Theory of Computing 2019 2020 — различия между версиями
Материал из Wiki - Факультет компьютерных наук
| Строка 9: | Строка 9: | ||
== Course Materials == | == Course Materials == | ||
| − | + | {| class="wikitable" | |
| + | |- | ||
| + | ! Date !! Summary !! Problem list | ||
| + | |- | ||
| + | || 06.09 || || [https://www.dropbox.com/s/lxoenwqohopsoca/prob_1.pdf?dl=0 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. || [http://www.mi.ras.ru/~podolskii/files/computability1819/prob_2.pdf Problem list 2 ] | ||
| + | |- | ||
| + | || 18/9 || NP-completeness: Circuit-SAT, 3-SAT, NAE-3-SAT, IND-SET || [http://www.mi.ras.ru/~podolskii/files/computability1819/prob_3.pdf Problem list 3] | ||
| + | |- | ||
| + | || 25/9 || NP-completeness: Subset-SUM, 3COLORING || [http://www.mi.ras.ru/~podolskii/files/computability1819/prob_4.pdf Problem list 4] | ||
| + | |- | ||
| + | || 2/10 || 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). || [http://www.mi.ras.ru/~podolskii/files/computability1819/prob_5.pdf Problem list 5] | ||
| + | |- | ||
| + | || 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] | ||
| + | |- | ||
| + | || 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. | ||
| + | || [https://www.dropbox.com/s/adl3acqeqebctbk/prob_7.pdf?dl=0 Problem list 7] | ||
| + | |- | ||
| + | || 30/10 || 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. | ||
| + | || [https://www.dropbox.com/s/n18684gtl9kd9i9/prob_8.pdf?dl=0 Problem list 8] | ||
| + | |- | ||
| + | || 6/11 || Circuit complexity: directed reachability in AC1, NC0 is trivial, polynomial size Boolean formulas equal NC_1, relations with L and NL. [https://www.dropbox.com/s/txpwymgx1s7f4id/09lect.pdf?dl=0 Lecture notes] | ||
| + | || [http://www.mi.ras.ru/~podolskii/files/computability1819/prob_9.pdf Problem list 9] | ||
| + | |- | ||
| + | || 13/11 || Streaming algorithms: finding the majority element, computation of moments F_0 and F_2 in logarithmic space, lower-bounds using one-shot communication complexity. [http://theory.stanford.edu/~tim/w15/l/l1.pdf Roughgarden's lecture notes] | ||
| + | || [https://www.dropbox.com/s/z6qygibdhoioo4g/prob_10.pdf?dl=0 Problem list 10] | ||
| + | |- | ||
| + | || 20/11 || Communication protocols. Functions EQ, GT, DISJ, IP. Fooling sets. Combinatorial rectangles. Rectangle size lower bound. Rank lower bound. Book: [http://infotheorytcs.wikischolars.columbia.edu/file/view/Noam+Nisan+and+Eyal+Kushilevitz+-+Communication+Complexity.pdf Nisan Kushilevich: communication complexity, 1997] | ||
| + | || [https://www.dropbox.com/s/08slc776301dhfk/prob_11.pdf?dl=0 Problem list 11] | ||
| + | |- | ||
| + | || 27/11 || Nondeterministic communication complexity. D(f) < O(N^0(f) N^1(f)). Deterministic complexity vs number of leafs in a protocol tree. Randomized communication complexity: definitions. Functions EQ, GT, MCE. | ||
| + | || [https://www.dropbox.com/s/3e1as6lok0h1oxw/prob_12.pdf?dl=0 Problem list 12] | ||
| + | |- | ||
| + | || 4/12 || Probabilistic versus deterministic complexity. Newman's theorem. Space-time tradeoffs for Turing machines. See Nisan Kushilevich chapters 3 and 12. Lower bound for randomized 1-shot communication complexity of set disjointness, see Roughgarden's [http://theory.stanford.edu/~tim/w15/l/l2.pdf lecture notes]). | ||
| + | || [https://www.dropbox.com/s/nsa2tped7qp39ch/prob_13.pdf?dl=0 Problem list 13] | ||
| + | |- | ||
| + | || 11/12 || Linear programming is in NP, NP-completeness of Hamiltonian path, TQBF as a game, PSPACE-completeness of generalized geography. Various other NP-complete problems. || [https://www.dropbox.com/s/cifs60rf6vpfn3i/prob_14.pdf?dl=0 Problem list 14] | ||
| + | |- | ||
| + | || 18/12 || Questions from students about exercises and homework. Kolmogorov complexity, symmetry of information. [Optional lecture, not for the exams.] || [https://www.dropbox.com/s/b3g60wwwbqpmotm/prob_15.pdf?dl=0 Problem list 15]---> | ||
| + | |} | ||
== Office hours == | == Office hours == | ||
Версия 12:16, 6 сентября 2019
General Information
Classes: Fridays, 15:10-18:00, R406
Dates and Deadlines
Homework 1, deadline: 4 October, before the lecture
Course Materials
| Date | Summary | Problem list |
|---|---|---|
| 06.09 | Problem list 1 |
Office hours
| Person | Monday | Tuesday | Wednesday | Thursday | Friday |
|---|---|---|---|---|---|
| Vladimir Podolskii, room S830 | |||||
| Bruno Bauwens, room S834 |
