquium: December 7, 14:40–17:40&lt;br /&gt;
&lt;br /&gt;
= Grading =&lt;br /&gt;
Colloquium: 0.35&amp;lt;br&amp;gt;&lt;br /&gt;
Homework: 0.35&amp;lt;br&amp;gt;&lt;br /&gt;
Exam: 0.3&lt;br /&gt;
&lt;br /&gt;
= Course Materials =&lt;br /&gt;
&lt;br /&gt;
The main reference is Sipser&#039;s book &amp;quot;Introduction to the theory of computation&amp;quot;, chapters 3, 7–10.&lt;br /&gt;
&lt;br /&gt;
If you need some background in math, consider these two sources:&amp;lt;br&amp;gt;&lt;br /&gt;
[http://www.cs.elte.hu/~lovasz/dmbook.ps Lecture notes: Discrete Mathematics], L. Lovasz, K. Vesztergombi&amp;lt;br&amp;gt;&lt;br /&gt;
[http://rubtsov.su/public/DM-HSE-Draft.pdf Лекции по дискретной математике] (черновик учебника, in Russian)&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
|-&lt;br /&gt;
! Date !! Summary !! Problem list&lt;br /&gt;
|-&lt;br /&gt;
 || 07.09 || Turing machines, multitape Turing machines, connection between them. Universal Turing machine. Examples. Time and space complexity. Complexity classes P, PSPACE, EXP. ||&lt;br /&gt;
|-&lt;br /&gt;
|| 14.09 ||  Time and space hierarchy theorem. Time and space constructible functions. ||&lt;br /&gt;
|-&lt;br /&gt;
 || 21.09 || Circuit complexity. Examples. All functions are computed by circuits. Existence of functions with exponential circuit complexity. P is in P/poly.&lt;br /&gt;
 || &lt;br /&gt;
|-&lt;br /&gt;
 || 28.09 ||  Complexity class NP. Examples. Inclusions between P, NP and PSPACE. Non-deterministic TMs. Another definition of NP. Polynomial reductions, their properties. NP-hardness and NP-completeness, their properties.  ||&lt;br /&gt;
|-&lt;br /&gt;
 || 05.10 || Proving NP-hardness by reduction from an NP-complete problem. Examples of NP-complete problems. || &lt;br /&gt;
|-&lt;br /&gt;
 || 12.10 || Cook–Levin theorem. ||&lt;br /&gt;
|-&lt;br /&gt;
 || 26.10 || Space complexity. ||&lt;br /&gt;
|- &lt;br /&gt;
|| 02.11 || Oracle computation definitions. There exists an oracle &#039;&#039;A&#039;&#039; for which P&amp;lt;sup&amp;gt;&#039;&#039;A&#039;&#039;&amp;lt;/sup&amp;gt; = NP&amp;lt;sup&amp;gt;&#039;&#039;A&#039;&#039;&amp;lt;/sup&amp;gt;. There is an oracle B such that P&amp;lt;sup&amp;gt;&#039;&#039;B&#039;&#039;&amp;lt;/sup&amp;gt; is not equal to NP&amp;lt;sup&amp;gt;&#039;&#039;B&#039;&#039;&amp;lt;/sup&amp;gt;. ||&lt;br /&gt;
|-&lt;br /&gt;
 || 09.11 || Probabilistic computation. Probabilistic machines, the class BPP, invariance of the definition BPP for different thresholds, RP, coRP, PP, ZPP. BPP is in P/poly. || &lt;br /&gt;
|-&lt;br /&gt;
 || 16.11 ||  Streaming algorithms: finding the majority element, computation of the moment &#039;&#039;F&#039;&#039;&amp;lt;sub&amp;gt;2&amp;lt;/sub&amp;gt; in logarithmic space. ||&lt;br /&gt;
|-&lt;br /&gt;
 || 23.11 || Finding the frequent items in streams of data: SpaceSaving and Count-Min Sketch. ||&lt;br /&gt;
|-&lt;br /&gt;
 || 30.11 || Approximation algorithms. Approximate solutions for Vertex Cover, Weighted Vertex Cover, and TSP. ||&lt;br /&gt;
 &lt;br /&gt;
|-&lt;br /&gt;
 || 07.12 || Colloquium. ||&lt;br /&gt;
|-&lt;br /&gt;
 || 14.12 || Complexity of clustering: an exact algorithm for maximising the inter-cluster distance and an approximate algorithm for minimising the intra-class distance.&lt;br /&gt;
 || &lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
= Office hours =&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
|-&lt;br /&gt;
!  Person !! Monday !! Tuesday !! Wednesday !! Thursday !! Friday &lt;br /&gt;
|-&lt;br /&gt;
|  [https://www.hse.ru/en/org/persons/160550073 Bruno Bauwens] ||  || ||  ||  || &lt;br /&gt;
|-&lt;br /&gt;
|  [https://www.hse.ru/en/staff/obiedkov Sergei Obiedkov], T915, [https://zoom.us/j/99663354582?pwd=K1B5R3NXWEhWbFozR2lqMkFWYW5Ydz09 Zoom] ||  ||  || 16:30–18:00 || 16:30–18:00 ||  &lt;br /&gt;
|}&lt;/div&gt;</summary>
		<author><name>.obj</name></author>
	</entry>
	<entry>
		<id>https://wiki.cs.hse.ru/index.php?title=Theory_of_Computation_2021&amp;diff=56662</id>
		<title>Theory of Computation 2021</title>
		<link rel="alternate" type="text/html" href="https://wiki.cs.hse.ru/index.php?title=Theory_of_Computation_2021&amp;diff=56662"/>
		<updated>2021-08-25T13:06:01Z</updated>

		<summary type="html">&lt;p&gt;.obj: /* Grading */&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;= Classes =&lt;br /&gt;
&lt;br /&gt;
Tuesdays, 14:40–17:40.&lt;br /&gt;
&lt;br /&gt;
= Dates and Deadlines =&lt;br /&gt;
&lt;br /&gt;
Homework 1, deadline: October 5, 14:00 &amp;lt;br&amp;gt;&lt;br /&gt;
Homework 2, deadline: November 2, 14:00 &amp;lt;br&amp;gt;&lt;br /&gt;
Homework 3, deadline: December 7, 14:00 &amp;lt;br&amp;gt;&lt;br /&gt;
Colloquium: December 7, 14:40–17:40&lt;br /&gt;
&lt;br /&gt;
= Grading =&lt;br /&gt;
Colloquium: 0.35&amp;lt;br&amp;gt;&lt;br /&gt;
Homework: 0.35&amp;lt;br&amp;gt;&lt;br /&gt;
Exam: 0.3&lt;br /&gt;
&lt;br /&gt;
= Course Materials =&lt;br /&gt;
&lt;br /&gt;
The main reference is Sipser&#039;s book &amp;quot;Introduction to the theory of computation&amp;quot;, chapters 3, 7–10.&lt;br /&gt;
&lt;br /&gt;
If you need some background in math, consider these two sources:&amp;lt;br&amp;gt;&lt;br /&gt;
[http://www.cs.elte.hu/~lovasz/dmbook.ps Lecture notes: Discrete Mathematics], L. Lovasz, K. Vesztergombi&amp;lt;br&amp;gt;&lt;br /&gt;
[http://rubtsov.su/public/DM-HSE-Draft.pdf Лекции по дискретной математике] (черновик учебника, in Russian)&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
|-&lt;br /&gt;
! Date !! Summary !! Problem list&lt;br /&gt;
|-&lt;br /&gt;
 || 07.09 || Turing machines, multitape Turing machines, connection between them. Universal Turing machine. Examples. Time and space complexity. Complexity classes P, PSPACE, EXP. ||&lt;br /&gt;
|-&lt;br /&gt;
|| 14.09 ||  Time and space hierarchy theorem. Time and space constructible functions. ||&lt;br /&gt;
|-&lt;br /&gt;
 || 21.09 || Circuit complexity. Examples. All functions are computed by circuits. Existence of functions with exponential circuit complexity. P is in P/poly.&lt;br /&gt;
 || &lt;br /&gt;
|-&lt;br /&gt;
 || 28.09 ||  Complexity class NP. Examples. Inclusions between P, NP and PSPACE. Non-deterministic TMs. Another definition of NP. Polynomial reductions, their properties. NP-hardness and NP-completeness, their properties.  ||&lt;br /&gt;
|-&lt;br /&gt;
 || 05.10 || Proving NP-hardness by reduction from an NP-complete problem. Examples of NP-complete problems. || &lt;br /&gt;
|-&lt;br /&gt;
 || 12.10 || Cook–Levin theorem. ||&lt;br /&gt;
|-&lt;br /&gt;
 || 26.10 || Space complexity. ||&lt;br /&gt;
|- &lt;br /&gt;
|| 02.11 || Oracle computation definitions. There exists an oracle &#039;&#039;A&#039;&#039; for which P&amp;lt;sup&amp;gt;&#039;&#039;A&#039;&#039;&amp;lt;/sup&amp;gt; = NP&amp;lt;sup&amp;gt;&#039;&#039;A&#039;&#039;&amp;lt;/sup&amp;gt;. There is an oracle B such that P&amp;lt;sup&amp;gt;&#039;&#039;B&#039;&#039;&amp;lt;/sup&amp;gt; is not equal to NP&amp;lt;sup&amp;gt;&#039;&#039;B&#039;&#039;&amp;lt;/sup&amp;gt;. ||&lt;br /&gt;
|-&lt;br /&gt;
 || 09.11 || Probabilistic computation. Probabilistic machines, the class BPP, invariance of the definition BPP for different thresholds, RP, coRP, PP, ZPP. BPP is in P/poly. || &lt;br /&gt;
|-&lt;br /&gt;
 || 16.11 ||  Streaming algorithms: finding the majority element, computation of the moment &#039;&#039;F&#039;&#039;&amp;lt;sub&amp;gt;2&amp;lt;/sub&amp;gt; in logarithmic space. ||&lt;br /&gt;
|-&lt;br /&gt;
 || 23.11 || Finding the frequent items in streams of data: SpaceSaving and Count-Min Sketch. ||&lt;br /&gt;
|-&lt;br /&gt;
 || 30.11 || Approximation algorithms. Approximate solutions for Vertex Cover, Weighted Vertex Cover, and TSP. ||&lt;br /&gt;
 &lt;br /&gt;
|-&lt;br /&gt;
 || 07.12 || Colloquium ||&lt;br /&gt;
|-&lt;br /&gt;
 || 14.12 || Complexity of clustering: an exact algorithm for maximising the inter-cluster distance and an approximate algorithm for minimising the intra-class distance.&lt;br /&gt;
 || &lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
