Bachelor
2022/2023
Computational Complexity Theory
Category 'Best Course for Broadening Horizons and Diversity of Knowledge and Skills'
Type:
Elective course (Software Engineering)
Area of studies:
Software Engineering
Delivered by:
Big Data and Information Retrieval School
Where:
Faculty of Computer Science
When:
4 year, 1-3 module
Mode of studies:
offline
Open to:
students of one campus
Language:
English
ECTS credits:
10
Contact hours:
62
Course Syllabus
Abstract
This course teaches a mathematical theory that helps to invent better algorithms. With “better” we mean that the algorithms use fewer resources such as time or memory. We also consider parallel computation, distributed systems and learning problems. In these settings we might also optimize other types of resources. For example, in distributed systems we might want to minimize the amount of communication. We focuss on worst case guarantees. A large part of our time is devoted to the study of what is not possible. In other words, we study fundamental barriers for the existence of programs that use fewer resources than a given bound.
Learning Objectives
- understand the concepts of the complexity classes P, NP, coNP, #P, EXP, NEXP, L, NL, PSPACE, EXPSPACE, BPP, RP
- be able to critically analyse resources used by a program (and optimize them at a high level)
- be able to recognize intractable problems and categorize their difficulty
- have deeper understanding and trained problem solving skills of known materials in: algebra, probability theory, discrete math, algorithms
Expected Learning Outcomes
- Be able to work with complexity classes P, PSPACE, EXP.
- Be able to understand hierarchy theorems
Assessment Elements
- Homework
- Colloquium
- ProjectDuring the 3rd module Januari till March 2023. The task is to understand a theoretical paper better by either (Th) Rewrite some mathematical proof of a research paper in a more accessible way using your own words. You also need to give a lecture (you are not allowed to look at the paper during the lecture). I need to work out examples. Possibly examples that I give you on the spot. (Imp) Implement an algorithm (or parts of an algorithm) from a research paper and demonstrate that it works. You can propose projects yourself, but it is not allowed to have a theoretical paper about software verification. (Because there are too many definitions, and during the lecture it usually turns out the student does not understand them.)
- ExamThe exam consists out of 8 exercises that you must solve in 3 hours time. There will be copies of Sipser's book available (as well as Arora and Barak and Mertens and Moore). You may bring your own copy if you have it, as well as handwritten notes. You can do the colloquium and the exam online if you received permission from the student office.
Interim Assessment
- 2022/2023 2nd module0.5 * Homework + 0.5 * Colloquium
- 2022/2023 3rd module0.25 * Colloquium + 0.25 * Homework + 0.25 * Project + 0.25 * Exam
Bibliography
Recommended Core Bibliography
- Michael Sipser. (2005). Introduction to the Theory of Computation, Second Edition.
- Лекции по дискретной математике : учебник, , 2021
Recommended Additional Bibliography
- Parameterized Algorithms. Marek Cygan, Fedor V. Fomin, Łukasz Kowalik, Daniel Lokshtanov, Daniel Marx, Marcin Pilipczuk, Michał Pilipczuk, Saket Saurabh. - 2015, Springer International Publishing