# Theory of Computation 2021

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# Classes

Tuesdays 14:40–17:40, ruz

Lectures 14:40 in room M303, also streamed here

Seminars 16:20 in room ??, also streamed here

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

Colloquium: 0.35
Homework: 0.35
Exam: 0.3

# 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. 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.
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.

# Office hours

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