IB107 Computability and Complexity

Faculty of Informatics
Autumn 2024
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).
In-person direct teaching
Teacher(s)
prof. RNDr. Jan Strejček, Ph.D. (lecturer)
Mgr. Paulína Ayaziová (seminar tutor)
RNDr. Martin Jonáš, Ph.D. (seminar tutor)
Bc. David Dokoupil (assistant)
Bc. Ondřej Huvar (assistant)
RNDr. David Klaška (assistant)
Mgr. Martin Kurečka (assistant)
Matúš Miškuf (assistant)
Bc. Jindřich Sedláček (assistant)
RNDr. Vojtěch Suchánek (assistant)
Bc. Jakub Šárník (assistant)
Bc. Adéla Štěpková (assistant)
Guaranteed by
prof. RNDr. Jan Strejček, Ph.D.
Department of Computer Science – Faculty of Informatics
Supplier department: Department of Computer Science – Faculty of Informatics
Timetable
Mon 23. 9. to Mon 16. 12. Mon 10:00–11:50 D1
  • Timetable of Seminar Groups:
IB107/A: Thu 26. 9. to Thu 21. 11. Thu 14:00–15:50 C511, Thu 28. 11. to Thu 19. 12. Thu 14:00–15:50 S209, J. Strejček
IB107/02: Tue 24. 9. to Tue 17. 12. Tue 15:00–15:50 A218, J. Strejček
IB107/03: Tue 24. 9. to Tue 17. 12. Tue 13:00–13:50 A218, M. Jonáš
IB107/04: Tue 24. 9. to Tue 17. 12. Tue 12:00–12:50 A218, M. Jonáš
IB107/05: Tue 24. 9. to Tue 17. 12. Tue 16:00–16:50 A218, P. Ayaziová
Prerequisites (in Czech)
IB005 Formal languages and Automata
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
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 the use of computers and the implications that these limitations have for the developent of information technology.
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.
  • Reduction and 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 open-book exam. Student can attend the final exam providing she/he has acquired a given number of points from homeworks.
Language of instruction
Czech
Follow-Up Courses
Further Comments
Study Materials
The course is taught annually.
Listed among pre-requisites of other courses
The course is also listed under the following terms Autumn 2003, Autumn 2004, Autumn 2005, Autumn 2006, Autumn 2007, Autumn 2008, Autumn 2009, Autumn 2010, Autumn 2011, Autumn 2012, Autumn 2013, Autumn 2014, Autumn 2015, Autumn 2016, Autumn 2017, Autumn 2018, Autumn 2019, Autumn 2020, Autumn 2021, Autumn 2022, Autumn 2023.
  • Enrolment Statistics (recent)
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