= Office hours =&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
|-&lt;br /&gt;
!  Person !! Monday !! Tuesday !! Wednesday !! Thursday !! Friday &lt;br /&gt;
|-&lt;br /&gt;
|  [https://www.hse.ru/en/org/persons/160550073 Bruno Bauwens] ||  || ||  ||  || &lt;br /&gt;
|-&lt;br /&gt;
|  [https://www.hse.ru/en/staff/obiedkov Sergei Obiedkov], T915, [https://zoom.us/j/99663354582?pwd=K1B5R3NXWEhWbFozR2lqMkFWYW5Ydz09 Zoom] ||  ||  || 16:30–18:00 || 16:30–18:00 ||  &lt;br /&gt;
|}&lt;/div&gt;</summary>
		<author><name>.obj</name></author>
	</entry>
	<entry>
		<id>https://wiki.cs.hse.ru/index.php?title=Theory_of_Computation_2021&amp;diff=56661</id>
		<title>Theory of Computation 2021</title>
		<link rel="alternate" type="text/html" href="https://wiki.cs.hse.ru/index.php?title=Theory_of_Computation_2021&amp;diff=56661"/>
		<updated>2021-08-25T13:05:49Z</updated>

		<summary type="html">&lt;p&gt;.obj: /* Grading */&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;= Classes =&lt;br /&gt;
&lt;br /&gt;
Tuesdays, 14:40–17:40.&lt;br /&gt;
&lt;br /&gt;
= Dates and Deadlines =&lt;br /&gt;
&lt;br /&gt;
Homework 1, deadline: October 5, 14:00 &amp;lt;br&amp;gt;&lt;br /&gt;
Homework 2, deadline: November 2, 14:00 &amp;lt;br&amp;gt;&lt;br /&gt;
Homework 3, deadline: December 7, 14:00 &amp;lt;br&amp;gt;&lt;br /&gt;
Colloquium: December 7, 14:40–17:40&lt;br /&gt;
&lt;br /&gt;
= Grading =&lt;br /&gt;
Colloquium: 0.35&lt;br /&gt;
Homework: 0.35&lt;br /&gt;
Exam: 0.3&lt;br /&gt;
&lt;br /&gt;
= Course Materials =&lt;br /&gt;
&lt;br /&gt;
The main reference is Sipser&#039;s book &amp;quot;Introduction to the theory of computation&amp;quot;, chapters 3, 7–10.&lt;br /&gt;
&lt;br /&gt;
If you need some background in math, consider these two sources:&amp;lt;br&amp;gt;&lt;br /&gt;
[http://www.cs.elte.hu/~lovasz/dmbook.ps Lecture notes: Discrete Mathematics], L. Lovasz, K. Vesztergombi&amp;lt;br&amp;gt;&lt;br /&gt;
[http://rubtsov.su/public/DM-HSE-Draft.pdf Лекции по дискретной математике] (черновик учебника, in Russian)&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
|-&lt;br /&gt;
! Date !! Summary !! Problem list&lt;br /&gt;
|-&lt;br /&gt;
 || 07.09 || Turing machines, multitape Turing machines, connection between them. Universal Turing machine. Examples. Time and space complexity. Complexity classes P, PSPACE, EXP. ||&lt;br /&gt;
|-&lt;br /&gt;
|| 14.09 ||  Time and space hierarchy theorem. Time and space constructible functions. ||&lt;br /&gt;
|-&lt;br /&gt;
 || 21.09 || Circuit complexity. Examples. All functions are computed by circuits. Existence of functions with exponential circuit complexity. P is in P/poly.&lt;br /&gt;
 || &lt;br /&gt;
|-&lt;br /&gt;
 || 28.09 ||  Complexity class NP. Examples. Inclusions between P, NP and PSPACE. Non-deterministic TMs. Another definition of NP. Polynomial reductions, their properties. NP-hardness and NP-completeness, their properties.  ||&lt;br /&gt;
|-&lt;br /&gt;
 || 05.10 || Proving NP-hardness by reduction from an NP-complete problem. Examples of NP-complete problems. || &lt;br /&gt;
|-&lt;br /&gt;
 || 12.10 || Cook–Levin theorem. ||&lt;br /&gt;
|-&lt;br /&gt;
 || 26.10 || Space complexity. ||&lt;br /&gt;
|- &lt;br /&gt;
|| 02.11 || Oracle computation definitions. There exists an oracle &#039;&#039;A&#039;&#039; for which P&amp;lt;sup&amp;gt;&#039;&#039;A&#039;&#039;&amp;lt;/sup&amp;gt; = NP&amp;lt;sup&amp;gt;&#039;&#039;A&#039;&#039;&amp;lt;/sup&amp;gt;. There is an oracle B such that P&amp;lt;sup&amp;gt;&#039;&#039;B&#039;&#039;&amp;lt;/sup&amp;gt; is not equal to NP&amp;lt;sup&amp;gt;&#039;&#039;B&#039;&#039;&amp;lt;/sup&amp;gt;. ||&lt;br /&gt;
|-&lt;br /&gt;
 || 09.11 || Probabilistic computation. Probabilistic machines, the class BPP, invariance of the definition BPP for different thresholds, RP, coRP, PP, ZPP. BPP is in P/poly. || &lt;br /&gt;
|-&lt;br /&gt;
 || 16.11 ||  Streaming algorithms: finding the majority element, computation of the moment &#039;&#039;F&#039;&#039;&amp;lt;sub&amp;gt;2&amp;lt;/sub&amp;gt; in logarithmic space. ||&lt;br /&gt;
|-&lt;br /&gt;
 || 23.11 || Finding the frequent items in streams of data: SpaceSaving and Count-Min Sketch. ||&lt;br /&gt;
|-&lt;br /&gt;
 || 30.11 || Approximation algorithms. Approximate solutions for Vertex Cover, Weighted Vertex Cover, and TSP. ||&lt;br /&gt;
 &lt;br /&gt;
|-&lt;br /&gt;
 || 07.12 || Colloquium ||&lt;br /&gt;
|-&lt;br /&gt;
 || 14.12 || Complexity of clustering: an exact algorithm for maximising the inter-cluster distance and an approximate algorithm for minimising the intra-class distance.&lt;br /&gt;
 || &lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
= Office hours =&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
|-&lt;br /&gt;
!  Person !! Monday !! Tuesday !! Wednesday !! Thursday !! Friday &lt;br /&gt;
|-&lt;br /&gt;
|  [https://www.hse.ru/en/org/persons/160550073 Bruno Bauwens] ||  || ||  ||  || &lt;br /&gt;
|-&lt;br /&gt;
|  [https://www.hse.ru/en/staff/obiedkov Sergei Obiedkov], T915, [https://zoom.us/j/99663354582?pwd=K1B5R3NXWEhWbFozR2lqMkFWYW5Ydz09 Zoom] ||  ||  || 16:30–18:00 || 16:30–18:00 ||  &lt;br /&gt;
|}&lt;/div&gt;</summary>
		<author><name>.obj</name></author>
	</entry>
	<entry>
		<id>https://wiki.cs.hse.ru/index.php?title=Theory_of_Computation_2021&amp;diff=56660</id>
		<title>Theory of Computation 2021</title>
		<link rel="alternate" type="text/html" href="https://wiki.cs.hse.ru/index.php?title=Theory_of_Computation_2021&amp;diff=56660"/>
		<updated>2021-08-25T13:05:20Z</updated>

		<summary type="html">&lt;p&gt;.obj: /* Course Materials */&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;= Classes =&lt;br /&gt;
&lt;br /&gt;
Tuesdays, 14:40–17:40.&lt;br /&gt;
&lt;br /&gt;
= Dates and Deadlines =&lt;br /&gt;
&lt;br /&gt;
Homework 1, deadline: October 5, 14:00 &amp;lt;br&amp;gt;&lt;br /&gt;
Homework 2, deadline: November 2, 14:00 &amp;lt;br&amp;gt;&lt;br /&gt;
Homework 3, deadline: December 7, 14:00 &amp;lt;br&amp;gt;&lt;br /&gt;
Colloquium: December 7, 14:40–17:40&lt;br /&gt;
&lt;br /&gt;
= Grading =&lt;br /&gt;
Colloquium: 0.35&lt;br /&gt;
&lt;br /&gt;
Homework: 0.35&lt;br /&gt;
&lt;br /&gt;
Exam: 0.3&lt;br /&gt;
&lt;br /&gt;
= Course Materials =&lt;br /&gt;
&lt;br /&gt;
The main reference is Sipser&#039;s book &amp;quot;Introduction to the theory of computation&amp;quot;, chapters 3, 7–10.&lt;br /&gt;
&lt;br /&gt;
If you need some background in math, consider these two sources:&amp;lt;br&amp;gt;&lt;br /&gt;
[http://www.cs.elte.hu/~lovasz/dmbook.ps Lecture notes: Discrete Mathematics], L. Lovasz, K. Vesztergombi&amp;lt;br&amp;gt;&lt;br /&gt;
[http://rubtsov.su/public/DM-HSE-Draft.pdf Лекции по дискретной математике] (черновик учебника, in Russian)&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
|-&lt;br /&gt;
! Date !! Summary !! Problem list&lt;br /&gt;
|-&lt;br /&gt;
 || 07.09 || Turing machines, multitape Turing machines, connection between them. Universal Turing machine. Examples. Time and space complexity. Complexity classes P, PSPACE, EXP. ||&lt;br /&gt;
|-&lt;br /&gt;
|| 14.09 ||  Time and space hierarchy theorem. Time and space constructible functions. ||&lt;br /&gt;
|-&lt;br /&gt;
 || 21.09 || Circuit complexity. Examples. All functions are computed by circuits. Existence of functions with exponential circuit complexity. P is in P/poly.&lt;br /&gt;
 || &lt;br /&gt;
|-&lt;br /&gt;
 || 28.09 ||  Complexity class NP. Examples. Inclusions between P, NP and PSPACE. Non-deterministic TMs. Another definition of NP. Polynomial reductions, their properties. NP-hardness and NP-completeness, their properties.  ||&lt;br /&gt;
|-&lt;br /&gt;
 || 05.10 || Proving NP-hardness by reduction from an NP-complete problem. Examples of NP-complete problems. || &lt;br /&gt;
|-&lt;br /&gt;
 || 12.10 || Cook–Levin theorem. ||&lt;br /&gt;
|-&lt;br /&gt;
 || 26.10 || Space complexity. ||&lt;br /&gt;
|- &lt;br /&gt;
