Theory of Computing 2019 2020 — различия между версиями
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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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| − | || | + | || 18/10 || 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). || [https://www.dropbox.com/s/nllomqsrocqcjcv/prob_7.pdf?dl=0 Problem list 7] |
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|| 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) || [http://www.mi.ras.ru/~podolskii/files/computability1819/prob_6.pdf Problem list 6] | || 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) || [http://www.mi.ras.ru/~podolskii/files/computability1819/prob_6.pdf Problem list 6] | ||
Версия 19:59, 18 октября 2019
General Information
Classes: Fridays, 15:10-18:00, R406
Dates and Deadlines
Homework 1, deadline: 4 October, before the lecture
Course Materials
In the first several lecture we follow Sipser's book "Introduction to the theory of computation"
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). | Problem list 7 |
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 |
