Просмотр исходного текста страницы Theory of computation 2025


= Classes =

Lectures:  Friday 13h00 - 14h20 in Pokrovkaya, see [https://docs.google.com/spreadsheets/d/1EAbqb8wf48evEi5Bf2M0xmZXQSrpd_FJbsnevXDQxaQ/edit?gid=614347250#gid=614347250 here] for the room, and in [https://us02web.zoom.us/j/82300259484?pwd=NWxXekxBeE5yMm9UTmwvLzNNNGlnUT09 zoom] by [https://www.hse.ru/en/org/persons/160550073 Bruno Bauwens]. Starting 19.09.

Seminars: Friday 14h40 - 16h00 in Pokrovkaya, see [https://docs.google.com/spreadsheets/d/1EAbqb8wf48evEi5Bf2M0xmZXQSrpd_FJbsnevXDQxaQ/edit?gid=614347250#gid=614347250 here] for the room, and in [https://us06web.zoom.us/j/84205097860?pwd=PQpzn1Oqf9G2fjO2vwcUVsMdCnRUuc.1 zoom] by Prof. Subin Pulari

Telegram group for announcements and discussions [https://t.me/+7BOrITRebjk5MTc0 invite link.] The course is similar to [http://wiki.cs.hse.ru/Theory_of_computation_2024 last year's one].

For students programming engineering this course is called "computational complexity theory" and the course has an extra part in the 3rd module. 


= Homeworks =

Deadlines: every 2 weeks, before the lecture. Submit in pdf or fotos of handwritten text in [https://classroom.google.com/c/ODEwMjk4NDQxMTU1?cjc=n5dttaev google class]. 

Tasks are in the problem lists from the seminar. Deadlines: problem lists 1 and 2: at the start of 3rd lecture, lists 3 and 4 at the start of the 5th lecture, etc.

Late policy: 1 homework can be submitted at most 24h late without explanations.

All homework scores are available in the following Google Sheet: [https://docs.google.com/spreadsheets/d/1QvyOh7kk7W-IhgMNcyFJ5NUNj9Tw-9z12ora_ZBW8eA/edit?usp=sharing link]

= Course Materials =

The main reference is Sipser's book "Introduction to the theory of computation", chapters 3, 4, 7–9.

If you need some background in math, consider
<!-- [http://www.cs.elte.hu/~lovasz/dmbook.ps Lecture notes: Discrete Mathematics], L. Lovasz, K. Vesztergombi and -->
[http://rubtsov.su/public/DM-HSE-Draft.pdf Лекции по дискретной математике].

