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Combinatorics on Words - NALG083

Title:	Kombinatorika na slovech
Guaranteed by:	Department of Algebra (32-KA)
Faculty:	Faculty of Mathematics and Physics
Actual:	from 2018
Semester:	winter
E-Credits:	3
Hours per week, examination:	winter s.:2/0, Ex [HT]
Capacity:	unlimited
Min. number of students:	unlimited
4EU+:	no
Virtual mobility / capacity:	no
State of the course:	cancelled
Language:	Czech
Teaching methods:	full-time
Note:	course can be enrolled in outside the study plan

Guarantor:	doc. Mgr. Štěpán Holub, Ph.D.
Classification:	Mathematics > Algebra
Interchangeability :	NMAG444
Is incompatible with:	NMAG444
Is interchangeable with:	NMAG444

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Annotation -

The lecture introduces to combinatorial properties of free monoids (semigroups resp.). It deals mainly with the structure of submonoids, with morphisms, and with solutions of equations. Some questions concerning equality sets represent a more advanced part of the lecture.

Last update: T_KA (29.04.2002)

Literature - Czech

C. Choffrut and J. Karhumäki, Combinatorics on words, in: Handbook of Formal Languages (G. Rozenberg and A. Salomaa, eds.), vol. I, Springer-Verlag, Berlin Heidelberg 1997, pp. 329-438.

T. Harju and J. Karhumäki, Morphisms, in: Handbook of Formal Languages (G. Rozenberg and A. Salomaa, eds.), vol. I, Springer-Verlag, Berlin Heidelberg 1997, pp. 439-510.

M. Lothaire, Combinatorics on words, Addison-Wesley, Reading Masachusetts, 1983.

M. Lothaire, Algebraic Combinatorics on words, Cambridge University Press, 2002.

J. Berstel and D. Perrin, Theory of Codes, Academic Press, London 1985.

Last update: Zakouřil Pavel, RNDr., Ph.D. (05.08.2002)

Syllabus -

1. Properties of submonoids of free monoids. Code. Rank of subsemigroup. F-semigroups. 2. Morphisms. Equation and its solution. Systems of equations and equivalent subsystems. Compactness Theorem. ( "Ehrenfeucht's conjecture"). 3. Test sets. Existence of a finite test set. Equivalence with the Compactness Theorem. 4. Post Correspondence Problem (PCP) and its modofications. Binary equality sets and their structure. Regular equality sets.

Literature:

C. Choffrut and J. Karhumäki, Combinatorics on words, in: Handbook of Formal Languages (G. Rozenberg and A. Salomaa, eds.), vol. I, Springer-Verlag, Berlin Heidelberg 1997, pp. 329-438.

T. Harju and J. Karhumäki, Morphisms, in: Handbook of Formal Languages (G. Rozenberg and A. Salomaa, eds.), vol. I, Springer-Verlag, Berlin Heidelberg 1997, pp. 439-510.

M. Lothaire, Combinatorics on words, Addison-Wesley, Reading Masachusetts, 1983.

M. Lothaire, Algebraic Combinatorics on words, Cambridge University Press, 2002.

J. Berstel and D. Perrin, Theory of Codes, Academic Press, London 1985.

Last update: T_KA (14.05.2002)