## IB107 Computability and Complexity

Faculty of Informatics
Autumn 2021
Extent and Intensity
2/1/0. 3 credit(s) (plus extra credits for completion). Recommended Type of Completion: zk (examination). Other types of completion: z (credit).
Taught online.
Teacher(s)
doc. RNDr. Jan Strejček, Ph.D. (lecturer)
Marek Jankola (seminar tutor)
RNDr. Petr Novotný, Ph.D. (seminar tutor)
Mgr. Samuel Pastva (seminar tutor)
Mgr. Juraj Major (assistant)
Bc. Kristýna Pekárková (assistant)
Mgr. Vojtěch Suchánek (assistant)
Guaranteed by
doc. RNDr. Jan Strejček, Ph.D.
Department of Computer Science - Faculty of Informatics
Supplier department: Department of Computer Science - Faculty of Informatics
Prerequisites (in Czech)
IB005 Formal languages and Automata || IB102 Automata and Grammars
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
there are 60 fields of study the course is directly associated with, display
Course objectives
The course introduces basic approaches and methods for classification of problems with respect to their algorithmic solvability. It explores theoretical and practical limits of computers usage and consequences these limitations have for advancing information technologies.
At the end of the course the students will be able: to understand basic notions of computability and complexity; to understand the main techniques used to classify problems (reductions, diagonalisation, closure properties), and to apply them in some simple cases.
Learning outcomes
After enrolling the course student will be able to:
- use asymptotic notation, both actively and passively;
- explain difference between complexity of an algorithm and of a problem;
- independently decide to which complexity class a given problem belongs;
- do practical decisions based on a complexity classification of a particular problem;
- explain that some problems are not computable, give examples of such problems;
- explain the difference between various classes of not-computable problems;
Syllabus
• Algorithms and models of computation. Church thesis.
• Classification of problems. Decidable, undecidable and partially decidable problems. Computable functions.
• Closure properties. Rice theorems.
• Computational complexity. Feasible and unfeasible problems. Polynomial computational thesis.
• Reduction a completeness in problem classes. Many-one reduction and polynomial reduction. Complete problems with respect to decidability, NP-complete problems. Applications.
Literature
• KOZEN, Dexter C. Automata and computability. New York: Springer, 1997. xiii, 400. ISBN 0387949070. info
• SIPSER, Michael. Introduction to the theory of computation. Boston: PWS Publishing Company, 1997. xv, 396 s. ISBN 0-534-94728-X. info
• BOVET, D. and Pierluigi CRESCENZI. Introduction to the theory of complexity. New York: Prentice-Hall, 1994. xi, 282 s. ISBN 0-13-915380-2. info
• KFOURY, A. J., Robert N. MOLL and Michael A. ARBIB. A programming approach to computability. New York: Springer-Verlag, 1982. viii, 251. ISBN 0-387-90743-2. info
Teaching methods
lectures, support sessions, homeworks
Assessment methods
The course has a form of a lecture with a seminar. During the term students are assigned homeworks. The course is concluded by the written exam. Student can attend the final exam providing she/he has acquired given number of points from homeworks.
Language of instruction
Czech
Follow-Up Courses