Theory of Computing 2018 2019 — различия между версиями
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|| 25/9 || NP-completeness: Subset-SUM, 3COLORING || [https://www.dropbox.com/s/h5or8izfv7m5pn8/prob_4.pdf?dl=0 Problem list 4] | || 25/9 || NP-completeness: Subset-SUM, 3COLORING || [https://www.dropbox.com/s/h5or8izfv7m5pn8/prob_4.pdf?dl=0 Problem list 4] | ||
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| + | || 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). || [https://www.dropbox.com/s/0lqvrn7v1updjug/prob_5.pdf?dl=0 Problem list 5] | ||
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| − | || 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. | + | || 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. |
|| [http://www.mi.ras.ru/~podolskii/files/computability/prob_5.pdf Problem list 5] | || [http://www.mi.ras.ru/~podolskii/files/computability/prob_5.pdf Problem list 5] | ||
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Версия 21:03, 2 октября 2018
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.
Dates and Deadlines
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 |
| 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 |
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 | |
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Vladimir Podolskii, room 621 | 18:00–19:00 | 16:40–18:00 | |||
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Bruno Bauwens, room 620 | 16:40–19:00 | 15:00–18:00 |
