Theory of Computation 2021 — различия между версиями

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  || 23.11 || Finding the frequent items in streams of data: SpaceSaving and Count-Min Sketch. ||
 
  || 23.11 || Finding the frequent items in streams of data: SpaceSaving and Count-Min Sketch. ||
 
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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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  || 30.11] || Approximation algorithms. Approximate solutions for Vertex Cover, Weighted Vertex Cover, and TSP. ||
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|| [https://www.dropbox.com/s/1qhktxnd95ww146/prob_12.pdf?dl=0 Problem list 12]
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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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  || 7.12] || Colloquium ||
 
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  || 15-16.12 || Colloquium.
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  || 14.12 || Complexity of clustering: an exact algorithm for maximising the inter-cluster distance and an approximate algorithm for minimising the intra-class distance.
 
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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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|| 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]
 
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Версия 15:41, 25 августа 2021

General Information

Classes: Tuesdays, 14:40–17:40.

Dates and Deadlines

Homework 1, deadline: October 5, 14:00
Homework 2, deadline: November 2, 14:00
Homework 3, deadline: December 7, 14:00
Colloquium: December 7, 14:40–17:40

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/Movie Summary Problem list
07.09 Turing machines, multitape Turing machines, connection between them. Universal Turing machine. Examples. Time and space complexity. Complexity classes P, PSPACE, EXP.
14.09 Time and space hierarchy theorem. Time and space constructible functions.
21.09 Circuit complexity. Examples. All functions are computed by circuits. Existence of functions with exponential circuit complexity. P is in P/poly.
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.
05.10 Proving NP-hardness by reduction from an NP-complete problem. Examples of NP-complete problems.
12.10 Cook–Levin theorem.
26.10 Space complexity.
2.11 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.
9.11 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.
7.12] 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, 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
Источник — «http://wiki.cs.hse.ru/index.php?title=Theory_of_Computation_2021&oldid=56644»