M7250 Semigroups and formal languages

Faculty of Science
Autumn 2019
Extent and Intensity
2/0. 2 credit(s) (příf plus uk k 1 zk 2 plus 1 > 4). Type of Completion: zk (examination).
Teacher(s)
doc. Mgr. Michal Kunc, Ph.D. (lecturer)
Guaranteed by
doc. Mgr. Michal Kunc, Ph.D.
Department of Mathematics and Statistics - Departments - Faculty of Science
Contact Person: doc. Mgr. Michal Kunc, Ph.D.
Supplier department: Department of Mathematics and Statistics - Departments - Faculty of Science
Timetable
Mon 10:00–11:50 M3,01023
Prerequisites
Algebra I.
Recommended knowledge: Formal languages and automata I, basics of universal algebra (Algebra II) and metric spaces (Mathematical analysis II).
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 presents two closely related areas of theoretical computer science and mathematics: theory of regular languages and finite semigroups.
Learning outcomes
After passing the course, students will: be familiar with modern methods of the theory of regular languages; understand the connection between classes of regular languages and finite semigroups; be able to use pseudovarieties of semigroups to describe properties of regular languages; master basic notions and techniques of the structure theory of finite semigroups.
Syllabus
  • 1. Recognizable and rational sets: definitions, relations between them, closure properties.
  • 2. Structure of finite semigroups: Green's relations, 0-simple semigroups, factorization forests.
  • 3. Eilenberg correspondence: pseudovarieties, pseudoidentities, examples.
  • 4. Well quasiorders in formal language theory.
Literature
  • PIN, J.-E. Varieties of formal languages. New York: Plenum Publishing Corporation, 1986. 138 pp. Foundations of Computer Science. ISBN 0-306-42294-8. info
  • SAKAROVITCH, Jacques. Elements of Automata Theory. Cambridge: Cambridge University Press, 2009. 782 pp. ISBN 978-0-521-84425-3. info
  • Handbook of formal languages. Vol. 1 Word, language, grammar. Edited by Grzegorz Rozenberg - Arto Salomaa. Berlin: Springer, 1997. xvii, 873. ISBN 3-540-60420-0. info
  • HOWIE, John M. Fundamentals of semigroup theory. Oxford: The Clarendon Press, 1995. x, 351. ISBN 0198511949. info
  • GRILLET, Pierre Antoine. Semigroups : an introduction to the structure theory. New York: Marcel Dekker, 1995. ix, 398. ISBN 0824796624. info
  • ALMEIDA, Jorge. Finite semigroups and universal algebra. Singapore: World Scientific, 1994. 511 pp. ISBN 81-02-1895-8. info
  • DE LUCA, Aldo and Stefano VARRICCHIO. Finiteness and regularity in semigroups and formal languages. Berlin: Springer, 1999. 240 pp. EATCS Monographs on Theoretical Computer Science. ISBN 3-540-63771-0. info
Teaching methods
Lectures: theoretical explanation, homework exercises.
Assessment methods
Oral examination.
Language of instruction
Czech
Further Comments
Study Materials
The course is taught once in two years.
Teacher's information
https://www.math.muni.cz/~kunc/vyuka/vyuka.html
The course is also listed under the following terms Autumn 2010 - only for the accreditation, Autumn 2010, Autumn 2011 - acreditation, Autumn 2012, Autumn 2014, autumn 2017.
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