Theory of Computing 2019 2020
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Версия от 12:17, 6 ноября 2019; Vpodolskii (обсуждение | вклад)
General Information
Classes: Fridays, 15:10-18:00, R406
Homework results (some results are still not added)
Dates and Deadlines
Homework 1, deadline: 4 October, before the lecture
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 |
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 |