|| 02.11 || Oracle computation definitions. There exists an oracle &#039;&#039;A&#039;&#039; for which P&amp;lt;sup&amp;gt;&#039;&#039;A&#039;&#039;&amp;lt;/sup&amp;gt; = NP&amp;lt;sup&amp;gt;&#039;&#039;A&#039;&#039;&amp;lt;/sup&amp;gt;. There is an oracle B such that P&amp;lt;sup&amp;gt;&#039;&#039;B&#039;&#039;&amp;lt;/sup&amp;gt; is not equal to NP&amp;lt;sup&amp;gt;&#039;&#039;B&#039;&#039;&amp;lt;/sup&amp;gt;. ||&lt;br /&gt;
|-&lt;br /&gt;
 || 09.11 || Probabilistic computation. Probabilistic machines, the class BPP, invariance of the definition BPP for different thresholds, RP, coRP, PP, ZPP. BPP is in P/poly. || &lt;br /&gt;
|-&lt;br /&gt;
 || 16.11 ||  Streaming algorithms: finding the majority element, computation of the moment &#039;&#039;F&#039;&#039;&amp;lt;sub&amp;gt;2&amp;lt;/sub&amp;gt; in logarithmic space. ||&lt;br /&gt;
|-&lt;br /&gt;
 || 23.11 || Finding the frequent items in streams of data: SpaceSaving and Count-Min Sketch. ||&lt;br /&gt;
|-&lt;br /&gt;
 || 30.11 || Approximation algorithms. Approximate solutions for Vertex Cover, Weighted Vertex Cover, and TSP. ||&lt;br /&gt;
 &lt;br /&gt;
|-&lt;br /&gt;
 || 07.12 || Colloquium ||&lt;br /&gt;
|-&lt;br /&gt;
 || 14.12 || Complexity of clustering: an exact algorithm for maximising the inter-cluster distance and an approximate algorithm for minimising the intra-class distance.&lt;br /&gt;
 || &lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
= Office hours =&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
|-&lt;br /&gt;
!  Person !! Monday !! Tuesday !! Wednesday !! Thursday !! Friday &lt;br /&gt;
|-&lt;br /&gt;
|  [https://www.hse.ru/en/org/persons/160550073 Bruno Bauwens] ||  || ||  ||  || &lt;br /&gt;
|-&lt;br /&gt;
|  [https://www.hse.ru/en/staff/obiedkov Sergei Obiedkov], T915, [https://zoom.us/j/99663354582?pwd=K1B5R3NXWEhWbFozR2lqMkFWYW5Ydz09 Zoom] ||  ||  || 16:30–18:00 || 16:30–18:00 ||  &lt;br /&gt;
|}&lt;/div&gt;</summary>
		<author><name>.obj</name></author>
	</entry>
	<entry>
		<id>https://wiki.cs.hse.ru/index.php?title=Theory_of_Computation_2021&amp;diff=56659</id>
		<title>Theory of Computation 2021</title>
		<link rel="alternate" type="text/html" href="https://wiki.cs.hse.ru/index.php?title=Theory_of_Computation_2021&amp;diff=56659"/>
		<updated>2021-08-25T13:04:48Z</updated>

		<summary type="html">&lt;p&gt;.obj: /* Grading */&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;= Classes =&lt;br /&gt;
&lt;br /&gt;
Tuesdays, 14:40–17:40.&lt;br /&gt;
&lt;br /&gt;
= Dates and Deadlines =&lt;br /&gt;
&lt;br /&gt;
Homework 1, deadline: October 5, 14:00 &amp;lt;br&amp;gt;&lt;br /&gt;
Homework 2, deadline: November 2, 14:00 &amp;lt;br&amp;gt;&lt;br /&gt;
Homework 3, deadline: December 7, 14:00 &amp;lt;br&amp;gt;&lt;br /&gt;
Colloquium: December 7, 14:40–17:40&lt;br /&gt;
&lt;br /&gt;
= Grading =&lt;br /&gt;
Colloquium: 0.35&lt;br /&gt;
&lt;br /&gt;
Homework: 0.35&lt;br /&gt;
&lt;br /&gt;
Exam: 0.3&lt;br /&gt;
&lt;br /&gt;
= Course Materials =&lt;br /&gt;
&lt;br /&gt;
The main reference is Sipser&#039;s book &amp;quot;Introduction to the theory of computation&amp;quot; Chapters 3, 7–10.&lt;br /&gt;
&lt;br /&gt;
If you need some background in math, consider these two sources:&amp;lt;br&amp;gt;&lt;br /&gt;
[http://www.cs.elte.hu/~lovasz/dmbook.ps Lecture notes: Discrete Mathematics], L. Lovasz, K. Vesztergombi&amp;lt;br&amp;gt;&lt;br /&gt;
[http://rubtsov.su/public/DM-HSE-Draft.pdf Лекции по дискретной математике] (черновик учебника, in Russian)&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
|-&lt;br /&gt;
! Date !! Summary !! Problem list&lt;br /&gt;
|-&lt;br /&gt;
 || 07.09 || Turing machines, multitape Turing machines, connection between them. Universal Turing machine. Examples. Time and space complexity. Complexity classes P, PSPACE, EXP. ||&lt;br /&gt;
|-&lt;br /&gt;
|| 14.09 ||  Time and space hierarchy theorem. Time and space constructible functions. ||&lt;br /&gt;
|-&lt;br /&gt;
 || 21.09 || Circuit complexity. Examples. All functions are computed by circuits. Existence of functions with exponential circuit complexity. P is in P/poly.&lt;br /&gt;
 || &lt;br /&gt;
|-&lt;br /&gt;
 || 28.09 ||  Complexity class NP. Examples. Inclusions between P, NP and PSPACE. Non-deterministic TMs. Another definition of NP. Polynomial reductions, their properties. NP-hardness and NP-completeness, their properties.  ||&lt;br /&gt;
|-&lt;br /&gt;
 || 05.10 || Proving NP-hardness by reduction from an NP-complete problem. Examples of NP-complete problems. || &lt;br /&gt;
|-&lt;br /&gt;
 || 12.10 || Cook–Levin theorem. ||&lt;br /&gt;
|-&lt;br /&gt;
 || 26.10 || Space complexity. ||&lt;br /&gt;
|- &lt;br /&gt;
|| 02.11 || Oracle computation definitions. There exists an oracle &#039;&#039;A&#039;&#039; for which P&amp;lt;sup&amp;gt;&#039;&#039;A&#039;&#039;&amp;lt;/sup&amp;gt; = NP&amp;lt;sup&amp;gt;&#039;&#039;A&#039;&#039;&amp;lt;/sup&amp;gt;. There is an oracle B such that P&amp;lt;sup&amp;gt;&#039;&#039;B&#039;&#039;&amp;lt;/sup&amp;gt; is not equal to NP&amp;lt;sup&amp;gt;&#039;&#039;B&#039;&#039;&amp;lt;/sup&amp;gt;. ||&lt;br /&gt;
|-&lt;br /&gt;
 || 09.11 || Probabilistic computation. Probabilistic machines, the class BPP, invariance of the definition BPP for different thresholds, RP, coRP, PP, ZPP. BPP is in P/poly. || &lt;br /&gt;
|-&lt;br /&gt;
 || 16.11 ||  Streaming algorithms: finding the majority element, computation of the moment &#039;&#039;F&#039;&#039;&amp;lt;sub&amp;gt;2&amp;lt;/sub&amp;gt; in logarithmic space. ||&lt;br /&gt;
|-&lt;br /&gt;
 || 23.11 || Finding the frequent items in streams of data: SpaceSaving and Count-Min Sketch. ||&lt;br /&gt;
|-&lt;br /&gt;
 || 30.11 || Approximation algorithms. Approximate solutions for Vertex Cover, Weighted Vertex Cover, and TSP. ||&lt;br /&gt;
 &lt;br /&gt;
|-&lt;br /&gt;
 || 07.12 || Colloquium ||&lt;br /&gt;
|-&lt;br /&gt;
 || 14.12 || Complexity of clustering: an exact algorithm for maximising the inter-cluster distance and an approximate algorithm for minimising the intra-class distance.&lt;br /&gt;
 || &lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
= Office hours =&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
|-&lt;br /&gt;
!  Person !! Monday !! Tuesday !! Wednesday !! Thursday !! Friday &lt;br /&gt;
|-&lt;br /&gt;
|  [https://www.hse.ru/en/org/persons/160550073 Bruno Bauwens] ||  || ||  ||  || &lt;br /&gt;
|-&lt;br /&gt;
|  [https://www.hse.ru/en/staff/obiedkov Sergei Obiedkov], T915, [https://zoom.us/j/99663354582?pwd=K1B5R3NXWEhWbFozR2lqMkFWYW5Ydz09 Zoom] ||  ||  || 16:30–18:00 || 16:30–18:00 ||  &lt;br /&gt;
|}&lt;/div&gt;</summary>
		<author><name>.obj</name></author>
	</entry>
	<entry>
		<id>https://wiki.cs.hse.ru/index.php?title=Theory_of_Computation_2021&amp;diff=56658</id>
		<title>Theory of Computation 2021</title>
		<link rel="alternate" type="text/html" href="https://wiki.cs.hse.ru/index.php?title=Theory_of_Computation_2021&amp;diff=56658"/>
		<updated>2021-08-25T13:04:40Z</updated>

		<summary type="html">&lt;p&gt;.obj: &lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;= Classes =&lt;br /&gt;
&lt;br /&gt;
Tuesdays, 14:40–17:40.&lt;br /&gt;
&lt;br /&gt;
= Dates and Deadlines =&lt;br /&gt;
&lt;br /&gt;
Homework 1, deadline: October 5, 14:00 &amp;lt;br&amp;gt;&lt;br /&gt;
Homework 2, deadline: November 2, 14:00 &amp;lt;br&amp;gt;&lt;br /&gt;
Homework 3, deadline: December 7, 14:00 &amp;lt;br&amp;gt;&lt;br /&gt;
Colloquium: December 7, 14:40–17:40&lt;br /&gt;
&lt;br /&gt;
= Grading =&lt;br /&gt;
Colloquium: 0.35&lt;br /&gt;
&lt;br /&gt;
Homework: 0.35&lt;br /&gt;
&lt;br /&gt;
Written exam: 0.3&lt;br /&gt;
&lt;br /&gt;
= Course Materials =&lt;br /&gt;
&lt;br /&gt;
The main reference is Sipser&#039;s book &amp;quot;Introduction to the theory of computation&amp;quot; Chapters 3, 7–10.&lt;br /&gt;
&lt;br /&gt;
If you need some background in math, consider these two sources:&amp;lt;br&amp;gt;&lt;br /&gt;
[http://www.cs.elte.hu/~lovasz/dmbook.ps Lecture notes: Discrete Mathematics], L. Lovasz, K. Vesztergombi&amp;lt;br&amp;gt;&lt;br /&gt;
[http://rubtsov.su/public/DM-HSE-Draft.pdf Лекции по дискретной математике] (черновик учебника, in Russian)&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
