Theory of Computing 2019 2020 — различия между версиями
Материал из Wiki - Факультет компьютерных наук
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|| 11.10 || NP-completeness: Subset-SUM, 3COLORING. coNP, completeness of CIRC-TAUT || [https://www.dropbox.com/s/qa2t7bm7lmw6rbe/prob_6.pdf?dl=0 Problem list 6] | || 11.10 || NP-completeness: Subset-SUM, 3COLORING. coNP, completeness of CIRC-TAUT || [https://www.dropbox.com/s/qa2t7bm7lmw6rbe/prob_6.pdf?dl=0 Problem list 6] | ||
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| − | || 18 | + | || 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. || [https://www.dropbox.com/s/nllomqsrocqcjcv/prob_7.pdf?dl=0 Problem list 7] |
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| − | || 01 | + | || 01.11 || PSPACE-completeness of formula game and generalized geography. Oracle computation definitions. There exists a language A for which P^A = NP^A. || [https://www.dropbox.com/s/e5ccevcu9ig23lu/prob_8.pdf?dl=0 Problem list 8] |
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| − | || | + | || 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. || [https://www.dropbox.com/s/36ov36op8wvkdf7/prob_9.pdf?dl=0 Problem list 9] |
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|| 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. | || 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. | ||
Версия 17:19, 8 ноября 2019
General Information
Classes: Fridays, 15:10-18:00, R406
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 |
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 |
