Theory of Computation 2021 — различия между версиями

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Tuesdays 14:40–17:40, [https://ruz.hse.ru/ruz/main ruz]
 
Tuesdays 14:40–17:40, [https://ruz.hse.ru/ruz/main ruz]
  
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]
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Lectures: 14:40 in room M303 [https://us02web.zoom.us/j/83533615475?pwd=WDU3cHJ5RjREOGd2YU1qdDJCVm1idz09 zoomlink 26/10]
  
Seminars: 16:20 in room M203, also streamed [https://us02web.zoom.us/j/84546220686?pwd=U2dISk5UaFZpdmh3WTdFT3phRVNXZz09 here]
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Seminars: 16:20 in room M302  [https://us02web.zoom.us/j/84546220686?pwd=U2dISk5UaFZpdmh3WTdFT3phRVNXZz09 zoomlink 26/10]
  
 
= Dates and Deadlines =
 
= Dates and Deadlines =
 
Please send your homework by e-mail to both lecturers.<br>
 
Please send your homework by e-mail to both lecturers.<br>
Homework 1, deadline: October 5, 14:00 <br>
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Homework 1, deadline: October 5, 14:00; the deadline for the extra problems is November 2, 14:00<br>
 
Homework 2, deadline: November 2, 14:00 <br>
 
Homework 2, deadline: November 2, 14:00 <br>
 
Homework 3, deadline: December 7, 14:00 <br>
 
Homework 3, deadline: December 7, 14:00 <br>
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Homework: 35%<br>
 
Homework: 35%<br>
 
Exam: 30%
 
Exam: 30%
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==Homework Grading==
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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.
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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.
  
 
= Course Materials =
 
= Course Materials =
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  || 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]
 
  || 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]
 
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|| 14.09 ||  Time and space hierarchy theorem. Time and space constructible functions. ||
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|| 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]
 
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  || 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.  
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  || 21.09 || Complexity class NP. Examples. Polynomial reductions. NP-hardness and NP-completeness.  
  ||  
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  || [https://www.dropbox.com/s/bf68zicg4uh051x/prob_03.pdf?dl=0 Problem set 3]
 
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  || 28.09 ||  Proving NP-hardness by reduction from an NP-complete problem. Examples of NP-complete problems.  ||
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  || 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]
 
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  || 05.10 || Circuit complexity. Examples. All functions are computed by circuits. Existence of functions with exponential circuit complexity. P is in P/poly.||  
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  || 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]
 
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  || 12.10 || Cook–Levin theorem. ||
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  || 12.10 || Cook–Levin theorem. || [https://www.dropbox.com/s/y2y1lu29936xy9n/prob_06.pdf?dl=0 Problem set 6]
 
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  || 26.10 || Space complexity. ||
 
  || 26.10 || Space complexity. ||
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For interested students, there are 3 lectures in parameterized complexity.
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14 Sept: Fixed parameter tracktability and examples, [https://www.dropbox.com/s/zzzaulpmzql7x7u/parameterizedComplexity.pdf?dl=0 presentation].
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21 Sept: Topics from chapters 1 and 2 in "Parameterized algorithms" by Cygan, Fomin and others, 2016.
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28 Sept: The W-hierarchy, chapter 13 in the same book.
  
 
= Office hours =
 
= Office hours =
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!  Person !! Monday !! Tuesday !! Wednesday !! Thursday !! Friday  
 
!  Person !! Monday !! Tuesday !! Wednesday !! Thursday !! Friday  
 
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|  [https://www.hse.ru/en/org/persons/160550073 Bruno Bauwens] ||  || ||  ||  ||  
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|  [https://www.hse.ru/en/org/persons/160550073 Bruno Bauwens], S834, [https://us02web.zoom.us/j/82300259484?pwd=NWxXekxBeE5yMm9UTmwvLzNNNGlnUT09 Zoom] ||  || ||  ||  || 14:00-20:00
 
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|  [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 ||   
 
|  [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 ||   
 
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Версия 19:16, 24 октября 2021

Classes

Tuesdays 14:40–17:40, ruz

Lectures: 14:40 in room M303 zoomlink 26/10

Seminars: 16:20 in room M302 zoomlink 26/10

Dates and Deadlines

Please send your homework by e-mail to both lecturers.
Homework 1, deadline: October 5, 14:00; the deadline for the extra problems is November 2, 14:00
Homework 2, deadline: November 2, 14:00
Homework 3, deadline: December 7, 14:00
Colloquium: December 7, 14:40–17:40

Grading

Colloquium: 35%
Homework: 35%
Exam: 30%

Homework Grading

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.

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.

Course Materials

The main reference is Sipser's book "Introduction to the theory of computation", chapters 3, 7–10.

If you need some background in math, consider these two sources:
Lecture notes: Discrete Mathematics, L. Lovasz, K. Vesztergombi
Лекции по дискретной математике (черновик учебника, in Russian)

Date Summary Problem list
07.09 Turing machines, multitape Turing machines, connection between them. Universal Turing machine. Examples (one, two). Time and space complexity. Complexity classes P, PSPACE, EXP. Problem set 1
14.09 Time and space hierarchy theorem. Time and space constructible functions. Problem set 2
21.09 Complexity class NP. Examples. Polynomial reductions. NP-hardness and NP-completeness. Problem set 3
28.09 Non-deterministic TMs. Another definition of NP. Proving NP-hardness by reduction from an NP-complete problem. Examples of NP-complete problems. Problem set 4
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. Problem set 5
12.10 Cook–Levin theorem. Problem set 6
26.10 Space complexity.
02.11 Oracle computation definitions. There exists an oracle A for which PA = NPA. There is an oracle B such that PB is not equal to NPB.
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.
16.11 Streaming algorithms: finding the majority element, computation of the moment F2 in logarithmic space.
23.11 Finding the frequent items in streams of data: SpaceSaving and Count-Min Sketch.
30.11 Approximation algorithms. Approximate solutions for Vertex Cover, Weighted Vertex Cover, and TSP.
07.12 Colloquium.
14.12 Complexity of clustering: an exact algorithm for maximising the inter-cluster distance and an approximate algorithm for minimising the intra-class distance.

For interested students, there are 3 lectures in parameterized complexity.

14 Sept: Fixed parameter tracktability and examples, presentation.

21 Sept: Topics from chapters 1 and 2 in "Parameterized algorithms" by Cygan, Fomin and others, 2016.

28 Sept: The W-hierarchy, chapter 13 in the same book.

Office hours

Person Monday Tuesday Wednesday Thursday Friday
Bruno Bauwens, S834, Zoom 14:00-20:00
Sergei Obiedkov, T915, Zoom 16:30–18:00 16:30–18:00