|-&lt;br /&gt;
! Date !! Summary !! Problem list&lt;br /&gt;
|-&lt;br /&gt;
 || 07.09 || Turing machines, multitape Turing machines, connection between them. Universal Turing machine. Examples. Time and space complexity. Complexity classes P, PSPACE, EXP. ||&lt;br /&gt;
|-&lt;br /&gt;
|| 14.09 ||  Time and space hierarchy theorem. Time and space constructible functions. ||&lt;br /&gt;
|-&lt;br /&gt;
 || 21.09 || Circuit complexity. Examples. All functions are computed by circuits. Existence of functions with exponential circuit complexity. P is in P/poly.&lt;br /&gt;
 || &lt;br /&gt;
|-&lt;br /&gt;
 || 28.09 ||  Complexity class NP. Examples. Inclusions between P, NP and PSPACE. Non-deterministic TMs. Another definition of NP. Polynomial reductions, their properties. NP-hardness and NP-completeness, their properties.  ||&lt;br /&gt;
|-&lt;br /&gt;
 || 05.10 || Proving NP-hardness by reduction from an NP-complete problem. Examples of NP-complete problems. || &lt;br /&gt;
|-&lt;br /&gt;
 || 12.10 || Cook–Levin theorem. ||&lt;br /&gt;
|-&lt;br /&gt;
 || 26.10 || Space complexity. ||&lt;br /&gt;
|- &lt;br /&gt;
|| 02.11 || Oracle computation definitions. There exists an oracle &#039;&#039;A&#039;&#039; for which P&amp;lt;sup&amp;gt;&#039;&#039;A&#039;&#039;&amp;lt;/sup&amp;gt; = NP&amp;lt;sup&amp;gt;&#039;&#039;A&#039;&#039;&amp;lt;/sup&amp;gt;. There is an oracle B such that P&amp;lt;sup&amp;gt;&#039;&#039;B&#039;&#039;&amp;lt;/sup&amp;gt; is not equal to NP&amp;lt;sup&amp;gt;&#039;&#039;B&#039;&#039;&amp;lt;/sup&amp;gt;. ||&lt;br /&gt;
|-&lt;br /&gt;
 || 09.11 || Probabilistic computation. Probabilistic machines, the class BPP, invariance of the definition BPP for different thresholds, RP, coRP, PP, ZPP. BPP is in P/poly. || &lt;br /&gt;
|-&lt;br /&gt;
 || 16.11 ||  Streaming algorithms: finding the majority element, computation of the moment &#039;&#039;F&#039;&#039;&amp;lt;sub&amp;gt;2&amp;lt;/sub&amp;gt; in logarithmic space. ||&lt;br /&gt;
|-&lt;br /&gt;
 || 23.11 || Finding the frequent items in streams of data: SpaceSaving and Count-Min Sketch. ||&lt;br /&gt;
|-&lt;br /&gt;
 || 30.11 || Approximation algorithms. Approximate solutions for Vertex Cover, Weighted Vertex Cover, and TSP. ||&lt;br /&gt;
 &lt;br /&gt;
|-&lt;br /&gt;
 || 07.12 || Colloquium ||&lt;br /&gt;
|-&lt;br /&gt;
 || 14.12 || Complexity of clustering: an exact algorithm for maximising the inter-cluster distance and an approximate algorithm for minimising the intra-class distance.&lt;br /&gt;
 || &lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
= Office hours =&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
|-&lt;br /&gt;
!  Person !! Monday !! Tuesday !! Wednesday !! Thursday !! Friday &lt;br /&gt;
|-&lt;br /&gt;
|  [https://www.hse.ru/en/org/persons/160550073 Bruno Bauwens] ||  || ||  ||  || &lt;br /&gt;
|-&lt;br /&gt;
|  [https://www.hse.ru/en/staff/obiedkov Sergei Obiedkov], T915, [https://zoom.us/j/99663354582?pwd=K1B5R3NXWEhWbFozR2lqMkFWYW5Ydz09 Zoom] ||  ||  || 16:30–18:00 || 16:30–18:00 ||  &lt;br /&gt;
|}&lt;/div&gt;</summary>
		<author><name>.obj</name></author>
	</entry>
	<entry>
		<id>https://wiki.cs.hse.ru/index.php?title=Theory_of_Computation_2021&amp;diff=56657</id>
		<title>Theory of Computation 2021</title>
		<link rel="alternate" type="text/html" href="https://wiki.cs.hse.ru/index.php?title=Theory_of_Computation_2021&amp;diff=56657"/>
		<updated>2021-08-25T13:02:58Z</updated>

		<summary type="html">&lt;p&gt;.obj: /* Schedule */&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;== Classes ==&lt;br /&gt;
&lt;br /&gt;
Tuesdays, 14:40–17:40.&lt;br /&gt;
&lt;br /&gt;
== Dates and Deadlines ==&lt;br /&gt;
&lt;br /&gt;
Homework 1, deadline: October 5, 14:00 &amp;lt;br&amp;gt;&lt;br /&gt;
Homework 2, deadline: November 2, 14:00 &amp;lt;br&amp;gt;&lt;br /&gt;
Homework 3, deadline: December 7, 14:00 &amp;lt;br&amp;gt;&lt;br /&gt;
Colloquium: December 7, 14:40–17:40&lt;br /&gt;
&lt;br /&gt;
== Course Materials ==&lt;br /&gt;
&lt;br /&gt;
The main reference is Sipser&#039;s book &amp;quot;Introduction to the theory of computation&amp;quot; Chapters 3, 7–10.&lt;br /&gt;
&lt;br /&gt;
If you need some background in math, consider these two sources:&amp;lt;br&amp;gt;&lt;br /&gt;
[http://www.cs.elte.hu/~lovasz/dmbook.ps Lecture notes: Discrete Mathematics], L. Lovasz, K. Vesztergombi&amp;lt;br&amp;gt;&lt;br /&gt;
[http://rubtsov.su/public/DM-HSE-Draft.pdf Лекции по дискретной математике] (черновик учебника, in Russian)&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
|-&lt;br /&gt;
! Date !! Summary !! Problem list&lt;br /&gt;
|-&lt;br /&gt;
 || 07.09 || Turing machines, multitape Turing machines, connection between them. Universal Turing machine. Examples. Time and space complexity. Complexity classes P, PSPACE, EXP. ||&lt;br /&gt;
|-&lt;br /&gt;
|| 14.09 ||  Time and space hierarchy theorem. Time and space constructible functions. ||&lt;br /&gt;
|-&lt;br /&gt;
 || 21.09 || Circuit complexity. Examples. All functions are computed by circuits. Existence of functions with exponential circuit complexity. P is in P/poly.&lt;br /&gt;
 || &lt;br /&gt;
|-&lt;br /&gt;
 || 28.09 ||  Complexity class NP. Examples. Inclusions between P, NP and PSPACE. Non-deterministic TMs. Another definition of NP. Polynomial reductions, their properties. NP-hardness and NP-completeness, their properties.  ||&lt;br /&gt;
|-&lt;br /&gt;
 || 05.10 || Proving NP-hardness by reduction from an NP-complete problem. Examples of NP-complete problems. || &lt;br /&gt;
|-&lt;br /&gt;
 || 12.10 || Cook–Levin theorem. ||&lt;br /&gt;
|-&lt;br /&gt;
 || 26.10 || Space complexity. ||&lt;br /&gt;
|- &lt;br /&gt;
|| 02.11 || Oracle computation definitions. There exists an oracle &#039;&#039;A&#039;&#039; for which P&amp;lt;sup&amp;gt;&#039;&#039;A&#039;&#039;&amp;lt;/sup&amp;gt; = NP&amp;lt;sup&amp;gt;&#039;&#039;A&#039;&#039;&amp;lt;/sup&amp;gt;. There is an oracle B such that P&amp;lt;sup&amp;gt;&#039;&#039;B&#039;&#039;&amp;lt;/sup&amp;gt; is not equal to NP&amp;lt;sup&amp;gt;&#039;&#039;B&#039;&#039;&amp;lt;/sup&amp;gt;. ||&lt;br /&gt;
|-&lt;br /&gt;
 || 09.11 || Probabilistic computation. Probabilistic machines, the class BPP, invariance of the definition BPP for different thresholds, RP, coRP, PP, ZPP. BPP is in P/poly. || &lt;br /&gt;
|-&lt;br /&gt;
 || 16.11 ||  Streaming algorithms: finding the majority element, computation of the moment &#039;&#039;F&#039;&#039;&amp;lt;sub&amp;gt;2&amp;lt;/sub&amp;gt; in logarithmic space. ||&lt;br /&gt;
|-&lt;br /&gt;
 || 23.11 || Finding the frequent items in streams of data: SpaceSaving and Count-Min Sketch. ||&lt;br /&gt;
|-&lt;br /&gt;
 || 30.11 || Approximation algorithms. Approximate solutions for Vertex Cover, Weighted Vertex Cover, and TSP. ||&lt;br /&gt;
 &lt;br /&gt;
|-&lt;br /&gt;
 || 07.12 || Colloquium ||&lt;br /&gt;
|-&lt;br /&gt;
 || 14.12 || Complexity of clustering: an exact algorithm for maximising the inter-cluster distance and an approximate algorithm for minimising the intra-class distance.&lt;br /&gt;
 || &lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
== Office hours ==&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
|-&lt;br /&gt;
!  Person !! Monday !! Tuesday !! Wednesday !! Thursday !! Friday &lt;br /&gt;
|-&lt;br /&gt;
|  [https://www.hse.ru/en/org/persons/160550073 Bruno Bauwens] ||  || ||  ||  || &lt;br /&gt;
|-&lt;br /&gt;
|  [https://www.hse.ru/en/staff/obiedkov Sergei Obiedkov], T915, [https://zoom.us/j/99663354582?pwd=K1B5R3NXWEhWbFozR2lqMkFWYW5Ydz09 Zoom] ||  ||  || 16:30–18:00 || 16:30–18:00 ||  &lt;br /&gt;
|}&lt;/div&gt;</summary>
		<author><name>.obj</name></author>
	</entry>
	<entry>
		<id>https://wiki.cs.hse.ru/index.php?title=Theory_of_Computation_2021&amp;diff=56656</id>
		<title>Theory of Computation 2021</title>
		<link rel="alternate" type="text/html" href="https://wiki.cs.hse.ru/index.php?title=Theory_of_Computation_2021&amp;diff=56656"/>
		<updated>2021-08-25T13:01:41Z</updated>

