Theory of Computing 2018 2019
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.
Dates and Deadlines
Homework 1, deadline: 2 October
Homework 2, deadline: 6 November
Homework 3, deadline: 4 December
Before the lecture.
Date and time: December 10, 16:40
|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|
|16/10||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|
|30/10||Computations with oracles, its simple properties. There are oracles A and B such that P^A is equal to NP^A and P^B is not equal to NP^B.||Problem list 8|
|6/11||Circuit complexity: directed reachability in AC1, NC0 is trivial, polynomial size Boolean formulas equal NC_1, relations with L and NL. Lecture notes||Problem list 9|
|13/11||Streaming algorithms: finding the majority element, computation of moments F_0 and F_2 in logarithmic space, lower-bounds using one-shot communication complexity. Roughgarden's lecture notes||Problem list 10|
|20/11||Communication protocols. Functions EQ, GT, DISJ, IP. Fooling sets. Combinatorial rectangles. Rectangle size lower bound. Rank lower bound. Book: Nisan Kushilevich: communication complexity, 1997||Problem list 11|
|27/11||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.||Problem list 12|
During the first module, we follow Sipser's book Introduction to the theory of computation, chapters 7-9.
||Vladimir Podolskii, room 621||18:00–19:00||16:40–18:00|
||Bruno Bauwens, room 620||16:40–19:00||15:00–18:00|