Theory of Computation 2021 — различия между версиями
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|| 26.10 || Space complexity. || | || 26.10 || Space complexity. || | ||
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− | || | + | || 02.11 || Oracle computation definitions. There exists an oracle ''A'' for which P<sup>''A''</sup> = NP<sup>''A''</sup>. There is an oracle B such that P<sup>''B''</sup> is not equal to NP<sup>''B''</sup>. || |
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|| 9.11 || Probabilistic computation. Probabilistic machines, the class BPP, invariance of the definition BPP for different thresholds, RP, coRP, PP, ZPP. BPP is in P/poly. || | || 9.11 || Probabilistic computation. Probabilistic machines, the class BPP, invariance of the definition BPP for different thresholds, RP, coRP, PP, ZPP. BPP is in P/poly. || | ||
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− | || | + | || 07.12 || Colloquium || |
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|| 14.12 || Complexity of clustering: an exact algorithm for maximising the inter-cluster distance and an approximate algorithm for minimising the intra-class distance. | || 14.12 || Complexity of clustering: an exact algorithm for maximising the inter-cluster distance and an approximate algorithm for minimising the intra-class distance. |
Версия 15:44, 25 августа 2021
General Information
Classes: Tuesdays, 14:40–17:40.
Dates and Deadlines
Homework 1, deadline: October 5, 14:00
Homework 2, deadline: November 2, 14:00
Homework 3, deadline: December 7, 14:00
Colloquium: December 7, 14:40–17:40
Course Materials
The main reference is Sipser's book "Introduction to the theory of computation" Chapters 3, 7–10.
If you need some background in math, consider these two sources:
Lecture notes: Discrete Mathematics, L. Lovasz, K. Vesztergombi
Лекции по дискретной математике (черновик учебника, in Russian)
Date | Summary | Problem list |
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07.09 | Turing machines, multitape Turing machines, connection between them. Universal Turing machine. Examples. Time and space complexity. Complexity classes P, PSPACE, EXP. | |
14.09 | Time and space hierarchy theorem. Time and space constructible functions. | |
21.09 | Circuit complexity. Examples. All functions are computed by circuits. Existence of functions with exponential circuit complexity. P is in P/poly. | |
28.09 | 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. | |
05.10 | Proving NP-hardness by reduction from an NP-complete problem. Examples of NP-complete problems. | |
12.10 | Cook–Levin theorem. | |
26.10 | Space complexity. | |
02.11 | Oracle computation definitions. There exists an oracle A for which PA = NPA. There is an oracle B such that PB is not equal to NPB. | |
9.11 | Probabilistic computation. Probabilistic machines, the class BPP, invariance of the definition BPP for different thresholds, RP, coRP, PP, ZPP. BPP is in P/poly. | |
16.11 | Streaming algorithms: finding the majority element, computation of the moment F2 in logarithmic space. | |
23.11 | Finding the frequent items in streams of data: SpaceSaving and Count-Min Sketch. | |
30.11 | Approximation algorithms. Approximate solutions for Vertex Cover, Weighted Vertex Cover, and TSP. | |
07.12 | Colloquium | |
14.12 | Complexity of clustering: an exact algorithm for maximising the inter-cluster distance and an approximate algorithm for minimising the intra-class distance. |
For interested students, we give a few lectures about parameterized complexity. We follow the book Parameterized algorithms by Cygan, Marek, Fedor V. Fomin, Łukasz Kowalik, Daniel Lokshtanov, Dániel Marx, Marcin Pilipczuk, Michał Pilipczuk, and Saket Saurabh. Vol. 4, no. 8. Cham: Springer, 2015.
Office hours
Person | Monday | Tuesday | Wednesday | Thursday | Friday |
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Sergei Obiedkov, Zoom | 16:30–18:00 | 16:30–18:00 | |||
Bruno Bauwens, Zoom (email in advance) | 14h-18h | 16h15-19h |