Theory of Computation 2021

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Tuesdays 14:40–17:40, ruz

Lectures: 14:40 in room M303, also streamed here parallel session

Seminars: 16:20 in room M203, also streamed here

Dates and Deadlines

Please send your homework by e-mail to both lecturers.
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


Colloquium: 35%
Homework: 35%
Exam: 30%

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
07.09 Turing machines, multitape Turing machines, connection between them. Universal Turing machine. Examples (one, two). Time and space complexity. Complexity classes P, PSPACE, EXP. Problem set 1
14.09 Time and space hierarchy theorem. Time and space constructible functions. Problem set 2
21.09 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 set 3
28.09 Proving NP-hardness by reduction from an NP-complete problem. Examples of NP-complete problems.
05.10 Circuit complexity. Examples. All functions are computed by circuits. Existence of functions with exponential circuit complexity. P is in P/poly.
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.
09.11 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, there are 3 lectures in parameterized complexity.

14 Sept: Fixed parameter tracktability and examples, presentation.

21 Sept: Topics from chapters 1 and 2 in "Parameterized algorithms" by Cygan, Fomin and others, 2016.

28 Sept: The W-hierarchy, chapter 13 in the same book.

Office hours

Person Monday Tuesday Wednesday Thursday Friday
Bruno Bauwens, S834, Zoom 14:00-20:00
Sergei Obiedkov, T915, Zoom 16:30–18:00 16:30–18:00