{| class="wikitable"
|-
!  Rec !! Summary !! Problem list
|-
 || [https://www.youtube.com/watch?v=-VIr385nKVk 19.09] || Turing machines, multitape Turing machines, connection between them. Universal Turing machine. Examples. Time and space complexity. Complexity classes P, PSPACE, EXP. (Recording from previous year.) [https://drive.google.com/file/d/1Xby_fNyeVwZtVY6yfVJLBYNCaZVbOP61/view?usp=drive_link Notes]|| [https://drive.google.com/file/d/1bf3hhE82uw5D0bQGajXHl1-FhhyG-XnY/view?usp=drive_link problem list 1]
|-
|-
|| [https://www.youtube.com/watch?v=tnq5BkcGfk0 26.09] || Undecidability of the Halting problem. Time and space hierarchy theorems. See notes above. || [https://drive.google.com/file/d/1iyba3kM98oJCz5yvKmWRb0oOpIAhFPef/view?usp=drive_link problem list 2] 
|-
 || [https://www.youtube.com/watch?v=VR_A62kFXH8 03.10] || Complexity class NP. Examples. Non-deterministic machines and another definition of NP. Polynomial reductions. NP-hardness and NP-completeness. [https://drive.google.com/file/d/1chzfYehNELzNkDMDjmRo9gfIXv_9FYeG/view?usp=drive_link Notes], [https://drive.google.com/file/d/1leJcc3UqC-WIGGN3G7Zm2Y0jt84q13o1/view?usp=drive_link tex]. || [https://drive.google.com/file/d/17AF1Bj5I_S0XzwXkM4IeOugxX2Kr3i2u/view?usp=drive_link problem list 3]
|-
 || [https://rutube.ru/video/585774c956d226dde80929ca0b39f13e 10.10] ||  NP-completenes of independent-set, NAE-3SAT, 3colorability, subsetsum, knapsack problem. Notes above.  || [https://drive.google.com/file/d/1dVUT2KZ9hAyGBZITDJh3xtfLb992aX9L/view?usp=drive_link problem list 4] upd 10.10
|-
 || [https://rutube.ru/video/53f86ac57c92d812edb493b280e31a07 17.10] || Circuits 1: examples and all functions have exponential circuits. Classes P/poly, AC^i and NC^i. Some functions have exponential circuit complexity. <!-- NC1 = Boolean formulas of polynomial size. Addition in AC0. Multiplication is in NC1. P is in P/poly. 3SAT is NP-complete.-->  [https://drive.google.com/file/d/1Cqr4A6ohPLIaAVocG3jE6GYsNz4XgA4r/view?usp=drive_link Notes.pdf] upd 28.10, [https://drive.google.com/file/d/1rzL0-_fKq9ZbSu_zjTUUiM_cQNUGUX05/view?usp=drive_link tex].  || [https://drive.google.com/file/d/1uB12iMZptqzcoLpF6hZT-8X1Xh9-1nm4/view?usp=drive_link problem list 5]
|-
 || 23.10 || Circuits 2: NC0 = functions that depend on a constant number of inputs. P is in P/poly. 3SAT is NP-complete.  Seminar: addition in AC0. Multiplication is in NC1. Notes above. Last year's [https://www.youtube.com/watch?v=Jqy89FPbFj4  video]. || see list 5
|-
 || [https://drive.google.com/file/d/19vsMFBQfun7mf9URNF-F2R9JWbPlNN81/view?usp=drive_link 24.10] || Directed Reachability is in SPACE(log^2 n). TQBF problem, its PSPACE-completeness. PSPACE = NPSPACE. NSPACE(s(n)) is in SPACE(s(n)^2) for space constructible s.|| [https://drive.google.com/file/d/1j9XCMFYwsqcqIzGgKGSgDpJvmtz4-Wx8/view?usp=drive_link problem list 6] upd 28.10
|-
 || [https://youtube.com/live/W_uZuQXm53c 07.11] || 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>. || [https://drive.google.com/file/d/1v8dh4EAeAtq1et4ya_Q1VBO77_m3a6WS/view?usp=drive_link problem list 7]
|- 
|| [https://youtube.com/live/ALO6r52wuIU 14.11] ||  Probabilistic computation. Probabilistic machines, the class BPP, invariance of the definition BPP for different thresholds, RP, coRP, PP, ZPP. BPP is in P/poly. Most of it is also [https://www.youtube.com/watch?v=YSMgVbOqB-8&list=PLm3J0oaFux3YL5vLXpzOyJiLtqLp6dCW2&index=23 here] and [https://www.cs.cmu.edu/afs/cs/academic/class/15859-f04/www/scribes/lec2.pdf scribe1] [https://lucatrevisan.github.io/cs278-04/notes/lecture08.pdf scribe2] || [https://drive.google.com/file/d/1pMn1rzOKjnmjvW4X1WJA-jauQv08YFIh/view?usp=drive_link problem list 8] upd 20.11
|-
 || [https://rutube.ru/video/private/82810d471de9883b9215d0c9a3235c44/?p=8fTMLwkOD-WvpiQM1ACE0A 21.11] || Approximation algorithms. Definition c-approximation algorithm. 2-approximation for vertex cover and greedy vertex cover is not optimal. (ln n + 1)-approximation for set cover. PTAS for the makespan problem. Based on [https://www.youtube.com/watch?v=MEz1J9wY2iM&pp=ygUYYXBwcm94aW1hdGlvbiBhbGdvcml0aG1z MIT lecture].|| 
[https://drive.google.com/file/d/1TPC6D_81PrklhjlTfrfnEzE4_5vm3vPS/view?usp=drive_link problem list 9]
|-
 || [https://youtube.com/live/r9rP3ZojeqY 28.11] || Parameterized complexity: The classes FPT and XP. Kernelization. Examples for vertex cover.  [https://drive.google.com/file/d/1W9SU24HW0r5QhugzmrghpkzJUFuC8whq/view?usp=sharing Notes.] This year's [https://rutube.ru/video/private/18c6e2b7e1222f3411afbc933f317631/?p=9KNQCTTbSP-nKD-gg6tDOw recording]. || [https://drive.google.com/file/d/12GnrF5dpVZjMsHfG4Y6jmT3P6jsc8jjm/view?usp=drive_link problem list 10] 
|-
 || [https://rutube.ru/video/fdfba34cca0e6d23b7382e883f138aa2/ 05.12] || Parameterized complexity: W-hierarchy, hardness from the exponential time hypothesis. [https://drive.google.com/file/d/1f-085Gr7E01HepUR-brGJDet-fXJzUwb/view?usp=sharing presentation] [https://drive.google.com/file/d/1OIw7h31N2tt-npC0NrvVgNhYGw_HlJa_/view?usp=sharing Notes] Last year's [https://youtube.com/live/E4aNlvbYoLQ  rec]. || [https://drive.google.com/file/d/1xhUYMsj0iV2TMZfR8FtkxWUNlcCjdS-N/view?usp=sharing problem list 11] 
|- 
 || 12.12 || ''Colloquium.'' Also on 19.12. [https://drive.google.com/file/d/1no8CbHKJluGRx7FROpSS7BqXdjOVgdT1/view?usp=sharing Rules and questions.] (Same as last year.) Reserve a [https://docs.google.com/spreadsheets/d/1_vO5Q0wGkM0kU1OHNiP8lz24M4i-toLC2AmQg7tuRVE/edit?usp=sharing slot]. || [https://www.dropbox.com/s/37gdsbv2it8omnm/tc-sample-exam.pdf?dl=0 Sample exam] 
|}

