Theory of Computing
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Версия от 15:00, 13 октября 2017; Vpodolskii (обсуждение | вклад)
General Information
Dates and Deadlines
Homework 1 deadline: September 29, 2017, 23:59 AoE
Homework 1, Extra Problems deadline: October 6, 2017, before seminar
Homework 2 + Extra Problems deadline: November 3, 2017, before lecture
Course Materials
Summary | Problem list |
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Complexity classes P, PSPACE, EXP. Time and space hierarchy theorems (see also Sipser Section 9.1) | Problem list 1 |
Complexity class NP. Examples. Inclusions between P, NP and EXP. Non-deterministic TMs. Another definition of NP. Complexity class NEXP. Polynomial reductions, their properties. NP-hardness and NP-completeness, their properties. NP-completeness: CIRC-SAT, 3-SAT. | Problem list 2 |
NP-completeness: NAE-3-SAT, Exactly-1-3-SAT, IND-SET, Subset-SUM, 3-COLORING. | Problem list 3 |
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) (additional material). Interpretation of PSPACE in terms of games. | Problem list 4 |
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 5 |
Definition of Sigma_2 and Pi_2. BPP is in Sigma_2 and Pi_2. 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 6 Updated: 07.10.17 |
Communication protocols. Functions EQ, GT, DISJ, IP. Fooling sets. Combinatorial rectangles. Rectangle size lower bound. Rank lower bound. Non-deterministic complexity. Communication complexity classes P, NP, coNP, intersection of NP and coNP. | Problem list 7 |
Homework
Send homework assignments by email to posobin+hw[at]gmail.com, or submit them in person to one of the teachers or the teaching assistant (Gleb Posobin) before the deadline.
Office hours
Person | Monday | Tuesday | Wednesday | Thursday | Friday | |
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Vladimir Podolskii | 16:40–18:00, room 621 | ||||
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Bruno Bauwens | 15:05–18:00, room 620 | 15:05–18:00, room 620 |