Theory of Computing 2019 2020

General Information

Classes: Fridays, 15:10-18:00, R406

Grading

Homework results

Dates and Deadlines

Homework 1, deadline: 4 October, before the lecture
Homework 2, deadline: 8 November, before the lecture

Deadline for problem list 8 is extended till November 15
Problem 3.5 was restated in the problem list 9, new deadline is November 15

Course Materials

In the first 10 lectures, we follow Sipser's book "Introduction to the theory of computation" Chapters 7, 8, 9 (not Theorem 9.15), and Section 10.2.

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

Date	Summary	Problem list
06.09	Turing machines, multitape Turing machines, connection between them. Examples. Time and space complexity. Complexity classes P, PSPACE, EXP.	Problem list 1 Updated: 07.09.19
13.09	Universal Turing machine. Space hierarchy theorem. Space constructable functions.	Problem list 2
20.09	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
27.09	Circuit complexity. Examples. All functions are computed by circuits. Existence of functions with exponential circuit complexity. P is in P/poly.	Problem list 4
04.10	NP-completeness: Circuit-SAT, 3-SAT, IND-SET, BIN-INT-PROG	Problem list 5
11.10	NP-completeness: Subset-SUM, 3COLORING. coNP, completeness of CIRC-TAUT	Problem list 6
18.10	Space complexity. Classes L, NL, PSPACE and NPSPACE. Directed Reachability is in SPACE(log^2 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 constructable s.	Problem list 7
01.11	PSPACE-completeness of formula game and generalized geography. Oracle computation definitions. There exists a language A for which P^A = NP^A.	Problem list 8
08.11	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.	Problem list 9
13/11	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. Roughgarden's lecture notes	Problem list 10

For interested students: lecture notes on quantum computation

Office hours

Person	Monday	Tuesday	Wednesday	Thursday	Friday
Vladimir Podolskii, room S830
Bruno Bauwens, room S834			14-18h	14-19h	18-19h