Theory of Computing — различия между версиями

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(Course Materials)
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  || 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.
 
  || 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.
 
  || [http://www.mi.ras.ru/~podolskii/files/computability/prob_6.pdf Problem list 6] <span style="color:red">Updated: 07.10.17</span>
 
  || [http://www.mi.ras.ru/~podolskii/files/computability/prob_6.pdf Problem list 6] <span style="color:red">Updated: 07.10.17</span>
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|| 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.
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|| [http://www.mi.ras.ru/~podolskii/files/computability/prob_7.pdf Problem list 7]
 
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Версия 15:00, 13 октября 2017

General Information

Grading

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
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.

Results for extra problems

Office hours

Person Monday Tuesday Wednesday Thursday Friday
1
Vladimir Podolskii 16:40–18:00, room 621
2
Bruno Bauwens 15:05–18:00, room 620 15:05–18:00, room 620