		<summary type="html">&lt;p&gt;.obj: /* General Information */&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;== Schedule ==&lt;br /&gt;
&lt;br /&gt;
Classes: Tuesdays, 14:40–17:40.&lt;br /&gt;
&lt;br /&gt;
== Dates and Deadlines ==&lt;br /&gt;
&lt;br /&gt;
Homework 1, deadline: October 5, 14:00 &amp;lt;br&amp;gt;&lt;br /&gt;
Homework 2, deadline: November 2, 14:00 &amp;lt;br&amp;gt;&lt;br /&gt;
Homework 3, deadline: December 7, 14:00 &amp;lt;br&amp;gt;&lt;br /&gt;
Colloquium: December 7, 14:40–17:40&lt;br /&gt;
&lt;br /&gt;
== Course Materials ==&lt;br /&gt;
&lt;br /&gt;
The main reference is Sipser&#039;s book &amp;quot;Introduction to the theory of computation&amp;quot; Chapters 3, 7–10.&lt;br /&gt;
&lt;br /&gt;
If you need some background in math, consider these two sources:&amp;lt;br&amp;gt;&lt;br /&gt;
[http://www.cs.elte.hu/~lovasz/dmbook.ps Lecture notes: Discrete Mathematics], L. Lovasz, K. Vesztergombi&amp;lt;br&amp;gt;&lt;br /&gt;
[http://rubtsov.su/public/DM-HSE-Draft.pdf Лекции по дискретной математике] (черновик учебника, in Russian)&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
|-&lt;br /&gt;
! Date !! Summary !! Problem list&lt;br /&gt;
|-&lt;br /&gt;
 || 07.09 || Turing machines, multitape Turing machines, connection between them. Universal Turing machine. Examples. Time and space complexity. Complexity classes P, PSPACE, EXP. ||&lt;br /&gt;
|-&lt;br /&gt;
|| 14.09 ||  Time and space hierarchy theorem. Time and space constructible functions. ||&lt;br /&gt;
|-&lt;br /&gt;
 || 21.09 || Circuit complexity. Examples. All functions are computed by circuits. Existence of functions with exponential circuit complexity. P is in P/poly.&lt;br /&gt;
 || &lt;br /&gt;
|-&lt;br /&gt;
 || 28.09 ||  Complexity class NP. Examples. Inclusions between P, NP and PSPACE. Non-deterministic TMs. Another definition of NP. Polynomial reductions, their properties. NP-hardness and NP-completeness, their properties.  ||&lt;br /&gt;
|-&lt;br /&gt;
 || 05.10 || Proving NP-hardness by reduction from an NP-complete problem. Examples of NP-complete problems. || &lt;br /&gt;
|-&lt;br /&gt;
 || 12.10 || Cook–Levin theorem. ||&lt;br /&gt;
|-&lt;br /&gt;
 || 26.10 || Space complexity. ||&lt;br /&gt;
|- &lt;br /&gt;
|| 02.11 || Oracle computation definitions. There exists an oracle &#039;&#039;A&#039;&#039; for which P&amp;lt;sup&amp;gt;&#039;&#039;A&#039;&#039;&amp;lt;/sup&amp;gt; = NP&amp;lt;sup&amp;gt;&#039;&#039;A&#039;&#039;&amp;lt;/sup&amp;gt;. There is an oracle B such that P&amp;lt;sup&amp;gt;&#039;&#039;B&#039;&#039;&amp;lt;/sup&amp;gt; is not equal to NP&amp;lt;sup&amp;gt;&#039;&#039;B&#039;&#039;&amp;lt;/sup&amp;gt;. ||&lt;br /&gt;
|-&lt;br /&gt;
 || 09.11 || Probabilistic computation. Probabilistic machines, the class BPP, invariance of the definition BPP for different thresholds, RP, coRP, PP, ZPP. BPP is in P/poly. || &lt;br /&gt;
|-&lt;br /&gt;
 || 16.11 ||  Streaming algorithms: finding the majority element, computation of the moment &#039;&#039;F&#039;&#039;&amp;lt;sub&amp;gt;2&amp;lt;/sub&amp;gt; in logarithmic space. ||&lt;br /&gt;
|-&lt;br /&gt;
 || 23.11 || Finding the frequent items in streams of data: SpaceSaving and Count-Min Sketch. ||&lt;br /&gt;
|-&lt;br /&gt;
 || 30.11 || Approximation algorithms. Approximate solutions for Vertex Cover, Weighted Vertex Cover, and TSP. ||&lt;br /&gt;
 &lt;br /&gt;
|-&lt;br /&gt;
 || 07.12 || Colloquium ||&lt;br /&gt;
|-&lt;br /&gt;
 || 14.12 || Complexity of clustering: an exact algorithm for maximising the inter-cluster distance and an approximate algorithm for minimising the intra-class distance.&lt;br /&gt;
 || &lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
== Office hours ==&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
|-&lt;br /&gt;
!  Person !! Monday !! Tuesday !! Wednesday !! Thursday !! Friday &lt;br /&gt;
|-&lt;br /&gt;
|  [https://www.hse.ru/en/org/persons/160550073 Bruno Bauwens] ||  || ||  ||  || &lt;br /&gt;
|-&lt;br /&gt;
|  [https://www.hse.ru/en/staff/obiedkov Sergei Obiedkov], T915, [https://zoom.us/j/99663354582?pwd=K1B5R3NXWEhWbFozR2lqMkFWYW5Ydz09 Zoom] ||  ||  || 16:30–18:00 || 16:30–18:00 ||  &lt;br /&gt;
|}&lt;/div&gt;</summary>
		<author><name>.obj</name></author>
	</entry>
	<entry>
		<id>https://wiki.cs.hse.ru/index.php?title=Theory_of_Computation_2021&amp;diff=56655</id>
		<title>Theory of Computation 2021</title>
		<link rel="alternate" type="text/html" href="https://wiki.cs.hse.ru/index.php?title=Theory_of_Computation_2021&amp;diff=56655"/>
		<updated>2021-08-25T12:49:07Z</updated>

		<summary type="html">&lt;p&gt;.obj: /* Office hours */&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;== General Information ==&lt;br /&gt;
&lt;br /&gt;
Classes: Tuesdays, 14:40–17:40.&lt;br /&gt;
&lt;br /&gt;
== Dates and Deadlines ==&lt;br /&gt;
&lt;br /&gt;
Homework 1, deadline: October 5, 14:00 &amp;lt;br&amp;gt;&lt;br /&gt;
Homework 2, deadline: November 2, 14:00 &amp;lt;br&amp;gt;&lt;br /&gt;
Homework 3, deadline: December 7, 14:00 &amp;lt;br&amp;gt;&lt;br /&gt;
Colloquium: December 7, 14:40–17:40&lt;br /&gt;
&lt;br /&gt;
== Course Materials ==&lt;br /&gt;
&lt;br /&gt;
The main reference is Sipser&#039;s book &amp;quot;Introduction to the theory of computation&amp;quot; Chapters 3, 7–10.&lt;br /&gt;
&lt;br /&gt;
If you need some background in math, consider these two sources:&amp;lt;br&amp;gt;&lt;br /&gt;
[http://www.cs.elte.hu/~lovasz/dmbook.ps Lecture notes: Discrete Mathematics], L. Lovasz, K. Vesztergombi&amp;lt;br&amp;gt;&lt;br /&gt;
[http://rubtsov.su/public/DM-HSE-Draft.pdf Лекции по дискретной математике] (черновик учебника, in Russian)&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
|-&lt;br /&gt;
! Date !! Summary !! Problem list&lt;br /&gt;
|-&lt;br /&gt;
 || 07.09 || Turing machines, multitape Turing machines, connection between them. Universal Turing machine. Examples. Time and space complexity. Complexity classes P, PSPACE, EXP. ||&lt;br /&gt;
|-&lt;br /&gt;
|| 14.09 ||  Time and space hierarchy theorem. Time and space constructible functions. ||&lt;br /&gt;
|-&lt;br /&gt;
 || 21.09 || Circuit complexity. Examples. All functions are computed by circuits. Existence of functions with exponential circuit complexity. P is in P/poly.&lt;br /&gt;
 || &lt;br /&gt;
|-&lt;br /&gt;
 || 28.09 ||  Complexity class NP. Examples. Inclusions between P, NP and PSPACE. Non-deterministic TMs. Another definition of NP. Polynomial reductions, their properties. NP-hardness and NP-completeness, their properties.  ||&lt;br /&gt;
|-&lt;br /&gt;
 || 05.10 || Proving NP-hardness by reduction from an NP-complete problem. Examples of NP-complete problems. || &lt;br /&gt;
|-&lt;br /&gt;
 || 12.10 || Cook–Levin theorem. ||&lt;br /&gt;
|-&lt;br /&gt;
 || 26.10 || Space complexity. ||&lt;br /&gt;
|- &lt;br /&gt;
|| 02.11 || Oracle computation definitions. There exists an oracle &#039;&#039;A&#039;&#039; for which P&amp;lt;sup&amp;gt;&#039;&#039;A&#039;&#039;&amp;lt;/sup&amp;gt; = NP&amp;lt;sup&amp;gt;&#039;&#039;A&#039;&#039;&amp;lt;/sup&amp;gt;. There is an oracle B such that P&amp;lt;sup&amp;gt;&#039;&#039;B&#039;&#039;&amp;lt;/sup&amp;gt; is not equal to NP&amp;lt;sup&amp;gt;&#039;&#039;B&#039;&#039;&amp;lt;/sup&amp;gt;. ||&lt;br /&gt;
|-&lt;br /&gt;
 || 09.11 || Probabilistic computation. Probabilistic machines, the class BPP, invariance of the definition BPP for different thresholds, RP, coRP, PP, ZPP. BPP is in P/poly. || &lt;br /&gt;
|-&lt;br /&gt;
 || 16.11 ||  Streaming algorithms: finding the majority element, computation of the moment &#039;&#039;F&#039;&#039;&amp;lt;sub&amp;gt;2&amp;lt;/sub&amp;gt; in logarithmic space. ||&lt;br /&gt;
|-&lt;br /&gt;
 || 23.11 || Finding the frequent items in streams of data: SpaceSaving and Count-Min Sketch. ||&lt;br /&gt;
|-&lt;br /&gt;
 || 30.11 || Approximation algorithms. Approximate solutions for Vertex Cover, Weighted Vertex Cover, and TSP. ||&lt;br /&gt;
 &lt;br /&gt;
|-&lt;br /&gt;
 || 07.12 || Colloquium ||&lt;br /&gt;
|-&lt;br /&gt;