Artem Parfenov's [https://drive.google.com/file/d/16_ZP0X9wwza1RsrXZZGQsx5Igwk_vY9r/view?usp=sharing lecture summaries] [https://drive.google.com/drive/folders/1XsNL2B69akd3A9qaOEgC09NiZXLP8Wbz?usp=drive_link source] (Disclaimer: I did not check them):

{| class="wikitable"
|-
!  Date !! Software engineering: parameterized complexity, FPT algorithms !! Problem list
|-
 || [https://youtube.com/live/xDaTpuVF0Es 05.03] || Recap from last lecture. More examples of kernels: linear programming kernel for vertex cover problem.  [https://www.dropbox.com/scl/fi/x5gwdae4ny4u3zixoy4pw/student_vc_branching.ipynb?rlkey=5oowq1u3jhy490s84ogojg1s7&dl=0 programming task.] [https://www.dropbox.com/s/zzzaulpmzql7x7u/parameterizedComplexity.pdf?dl=0 presentation].|| [https://drive.google.com/file/d/1sXA5F4gUZ-KvigQspz0ScVLOA38ZcxHb/view?usp=sharing problem list 12] 
|-
 || [https://youtube.com/live/TBX8sWx7nO0 12.03] || Linear programming kernel for VC, color coding, dynamic programming. Colorcoding [https://drive.google.com/file/d/1RMoIpd6p_L1XXOVeV36g0pdJdbtltbPF/view?usp=sharing from slide 39]  || [https://drive.google.com/file/d/16wjIGqbS5UvEUZCxuUfGROUxk2RlLqZl/view?usp=sharing problem list 13] 
|-
 || 19.03 || Optional: problems that are FPT on graphs with small treewidth.(No recording, sorry.) || [https://drive.google.com/file/d/1mYkshv6q-c_5nY5qfHgosKxBd1zDDvGK/view?usp=sharing problem list 14]
|}

{| class="wikitable"
|-
! Seminars (2025) !! Recording link
|-
| Seminar 4 || [https://rutube.ru/video/private/6f4f908ef52b8af8e5bace950d8a9c0c/?p=5GnphSR3t1Jf4a9Mpqg2Zw link]
|-
| Seminar 5 || Part I: [https://rutube.ru/video/private/992b26e2a8e6c95c662d8d246c7f3e0d/?p=uYcEmJungpW_YPkyLlGMOA link] <br> Part II: [https://rutube.ru/video/private/9d17a54647262d3c63187aad06fab0b8/?p=8WfJJBBJUYFfE9tQkBJ1MA link]
|-
| Seminar 6 || [https://rutube.ru/video/private/6aa2f287bc39727ca82f4c713d2cc463/?p=2s6opSEa5_CjGYmJI3sOLg link]
|-
| Seminar 7 || [https://rutube.ru/video/private/88af4a5c6eb2699db4475dbcf88884b7/?p=k_1vuYG_fWnOAQld9-0aCQ link]
|-
| Seminar 8 || [https://rutube.ru/video/private/8978247dc6dcaaa8ef0e04ac3f4333af/?p=EGFH7-YuCIEiH2BYyKUqrg link]
|-
| Seminar 9 || [https://rutube.ru/video/private/2bfd76c0422f371bc506328c35c9e670/?p=3TXJi4AYqVMD1Idt8HyFmg link]
|-
| Seminar 10 || [https://rutube.ru/video/private/1ab525cc4cdeef5d66b736d6bce5887b/?p=Tvxh3q1LON2Y9O_AvXck1Q link]
|-
| Seminar 11 || [https://rutube.ru/video/private/5536256c687688c3d824a0bd6daba00e/?p=0Vn3ddYFyVunqH09vaiU-A link]
|}



