# Theory of Computing 2018 2019

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## General Information

Send your home assignments only in pdf format to the teacher assistant (Andrey Storozhenko) by email (storozhenkoaa [at] yandex.ru) with the following subject: "[Computing, Name Surname, HWx]". You can also submit them in person before the deadline.

Homework 1, deadline: 2 Oktober, before the lecture.

## Course Materials

Date Summary Problem list
4/9 Time and space hierarchy theorems (see also Sipser Section 9.1) Problem list 1
11/9 Complexity class NP. Examples. Inclusions between P, NP and EXP. Non-deterministic TMs. Another definition of NP. Polynomial reductions, their properties. NP-hardness and NP-completeness, their properties. Problem list 2
18/9 NP-completeness: Circuit-SAT, 3-SAT, NAE-3-SAT, IND-SET Problem list 3
25/9 NP-completeness: Subset-SUM, 3COLORING Problem list 4
2/10 Space complexity. Classes PSPACE and NPSPACE. Configuration graph. Inclusions between time and space classes. TQBF problem, its PSPACE-completeness. PSPACE = NPSPACE. NSPACE(s(n)) is in SPACE(s(n)^2). Problem list 5
9/10 Classes L and NL. Examples. Log-space reductions, their properties. REACHABILITY is NL-complete. NL is equal to coNL (proof is not included in the exams) Problem list 6
Interpretation of PSPACE in terms of games. Probabilistic computation. Probabilistic machines, the class BPP, prime testing and Carmichael numbers, invariance of the definition BPP for different thresholds, RP, coRP, PP, ZPP. BPP is in P/poly. Problem list 7

During the first module, we follow Sipser's book Introduction to the theory of computation, chapters 7-9.

## Office hours

Person Monday Tuesday Wednesday Thursday Friday
1
Vladimir Podolskii, room 621 18:00–19:00 16:40–18:00
2
Bruno Bauwens, room 620 16:40–19:00 15:00–18:00