 || 14.12 || Complexity of clustering: an exact algorithm for maximising the inter-cluster distance and an approximate algorithm for minimising the intra-class distance.&lt;br /&gt;
 || &lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
== Office hours ==&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
|-&lt;br /&gt;
!  Person !! Monday !! Tuesday !! Wednesday !! Thursday !! Friday &lt;br /&gt;
|-&lt;br /&gt;
|  [https://www.hse.ru/en/org/persons/160550073 Bruno Bauwens] ||  || ||  ||  || &lt;br /&gt;
|-&lt;br /&gt;
|  [https://www.hse.ru/en/staff/obiedkov Sergei Obiedkov], T915, [https://zoom.us/j/99663354582?pwd=K1B5R3NXWEhWbFozR2lqMkFWYW5Ydz09 Zoom] ||  ||  || 16:30–18:00 || 16:30–18:00 ||  &lt;br /&gt;
|}&lt;/div&gt;</summary>
		<author><name>.obj</name></author>
	</entry>
	<entry>
		<id>https://wiki.cs.hse.ru/index.php?title=Theory_of_computing,_AMI&amp;diff=56654</id>
		<title>Theory of computing, AMI</title>
		<link rel="alternate" type="text/html" href="https://wiki.cs.hse.ru/index.php?title=Theory_of_computing,_AMI&amp;diff=56654"/>
		<updated>2021-08-25T12:48:17Z</updated>

		<summary type="html">&lt;p&gt;.obj: /* Office hours */&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;&lt;br /&gt;
== Exam ==&lt;br /&gt;
&lt;br /&gt;
26 Dec, 13:00–15:40, [https://zoom.us/j/97631222267 Zoom]&lt;br /&gt;
&lt;br /&gt;
The exam consists of 8 questions of the same level as the homework.&lt;br /&gt;
&lt;br /&gt;
You may use all course materials (seminar sheets, Sipser&#039;s book, Noam Nissan&#039;s book, etc). You are not allowed to communicate with other students and to use social network sites like Telegram, Facebook, etc. You may not use your phone except in the end of the exam to submit your work.&lt;br /&gt;
&lt;br /&gt;
You must submit your answers in handwriting (exceptions can be asked at the beginning of the exam) by sending scanned or photographed copies to both lecturers.  &lt;br /&gt;
&lt;br /&gt;
[http://www.mi-ras.ru/~podolskii/files/computability1819/exam171222.pdf sample exam] (3 years ago, not all topics are the same, but questions 1,2,3,7 we have covered)&lt;br /&gt;
&lt;br /&gt;
Please check [https://docs.google.com/spreadsheets/d/1jPl3ZcOEt4v99IhAq0bpfJW9KRTTh3w5KsNZ4NKfDME/edit?usp=sharing All grades] for the results. If you have questions, you can ask them at 11:00 on December 29 via [https://zoom.us/j/97070495314 Zoom].&lt;br /&gt;
&lt;br /&gt;
== General Information ==&lt;br /&gt;
&lt;br /&gt;
Classes: Tuesdays, 13:00–16:00, [https://zoom.us/j/97070495314 Zoom].&lt;br /&gt;
&lt;br /&gt;
First lecture September 8.&lt;br /&gt;
&lt;br /&gt;
[https://www.dropbox.com/s/suzbqo0k37blw2b/grading.pdf?dl=0 Grading]&lt;br /&gt;
&lt;br /&gt;
Please send your homework to the teaching assistant, [mailto:myugolyadkin@edu.hse.ru Maxim Golyadkin].&lt;br /&gt;
&lt;br /&gt;
[https://docs.google.com/spreadsheets/d/1nb4rOB5rGWtKbXRw2RovFdLiRXcKccAFc7VknN0bQIg/edit#gid=0 Grades for the homework]&lt;br /&gt;
&lt;br /&gt;
[https://docs.google.com/spreadsheets/d/1jPl3ZcOEt4v99IhAq0bpfJW9KRTTh3w5KsNZ4NKfDME/edit?usp=sharing All grades]&lt;br /&gt;
&lt;br /&gt;
== Dates and Deadlines ==&lt;br /&gt;
&lt;br /&gt;
Homework 1, deadline: 6 October, before the lecture &amp;lt;br&amp;gt;&lt;br /&gt;
Homework 2, deadline: 3 November, before the lecture &amp;lt;br&amp;gt;&lt;br /&gt;
Homework 3, deadline: 8 December, before the lecture &lt;br /&gt;
&lt;br /&gt;
The lecture starts at 13h, it is not allowed to submit after this time. However, the first time you are less than 24 hours late, the homework will still be graded. &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
== Colloquium ==&lt;br /&gt;
&lt;br /&gt;
Dates: December 15 and 16. Choose your [https://docs.google.com/spreadsheets/d/1v_0RDvsnTRNa4IYSjOir9VYodfzzvAbJ8KHXtyy2K-M/edit#gid=0 time]&amp;lt;br&amp;gt; &lt;br /&gt;
Zoom links: go to the link above&amp;lt;br&amp;gt;&lt;br /&gt;
[https://www.dropbox.com/s/15w8s6dfkxu0cni/col.pdf?dl=0 Rules and questions]&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
== Course Materials ==&lt;br /&gt;
&lt;br /&gt;
In the first 9 lectures, we follow Sipser&#039;s book &amp;quot;Introduction to the theory of computation&amp;quot; Chapters 3, 7, 8, 9 (not Theorem 9.15), and Section 10.2.&lt;br /&gt;
&lt;br /&gt;
If you need some background in math, consider these two sourses:&amp;lt;br&amp;gt;&lt;br /&gt;
[http://www.cs.elte.hu/~lovasz/dmbook.ps Lecture notes: Discrete Mathematics], L. Lovasz, K. Vesztergombi&amp;lt;br&amp;gt;&lt;br /&gt;
[http://rubtsov.su/public/DM-HSE-Draft.pdf Лекции по дискретной математике] (черновик учебника, in Russian)&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
|-&lt;br /&gt;
! Date/Movie !! Summary !! Problem list&lt;br /&gt;
|-&lt;br /&gt;
 || 08.09 || Turing machines, multitape Turing machines, connection between them. Universal Turing machine. Examples. Time and space complexity. Complexity classes P, PSPACE, EXP. ||  [https://www.dropbox.com/s/2qwd0cqe1qhdzve/prob_01.pdf?dl=0 Problem list 1 ]&lt;br /&gt;
|-&lt;br /&gt;
|| 15.09 ||  Time and space hierarchy theorem. Time and space constructible functions. || [https://www.dropbox.com/s/knbvqjuvkuafvlq/prob_02.pdf?dl=0 Problem list 2] &amp;lt;span style=&amp;quot;color:red&amp;quot;&amp;gt;Update 15.09, problem 2.4&amp;lt;/span&amp;gt;&lt;br /&gt;
|-&lt;br /&gt;
 || 22.09 || Complexity class NP. Examples. Inclusions between P, NP and PSPACE. Non-deterministic TMs. Another definition of NP. Polynomial reductions, their properties. NP-hardness and NP-completeness, their properties. &lt;br /&gt;
 || [https://www.dropbox.com/s/9oxj6jxa2a27fk7/prob_03.pdf?dl=0 Problem list 3] &amp;lt;span style=&amp;quot;color:red&amp;quot;&amp;gt;Update 22.09, 3.5 and hint 3.8&amp;lt;/span&amp;gt;&lt;br /&gt;
|-&lt;br /&gt;
 || 29.09 ||  Circuit complexity. Examples. All functions are computed by circuits. Existence of functions with exponential circuit complexity. P is in P/poly.  || [https://www.dropbox.com/s/51am8w6jytz9dad/prob_04.pdf?dl=0 Problem list 4]&lt;br /&gt;
|-&lt;br /&gt;
 || 06.10 || NP-completeness: Circuit-SAT, 3-SAT, IND-SET, BIN-INT-PROG, Clique, Vertex-Cover, Exactly 1-3-SAT, NAE-3-SAT || [https://www.dropbox.com/s/jfbisdyolmhdohl/prob_05.pdf?dl=0 Problem list 5]&lt;br /&gt;
|-&lt;br /&gt;
 || 13.10 || NP-completeness: Subset-SUM, 3COLORING. coNP, completeness of CIRC-TAUT  || [https://www.dropbox.com/s/tzqj7l8il5drhk4/prob_06.pdf?dl=0 Problem list 6]&lt;br /&gt;
|-&lt;br /&gt;
 || [https://zoom.us/rec/share/3LrMJXXTJDAYF2lzH0r33hv336AWBjtufpF6yKdidy4ic6uFvsYEpK7BlZEKFNyV.xYkSb0P6NBjVRsao?startTime=1603793959000 27.10] || Space complexity. Classes L, NL, PSPACE and NPSPACE. Directed Reachability is in SPACE(log&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt; &#039;&#039;n&#039;&#039;). Configuration graph. Inclusions between time and space classes. TQBF problem, its PSPACE-completeness. PSPACE = NPSPACE. NSPACE(&#039;&#039;s&#039;&#039;(&#039;&#039;n&#039;&#039;)) is in SPACE(&#039;&#039;s&#039;&#039;(&#039;&#039;n&#039;&#039;)&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;) for space constructible &#039;&#039;s&#039;&#039;. || [https://www.dropbox.com/s/hlubofza612y6cj/prob_07.pdf?dl=0 Problem list 7]&lt;br /&gt;
|- &lt;br /&gt;
|| [https://zoom.us/rec/share/14xX_cDOu2Gr2fpFFxfmJKEclKNoDr57XCq2gyGqSGmsgilZdrTwyZihBHz6XRmO.OfTjHf0GXEA9Et4H 03.11] || [https://www.dropbox.com/s/5lt1z4qxhksgs15/WCM_def5d.mp4?dl=0 L ⊆ P]. [https://www.dropbox.com/s/rtizfkx2m2ebyec/NLsubsetP.png?dl=0 NL ⊆ P]. [https://www.dropbox.com/s/9jtajtadc8vrgby/reductions.mp4?dl=0 Log-space reductions and NL-completeness]. [https://www.dropbox.com/s/ca86r3h2fvm3q8o/WCM_09830.mp4?dl=0 Path is NL-][https://www.dropbox.com/s/3k5fld05zisqgrp/WCM_df84e.mp4?dl=0 complete] and, [https://www.dropbox.com/s/ko2zmvk31jqm0ma/WCM_03d13.mp4?dl=0 probably, outside L]. [https://www.dropbox.com/s/mhqz2n52hab37zw/WCM_695bc.mp4?dl=0 Class coNL]. [https://www.dropbox.com/s/ul739s45r3palqi/WCM_7ddbe.mp4?dl=0 NL] [https://www.dropbox.com/s/0tqcxf9uzpev711/WCM_65c40.mp4?dl=0 =] [https://www.dropbox.com/s/ecdy6tno88a1ffs/WCM_63463.mp4?dl=0 coNL]. [https://www.dropbox.com/s/hilscsxiicgr6ho/WCM_3c921.mp4?dl=0 Generalised Geography] and [https://www.dropbox.com/s/4tbu304rw7vje4q/WCM_81f5b.mp4?dl=0 Formula Game] are [https://www.dropbox.com/s/xrlz1u4ho2z1u5x/WCM_bc82a.mp4?dl=0 PSPACE-complete]. || [https://www.dropbox.com/s/2i4hj8ilp4exqr2/prob_08.pdf?dl=0 Problem list 8]&lt;br /&gt;
