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== Exam ==
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26 Dec, 13:00–15:40, [https://zoom.us/j/97631222267 Zoom]
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The exam consists of 8 questions of the same level as the homework.
 +
 +
You may use all course materials (seminar sheets, Sipser's book, Noam Nissan'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.
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 +
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. 
 +
 +
[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)
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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].
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== General Information ==
 
== General Information ==
  
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Please send your homework to the teaching assistant, [mailto:myugolyadkin@edu.hse.ru Maxim Golyadkin].
 
Please send your homework to the teaching assistant, [mailto:myugolyadkin@edu.hse.ru Maxim Golyadkin].
  
[https://docs.google.com/spreadsheets/d/1nb4rOB5rGWtKbXRw2RovFdLiRXcKccAFc7VknN0bQIg/edit#gid=0 Grades] (Solutions given during the seminar are not yet included.)
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[https://docs.google.com/spreadsheets/d/1nb4rOB5rGWtKbXRw2RovFdLiRXcKccAFc7VknN0bQIg/edit#gid=0 Grades for the homework]
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[https://docs.google.com/spreadsheets/d/1jPl3ZcOEt4v99IhAq0bpfJW9KRTTh3w5KsNZ4NKfDME/edit?usp=sharing All grades]
  
 
== Dates and Deadlines ==
 
== Dates and Deadlines ==
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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.  
 
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.  
  
<!--
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== Colloquium ==
 
== Colloquium ==
  
Date and time: December 13, 15:10<br>  
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Dates: December 15 and 16. Choose your [https://docs.google.com/spreadsheets/d/1v_0RDvsnTRNa4IYSjOir9VYodfzzvAbJ8KHXtyy2K-M/edit#gid=0 time]<br>  
Room: R405<br>
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Zoom links: go to the link above<br>
[https://www.dropbox.com/s/rbjd1hsuhtbmvzq/col.pdf?dl=0 Program] <span style="color:red">Updated: 11.12.19 (question 7 of part 2 is removed)</span>
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[https://www.dropbox.com/s/15w8s6dfkxu0cni/col.pdf?dl=0 Rules and questions]
--->
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== Course Materials ==
 
== Course Materials ==
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{| class="wikitable"
 
{| class="wikitable"
 
|-
 
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! Date !! Summary !! Problem list
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! Date/Movie !! Summary !! Problem list
 
|-
 
|-
 
  || 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 ]
 
  || 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 ]
Строка 55: Строка 72:
 
  || [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<sup>2</sup> ''n''). Configuration graph. Inclusions between time and space classes. TQBF problem, its PSPACE-completeness. PSPACE = NPSPACE. NSPACE(''s''(''n'')) is in SPACE(''s''(''n'')<sup>2</sup>) for space constructible ''s''. || [https://www.dropbox.com/s/hlubofza612y6cj/prob_07.pdf?dl=0 Problem list 7]
 
  || [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<sup>2</sup> ''n''). Configuration graph. Inclusions between time and space classes. TQBF problem, its PSPACE-completeness. PSPACE = NPSPACE. NSPACE(''s''(''n'')) is in SPACE(''s''(''n'')<sup>2</sup>) for space constructible ''s''. || [https://www.dropbox.com/s/hlubofza612y6cj/prob_07.pdf?dl=0 Problem list 7]
 
|-  
 
|-  
|| 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]. <span style="color:gray"> PSPACE-completeness of formula game and generalized geography. Oracle computation definitions. There exists a language A for which P^A = NP^A. </span>  || [https://www.dropbox.com/s/2i4hj8ilp4exqr2/prob_08.pdf?dl=0 Problem list 8]
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|| [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]
 
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  || 10.11 || <span style="color:gray"> There is an oracle B such that P^B is not equal to NP^B. Probabilistic computation. Probabilistic machines, the class BPP, invariance of the definition BPP for different thresholds, RP, coRP, PP, ZPP.  </span> ||  
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  || [https://zoom.us/rec/share/XqpUIS7G8bB2TjD4l0XZuGtpLOKdI5ICuyPA3PyMfaxSB0dsjO0x-U-9Yn0QAOcb.nZQA6cqTBv7ytmiP 10.11] || Oracle computation definitions. There exists an oracle ''A'' for which P<sup>''A''</sup> = NP<sup>''A''</sup>. There is an oracle ''B'' such that P<sup>''B''</sup> is not equal to NP<sup>''B''</sup>. || [https://www.dropbox.com/s/8h3a98h938162gz/prob_09.pdf?dl=0 Problem list 9]
 
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|-
  || 17.11 || <span style="color:gray"> Streaming algorithms: finding the majority element, computation of the moment F_2 in logarithmic space, lower-bound for exact and probabilistic computation of F_0 using one-shot communication complexity. [http://theory.stanford.edu/~tim/w15/l/l1.pdf Roughgarden's lecture notes] </span>
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  || [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.
||
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|| [https://www.dropbox.com/s/znj3cm1kb70o7px/prob_10.pdf?dl=0 Problem list 10]
 
