M7250 Semigroups and formal languages

Faculty of Science
Autumn 2024
Extent and Intensity
2/0. 2 credit(s) (příf plus uk k 1 zk 2 plus 1 > 4). Type of Completion: zk (examination).
In-person direct teaching
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
Tue 8:00–9:50 M3,01023
Prerequisites
M2150 Algebra I or MV008 Algebra I.
Recommended knowledge: IB005 Formal Languages and Automata, basics of universal algebra (M7350 Algebra III or MA009 Algebra II) and metric spaces (M2100 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, Jean-Éric. Mathematical Foundations of Automata Theory. 2022. URL info
  • 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
  • GRILLET, Pierre Antoine. Semigroups : an introduction to the structure theory. New York: Marcel Dekker, 1995, ix, 398. ISBN 0824796624. 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
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, Autumn 2019, autumn 2021.
  • Enrolment Statistics (recent)
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