|-&lt;br /&gt;
 || [https://zoom.us/rec/share/XqpUIS7G8bB2TjD4l0XZuGtpLOKdI5ICuyPA3PyMfaxSB0dsjO0x-U-9Yn0QAOcb.nZQA6cqTBv7ytmiP 10.11] || Oracle computation definitions. There exists an oracle &#039;&#039;A&#039;&#039; for which P&amp;lt;sup&amp;gt;&#039;&#039;A&#039;&#039;&amp;lt;/sup&amp;gt; = NP&amp;lt;sup&amp;gt;&#039;&#039;A&#039;&#039;&amp;lt;/sup&amp;gt;. There is an oracle &#039;&#039;B&#039;&#039; such that P&amp;lt;sup&amp;gt;&#039;&#039;B&#039;&#039;&amp;lt;/sup&amp;gt; is not equal to NP&amp;lt;sup&amp;gt;&#039;&#039;B&#039;&#039;&amp;lt;/sup&amp;gt;. || [https://www.dropbox.com/s/8h3a98h938162gz/prob_09.pdf?dl=0 Problem list 9]&lt;br /&gt;
|-&lt;br /&gt;
 || [https://zoom.us/rec/share/Nrq1IvUzofuo5fydjWN64LNjWt6c4Y22oC8kHFF53i3Q4SdYVjWdYjn53h4YlAwI.Py79jFGo7SUOoKV3 17.11] ||  Probabilistic computation. Probabilistic machines, the class BPP, invariance of the definition BPP for different thresholds, RP, coRP, PP, ZPP. BPP is in P/poly. &lt;br /&gt;
 || [https://www.dropbox.com/s/znj3cm1kb70o7px/prob_10.pdf?dl=0 Problem list 10]&lt;br /&gt;
|-&lt;br /&gt;
 || [https://zoom.us/rec/share/O0FgCvpOa1UcFlcGpRsFysaVe87nE9IFfYEK1Nn84VS1IugGncjlQcU55gefVZp8.ejQ1gh2kNiGdAN45 24.11] || Streaming algorithms: finding the majority element, computation of the moment F_2 in logarithmic space.  [http://theory.stanford.edu/~tim/w15/l/l1.pdf Roughgarden&#039;s lecture notes]  &lt;br /&gt;
 || [https://www.dropbox.com/s/vun7309n6qbdo17/prob_11.pdf?dl=0 Problem list 11]&lt;br /&gt;
|-&lt;br /&gt;
 || [https://zoom.us/rec/share/6ez6JQsyBdPjS4JvLi3aAGfvfydLZGJVfD0YFhHl_B5nADRMrY3npHaoC6-MVD-T.j_BzHsk3lNiL8go3 01.12] || Lower-bound for exact and probabilistic computation of F_0 using one-shot communication complexity. Communication protocols. Functions EQ, GT, DISJ. Fooling sets. Combinatorial rectangles. Book: Kushilevitz and Nisan, Communication Complexity, 1997 [https://epdf.pub/communication-complexity.html download]  &lt;br /&gt;
 || [https://www.dropbox.com/s/1qhktxnd95ww146/prob_12.pdf?dl=0 Problem list 12]&lt;br /&gt;
 &lt;br /&gt;
|-&lt;br /&gt;
 || [https://zoom.us/rec/share/dEfCBunsqqsp5ETfuOtGtbcwkfWMmxiHfEjHza2e2sPOybKqR3crQ7guJaVGDdf4.y_FzqoXfKUoztXW4 08.12] || Questions from students P vs NP vs PSPACE || [https://www.dropbox.com/s/00yfmblihuahvoa/prob_13.pdf?dl=0 Problem list 13]&lt;br /&gt;
|-&lt;br /&gt;
 || 15-16.12 || Colloquium.&lt;br /&gt;
 || &lt;br /&gt;
&amp;lt;!--&lt;br /&gt;
Lower bound for randomized 1-shot communication complexity of set disjointness, see Roughgarden&#039;s [http://theory.stanford.edu/~tim/w15/l/l2.pdf lecture notes]). &lt;br /&gt;
|-&lt;br /&gt;
 || 11/12 || Linear programming is in NP, NP-completeness of Hamiltonian path, TQBF as a game, PSPACE-completeness of generalized geography. Various other NP-complete problems. || [https://www.dropbox.com/s/cifs60rf6vpfn3i/prob_14.pdf?dl=0 Problem list 14] &lt;br /&gt;
|-&lt;br /&gt;
 ||---&amp;gt;&lt;br /&gt;
&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
For interested students, we give a few lectures about parameterized complexity. We follow the book [http://parameterized-algorithms.mimuw.edu.pl/parameterized-algorithms.pdf Parameterized algorithms] by Cygan, Marek, Fedor V. Fomin, Łukasz Kowalik, Daniel Lokshtanov, Dániel Marx, Marcin Pilipczuk, Michał Pilipczuk, and Saket Saurabh. Vol. 4, no. 8. Cham: Springer, 2015.&lt;br /&gt;
&lt;br /&gt;
== Office hours ==&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
|-&lt;br /&gt;
!  Person !! Monday !! Tuesday !! Wednesday !! Thursday !! Friday &lt;br /&gt;
|-&lt;br /&gt;
|  [https://www.hse.ru/en/staff/obiedkov Sergei Obiedkov], [https://zoom.us/j/99663354582 Zoom] ||  ||  || 16:30–18:00 || 16:30–18:00 ||  &lt;br /&gt;
|-&lt;br /&gt;
|  [https://www.hse.ru/en/org/persons/160550073 Bruno Bauwens], [https://zoom.us/j/5579743402 Zoom] || 14h-18h || 16h15-19h ||  ||  || &lt;br /&gt;
|}&lt;/div&gt;</summary>
		<author><name>.obj</name></author>
	</entry>
	<entry>
		<id>https://wiki.cs.hse.ru/index.php?title=Theory_of_computing,_AMI&amp;diff=56653</id>
		<title>Theory of computing, AMI</title>
		<link rel="alternate" type="text/html" href="https://wiki.cs.hse.ru/index.php?title=Theory_of_computing,_AMI&amp;diff=56653"/>
		<updated>2021-08-25T12:47:18Z</updated>

		<summary type="html">&lt;p&gt;.obj: /* Office hours */&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;&lt;br /&gt;
== Exam ==&lt;br /&gt;
&lt;br /&gt;
26 Dec, 13:00–15:40, [https://zoom.us/j/97631222267 Zoom]&lt;br /&gt;
&lt;br /&gt;
The exam consists of 8 questions of the same level as the homework.&lt;br /&gt;
&lt;br /&gt;
You may use all course materials (seminar sheets, Sipser&#039;s book, Noam Nissan&#039;s book, etc). You are not allowed to communicate with other students and to use social network sites like Telegram, Facebook, etc. You may not use your phone except in the end of the exam to submit your work.&lt;br /&gt;
&lt;br /&gt;
You must submit your answers in handwriting (exceptions can be asked at the beginning of the exam) by sending scanned or photographed copies to both lecturers.  &lt;br /&gt;
&lt;br /&gt;
[http://www.mi-ras.ru/~podolskii/files/computability1819/exam171222.pdf sample exam] (3 years ago, not all topics are the same, but questions 1,2,3,7 we have covered)&lt;br /&gt;
&lt;br /&gt;
Please check [https://docs.google.com/spreadsheets/d/1jPl3ZcOEt4v99IhAq0bpfJW9KRTTh3w5KsNZ4NKfDME/edit?usp=sharing All grades] for the results. If you have questions, you can ask them at 11:00 on December 29 via [https://zoom.us/j/97070495314 Zoom].&lt;br /&gt;
&lt;br /&gt;
== General Information ==&lt;br /&gt;
&lt;br /&gt;
Classes: Tuesdays, 13:00–16:00, [https://zoom.us/j/97070495314 Zoom].&lt;br /&gt;
&lt;br /&gt;
First lecture September 8.&lt;br /&gt;
&lt;br /&gt;
[https://www.dropbox.com/s/suzbqo0k37blw2b/grading.pdf?dl=0 Grading]&lt;br /&gt;
&lt;br /&gt;
Please send your homework to the teaching assistant, [mailto:myugolyadkin@edu.hse.ru Maxim Golyadkin].&lt;br /&gt;
&lt;br /&gt;
[https://docs.google.com/spreadsheets/d/1nb4rOB5rGWtKbXRw2RovFdLiRXcKccAFc7VknN0bQIg/edit#gid=0 Grades for the homework]&lt;br /&gt;
&lt;br /&gt;
[https://docs.google.com/spreadsheets/d/1jPl3ZcOEt4v99IhAq0bpfJW9KRTTh3w5KsNZ4NKfDME/edit?usp=sharing All grades]&lt;br /&gt;
&lt;br /&gt;
== Dates and Deadlines ==&lt;br /&gt;
&lt;br /&gt;
Homework 1, deadline: 6 October, before the lecture &amp;lt;br&amp;gt;&lt;br /&gt;
Homework 2, deadline: 3 November, before the lecture &amp;lt;br&amp;gt;&lt;br /&gt;
Homework 3, deadline: 8 December, before the lecture &lt;br /&gt;
&lt;br /&gt;
The lecture starts at 13h, it is not allowed to submit after this time. However, the first time you are less than 24 hours late, the homework will still be graded. &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
== Colloquium ==&lt;br /&gt;
&lt;br /&gt;
Dates: December 15 and 16. Choose your [https://docs.google.com/spreadsheets/d/1v_0RDvsnTRNa4IYSjOir9VYodfzzvAbJ8KHXtyy2K-M/edit#gid=0 time]&amp;lt;br&amp;gt; &lt;br /&gt;
Zoom links: go to the link above&amp;lt;br&amp;gt;&lt;br /&gt;
[https://www.dropbox.com/s/15w8s6dfkxu0cni/col.pdf?dl=0 Rules and questions]&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
== Course Materials ==&lt;br /&gt;
&lt;br /&gt;
In the first 9 lectures, we follow Sipser&#039;s book &amp;quot;Introduction to the theory of computation&amp;quot; Chapters 3, 7, 8, 9 (not Theorem 9.15), and Section 10.2.&lt;br /&gt;
&lt;br /&gt;
If you need some background in math, consider these two sourses:&amp;lt;br&amp;gt;&lt;br /&gt;