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|-
  || 24.11 || <span style="color:gray"> Communication protocols. Functions EQ, GT, DISJ, IP. Fooling sets. Combinatorial rectangles. Rectangle size lower bound. Rank lower bound. Book: Nisan and Kushilevich: communication complexity, 1997 [https://epdf.pub/communication-complexity.html download</span>
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  || [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's lecture notes]   
  ||  
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  || [https://www.dropbox.com/s/vun7309n6qbdo17/prob_11.pdf?dl=0 Problem list 11]
 
|-
 
|-
  || 01.12 || <span style="color:gray">  Nondeterministic communication complexity. D(f) < O(N^0(f) N^1(f)). Deterministic complexity vs number of leafs in a protocol tree. Randomized communication complexity: definitions. Functions EQ, GT, MCE. Newman's theorem (only the statement)  </span>
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  || [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] 
  ||  
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  || [https://www.dropbox.com/s/1qhktxnd95ww146/prob_12.pdf?dl=0 Problem list 12]
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|-
 
|-
  || 08.12 || <span style="color:gray"> Probabilistic versus deterministic complexity. Newman's theorem. Space-time tradeoffs for Turing machines. See Nisan Kushilevich chapters 3 and 12.  </span>
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  || [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]
||
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|-
 
|-
  || 22.12 || <span style="color:gray"> Questions from students about exercises and homework. Poly time reductions on graphs and NP-completeness of Hamiltonion graphs. Solving [http://www.mi-ras.ru/~podolskii/files/computability1819/exam171222.pdf the exam of 2 years ago]. </span>
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  || 15-16.12 || Colloquium.
 
  ||  
 
  ||  
 
 
<!--
 
<!--
 
Lower bound for randomized 1-shot communication complexity of set disjointness, see Roughgarden's [http://theory.stanford.edu/~tim/w15/l/l2.pdf lecture notes]).  
 
Lower bound for randomized 1-shot communication complexity of set disjointness, see Roughgarden's [http://theory.stanford.edu/~tim/w15/l/l2.pdf lecture notes]).  
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!  Person !! Monday !! Tuesday !! Wednesday !! Thursday !! Friday  
 
!  Person !! Monday !! Tuesday !! Wednesday !! Thursday !! Friday  
 
|-
 
|-
|  [https://www.hse.ru/en/staff/obiedkov Sergei Obiedkov], room&nbsp;T915 ||  ||  ||   || 16:30–18:00 ||   
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|  [https://www.hse.ru/en/staff/obiedkov Sergei Obiedkov], [https://zoom.us/j/99663354582 Zoom] ||  ||  || 16:30–18:00 || 16:30–18:00 ||   
 
|-
 
|-
|  Bruno Bauwens, room&nbsp;S834 || 14h-18h || 16h15-19h ||  ||  ||  
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[https://www.hse.ru/en/org/persons/160550073 Bruno Bauwens], [https://zoom.us/j/5579743402 Zoom] (email in advance) || 14h-18h || 16h15-19h ||  ||  ||  
 
|}
 
|}

Версия 16:37, 28 декабря 2020

Exam

26 Dec, 13:00–15:40, Zoom

The exam consists of 8 questions of the same level as the homework.

You may use all course materials (seminar sheets, Sipser's book, Noam Nissan'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.

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.

sample exam (3 years ago, not all topics are the same, but questions 1,2,3,7 we have covered)

Please check All grades for the results. If you have questions, you can ask them at 11:00 on December 29 via Zoom.

General Information

Classes: Tuesdays, 13:00–16:00, Zoom.

First lecture September 8.

Grading

Please send your homework to the teaching assistant, Maxim Golyadkin.

Grades for the homework

All grades

Dates and Deadlines

Homework 1, deadline: 6 October, before the lecture
Homework 2, deadline: 3 November, before the lecture
Homework 3, deadline: 8 December, before the lecture

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.


Colloquium

Dates: December 15 and 16. Choose your time
Zoom links: go to the link above
Rules and questions


Course Materials

In the first 9 lectures, we follow Sipser's book "Introduction to the theory of computation" Chapters 3, 7, 8, 9 (not Theorem 9.15), and Section 10.2.

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


Date/Movie Summary Problem list
08.09 Turing machines, multitape Turing machines, connection between them. Universal Turing machine. Examples. Time and space complexity. Complexity classes P, PSPACE, EXP. Problem list 1
15.09 Time and space hierarchy theorem. Time and space constructible functions. Problem list 2 Update 15.09, problem 2.4
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. Problem list 3 Update 22.09, 3.5 and hint 3.8
29.09 Circuit complexity. Examples. All functions are computed by circuits. Existence of functions with exponential circuit complexity. P is in P/poly. Problem list 4
06.10 NP-completeness: Circuit-SAT, 3-SAT, IND-SET, BIN-INT-PROG, Clique, Vertex-Cover, Exactly 1-3-SAT, NAE-3-SAT Problem list 5
13.10 NP-completeness: Subset-SUM, 3COLORING. coNP, completeness of CIRC-TAUT Problem list 6
27.10 Space complexity. Classes L, NL, PSPACE and NPSPACE. Directed Reachability is in SPACE(log2 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. Problem list 7
03.11 L ⊆ P. NL ⊆ P. Log-space reductions and NL-completeness. Path is NL-complete and, probably, outside L. Class coNL. NL = coNL. Generalised Geography and Formula Game are PSPACE-complete. Problem list 8
10.11 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. Problem list 9
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. Problem list 10
24.11 Streaming algorithms: finding the majority element, computation of the moment F_2 in logarithmic space. Roughgarden's lecture notes Problem list 11
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 download Problem list 12
08.12 Questions from students P vs NP vs PSPACE Problem list 13
15-16.12 Colloquium.

For interested students, we give a few lectures about parameterized complexity. We follow the book 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.

Office hours

Person Monday Tuesday Wednesday Thursday Friday
Sergei Obiedkov, Zoom 16:30–18:00 16:30–18:00
Bruno Bauwens, Zoom (email in advance) 14h-18h 16h15-19h