[https://www.youtube.com/playlist?list=PL8EKo81hBCTGfNPpZlIe7USiEPpZGYDte Recordings last year]

= Exam =

5 or 6 questions with the same difficulty as the homework questions. You have 3 hours time. 

Each year, 1 of the questions is to prove that some problem is NP-complete. Do not forget to say why the problem is in NP. 

Copies of Sipser's book, Arora&Barak, Mertens&Moore, will be available. (I you have these books or printed parts of them, please bring it.) Also, personal handwritten notes are allowed, but nothing else.  [https://www.dropbox.com/s/37gdsbv2it8omnm/tc-sample-exam.pdf?dl=0 Sample exam]. 


= Project (for PI students) =

During the 3rd module Januari till March 2024 there are projects where you need to implement algorithms from parameterized complexity. (For example, for the vertex cover algorithm and disjoint paths problems.) A grader will check whether your algorithm reaches certain time limits. 

There are 3 tasks: 2 of them about branching and kernelization, 1 task about linear programming bounds. See the table with lectures. The tasks have equal weight for the grade. 

Deadline March 31st, 23h59. 


= Additional reading = 

Recall that the most important book for our course is ''Sipser, Introduction to the theory of computation'' 3rd edition, 2013, chapters 3, 4, 7–9. This book is intended for Bachelor students. 

The following book is popular with students theoretical computer science, because it contains most materials of our course in a concise way. Moreover, it presents many important advanced topics. I find the style of some proofs rather technical, but I like the topics in this book. 

''S. Arora and B. Barak, Computational Complexity: A Modern Approach, 2009'' 

The course materials can also be found in various chapters of the following massive book (700 pages). It starts at beginning bachelor level and ends at an advanced master level. It is written in a pleasant style with excellent examples.

''C. Moore and S. Mertens, The nature of computation, 2011.''

This book gives an introduction to important recent research directions in computational hardness. It also studies specific topics (games and planar problems) in huge detail.

''E. Demaine, W Gasarch, Haijaghayi, Computational intractability: a guide to lower bounds, 2023'' [https://hardness.mit.edu/ current draft]

This is an advanced textbook with background on parameterized algorithms.

''M. Cygan, F. Fomin and 6 others, Parameterized algorithms, 2016''


= Grading =

For AMI students:

 Final score = 0.35 * [score homework] + 0.35 * [score colloquium] + 0.3 * [score exam] <br>

For PI students (the course is called "computational complexity" and takes 3 modules). There are 2 scores for this course. The first one, given in December is calculated by the above formula (but probably it does not mean anything, I will ask about it). The second score is given below, and it is the one that will be in the diploma. It includes a programming project. The assignment and grader, will be set up by the end of Februari, the deadline is the end of March.  

 Final score = 0.3 * [score homework] + 0.3 * [score colloquium] + 0.2 * [score exam] + 0.2 * [score project] <br>


Some homework assignments contain extra problems. Each solution of an extra problem will give 0.5 extra points on the final exam (which is graded out of 10). There will be around 10 extra problems. Rounding is applied only when the final score is transferred to the official grade. Arithmetic rounding is used. Autogrades. If only 6/10 for the exam is needed to get a final score of 10/10, then this will be given automatically. 


= Office hours =

Bruno Bauwens: Tuesday 15h -- 21h. Friday 15h -- 18h. 

Subin Pulari: Please contact via telegram or mail [mailto:spulari@hse.ru spulari@hse.ru]