[http://www.cs.elte.hu/~lovasz/dmbook.ps Lecture notes: Discrete Mathematics], L. Lovasz, K. Vesztergombi&amp;lt;br&amp;gt;&lt;br /&gt;
[http://rubtsov.su/public/DM-HSE-Draft.pdf Лекции по дискретной математике] (черновик учебника, in Russian)&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
|-&lt;br /&gt;
! Date/Movie !! Summary !! Problem list&lt;br /&gt;
|-&lt;br /&gt;
 || 08.09 || Turing machines, multitape Turing machines, connection between them. Universal Turing machine. Examples. Time and space complexity. Complexity classes P, PSPACE, EXP. ||  [https://www.dropbox.com/s/2qwd0cqe1qhdzve/prob_01.pdf?dl=0 Problem list 1 ]&lt;br /&gt;
|-&lt;br /&gt;
|| 15.09 ||  Time and space hierarchy theorem. Time and space constructible functions. || [https://www.dropbox.com/s/knbvqjuvkuafvlq/prob_02.pdf?dl=0 Problem list 2] &amp;lt;span style=&amp;quot;color:red&amp;quot;&amp;gt;Update 15.09, problem 2.4&amp;lt;/span&amp;gt;&lt;br /&gt;
|-&lt;br /&gt;
 || 22.09 || Complexity class NP. Examples. Inclusions between P, NP and PSPACE. Non-deterministic TMs. Another definition of NP. Polynomial reductions, their properties. NP-hardness and NP-completeness, their properties. &lt;br /&gt;
 || [https://www.dropbox.com/s/9oxj6jxa2a27fk7/prob_03.pdf?dl=0 Problem list 3] &amp;lt;span style=&amp;quot;color:red&amp;quot;&amp;gt;Update 22.09, 3.5 and hint 3.8&amp;lt;/span&amp;gt;&lt;br /&gt;
|-&lt;br /&gt;
 || 29.09 ||  Circuit complexity. Examples. All functions are computed by circuits. Existence of functions with exponential circuit complexity. P is in P/poly.  || [https://www.dropbox.com/s/51am8w6jytz9dad/prob_04.pdf?dl=0 Problem list 4]&lt;br /&gt;
|-&lt;br /&gt;
 || 06.10 || NP-completeness: Circuit-SAT, 3-SAT, IND-SET, BIN-INT-PROG, Clique, Vertex-Cover, Exactly 1-3-SAT, NAE-3-SAT || [https://www.dropbox.com/s/jfbisdyolmhdohl/prob_05.pdf?dl=0 Problem list 5]&lt;br /&gt;
|-&lt;br /&gt;
 || 13.10 || NP-completeness: Subset-SUM, 3COLORING. coNP, completeness of CIRC-TAUT  || [https://www.dropbox.com/s/tzqj7l8il5drhk4/prob_06.pdf?dl=0 Problem list 6]&lt;br /&gt;
|-&lt;br /&gt;
 || [https://zoom.us/rec/share/3LrMJXXTJDAYF2lzH0r33hv336AWBjtufpF6yKdidy4ic6uFvsYEpK7BlZEKFNyV.xYkSb0P6NBjVRsao?startTime=1603793959000 27.10] || Space complexity. Classes L, NL, PSPACE and NPSPACE. Directed Reachability is in SPACE(log&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt; &#039;&#039;n&#039;&#039;). Configuration graph. Inclusions between time and space classes. TQBF problem, its PSPACE-completeness. PSPACE = NPSPACE. NSPACE(&#039;&#039;s&#039;&#039;(&#039;&#039;n&#039;&#039;)) is in SPACE(&#039;&#039;s&#039;&#039;(&#039;&#039;n&#039;&#039;)&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;) for space constructible &#039;&#039;s&#039;&#039;. || [https://www.dropbox.com/s/hlubofza612y6cj/prob_07.pdf?dl=0 Problem list 7]&lt;br /&gt;
|- &lt;br /&gt;
|| [https://zoom.us/rec/share/14xX_cDOu2Gr2fpFFxfmJKEclKNoDr57XCq2gyGqSGmsgilZdrTwyZihBHz6XRmO.OfTjHf0GXEA9Et4H 03.11] || [https://www.dropbox.com/s/5lt1z4qxhksgs15/WCM_def5d.mp4?dl=0 L ⊆ P]. [https://www.dropbox.com/s/rtizfkx2m2ebyec/NLsubsetP.png?dl=0 NL ⊆ P]. [https://www.dropbox.com/s/9jtajtadc8vrgby/reductions.mp4?dl=0 Log-space reductions and NL-completeness]. [https://www.dropbox.com/s/ca86r3h2fvm3q8o/WCM_09830.mp4?dl=0 Path is NL-][https://www.dropbox.com/s/3k5fld05zisqgrp/WCM_df84e.mp4?dl=0 complete] and, [https://www.dropbox.com/s/ko2zmvk31jqm0ma/WCM_03d13.mp4?dl=0 probably, outside L]. [https://www.dropbox.com/s/mhqz2n52hab37zw/WCM_695bc.mp4?dl=0 Class coNL]. [https://www.dropbox.com/s/ul739s45r3palqi/WCM_7ddbe.mp4?dl=0 NL] [https://www.dropbox.com/s/0tqcxf9uzpev711/WCM_65c40.mp4?dl=0 =] [https://www.dropbox.com/s/ecdy6tno88a1ffs/WCM_63463.mp4?dl=0 coNL]. [https://www.dropbox.com/s/hilscsxiicgr6ho/WCM_3c921.mp4?dl=0 Generalised Geography] and [https://www.dropbox.com/s/4tbu304rw7vje4q/WCM_81f5b.mp4?dl=0 Formula Game] are [https://www.dropbox.com/s/xrlz1u4ho2z1u5x/WCM_bc82a.mp4?dl=0 PSPACE-complete]. || [https://www.dropbox.com/s/2i4hj8ilp4exqr2/prob_08.pdf?dl=0 Problem list 8]&lt;br /&gt;
|-&lt;br /&gt;
 || [https://zoom.us/rec/share/XqpUIS7G8bB2TjD4l0XZuGtpLOKdI5ICuyPA3PyMfaxSB0dsjO0x-U-9Yn0QAOcb.nZQA6cqTBv7ytmiP 10.11] || Oracle computation definitions. There exists an oracle &#039;&#039;A&#039;&#039; for which P&amp;lt;sup&amp;gt;&#039;&#039;A&#039;&#039;&amp;lt;/sup&amp;gt; = NP&amp;lt;sup&amp;gt;&#039;&#039;A&#039;&#039;&amp;lt;/sup&amp;gt;. There is an oracle &#039;&#039;B&#039;&#039; such that P&amp;lt;sup&amp;gt;&#039;&#039;B&#039;&#039;&amp;lt;/sup&amp;gt; is not equal to NP&amp;lt;sup&amp;gt;&#039;&#039;B&#039;&#039;&amp;lt;/sup&amp;gt;. || [https://www.dropbox.com/s/8h3a98h938162gz/prob_09.pdf?dl=0 Problem list 9]&lt;br /&gt;
|-&lt;br /&gt;
 || [https://zoom.us/rec/share/Nrq1IvUzofuo5fydjWN64LNjWt6c4Y22oC8kHFF53i3Q4SdYVjWdYjn53h4YlAwI.Py79jFGo7SUOoKV3 17.11] ||  Probabilistic computation. Probabilistic machines, the class BPP, invariance of the definition BPP for different thresholds, RP, coRP, PP, ZPP. BPP is in P/poly. &lt;br /&gt;
 || [https://www.dropbox.com/s/znj3cm1kb70o7px/prob_10.pdf?dl=0 Problem list 10]&lt;br /&gt;
|-&lt;br /&gt;
 || [https://zoom.us/rec/share/O0FgCvpOa1UcFlcGpRsFysaVe87nE9IFfYEK1Nn84VS1IugGncjlQcU55gefVZp8.ejQ1gh2kNiGdAN45 24.11] || Streaming algorithms: finding the majority element, computation of the moment F_2 in logarithmic space.  [http://theory.stanford.edu/~tim/w15/l/l1.pdf Roughgarden&#039;s lecture notes]  &lt;br /&gt;
 || [https://www.dropbox.com/s/vun7309n6qbdo17/prob_11.pdf?dl=0 Problem list 11]&lt;br /&gt;
|-&lt;br /&gt;
 || [https://zoom.us/rec/share/6ez6JQsyBdPjS4JvLi3aAGfvfydLZGJVfD0YFhHl_B5nADRMrY3npHaoC6-MVD-T.j_BzHsk3lNiL8go3 01.12] || Lower-bound for exact and probabilistic computation of F_0 using one-shot communication complexity. Communication protocols. Functions EQ, GT, DISJ. Fooling sets. Combinatorial rectangles. Book: Kushilevitz and Nisan, Communication Complexity, 1997 [https://epdf.pub/communication-complexity.html download]  &lt;br /&gt;
 || [https://www.dropbox.com/s/1qhktxnd95ww146/prob_12.pdf?dl=0 Problem list 12]&lt;br /&gt;
 &lt;br /&gt;
|-&lt;br /&gt;
 || [https://zoom.us/rec/share/dEfCBunsqqsp5ETfuOtGtbcwkfWMmxiHfEjHza2e2sPOybKqR3crQ7guJaVGDdf4.y_FzqoXfKUoztXW4 08.12] || Questions from students P vs NP vs PSPACE || [https://www.dropbox.com/s/00yfmblihuahvoa/prob_13.pdf?dl=0 Problem list 13]&lt;br /&gt;
|-&lt;br /&gt;
 || 15-16.12 || Colloquium.&lt;br /&gt;
 || &lt;br /&gt;
&amp;lt;!--&lt;br /&gt;
Lower bound for randomized 1-shot communication complexity of set disjointness, see Roughgarden&#039;s [http://theory.stanford.edu/~tim/w15/l/l2.pdf lecture notes]). &lt;br /&gt;
|-&lt;br /&gt;
 || 11/12 || Linear programming is in NP, NP-completeness of Hamiltonian path, TQBF as a game, PSPACE-completeness of generalized geography. Various other NP-complete problems. || [https://www.dropbox.com/s/cifs60rf6vpfn3i/prob_14.pdf?dl=0 Problem list 14] &lt;br /&gt;
|-&lt;br /&gt;
 ||---&amp;gt;&lt;br /&gt;
&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
For interested students, we give a few lectures about parameterized complexity. We follow the book [http://parameterized-algorithms.mimuw.edu.pl/parameterized-algorithms.pdf Parameterized algorithms] by Cygan, Marek, Fedor V. Fomin, Łukasz Kowalik, Daniel Lokshtanov, Dániel Marx, Marcin Pilipczuk, Michał Pilipczuk, and Saket Saurabh. Vol. 4, no. 8. Cham: Springer, 2015.&lt;br /&gt;
&lt;br /&gt;
== Office hours ==&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
|-&lt;br /&gt;
!  Person !! Monday !! Tuesday !! Wednesday !! Thursday !! Friday &lt;br /&gt;
|-&lt;br /&gt;
|  [https://www.hse.ru/en/staff/obiedkov Sergei Obiedkov], T915, [https://zoom.us/j/99663354582?pwd=K1B5R3NXWEhWbFozR2lqMkFWYW5Ydz09 Zoom] ||  ||  || 16:30–18:00 || 16:30–18:00 ||  &lt;br /&gt;
|-&lt;br /&gt;
|  [https://www.hse.ru/en/org/persons/160550073 Bruno Bauwens], [https://zoom.us/j/5579743402 Zoom] || 14h-18h || 16h15-19h ||  ||  || &lt;br /&gt;
|}&lt;/div&gt;</summary>
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