Abstract
The concept of irreducible automaton is introduced and every irreducible automaton is shown to be primitive. Reset primitive one-defect automata are proved to be irreducible. It is also shown that Munn-Ponizovsky’s theorem about irreducible representations of semigroups can be used for linear representations of automata.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
J. Cerny, “Poznamka k homogennym experimentom s konecnymy automatami,” Math.-Fyz. Cas. SAV, 14, 208–215 (1964).
J. Almeida and B. Steinberg, “Matrix mortality and the Cerny–Pin conjecture,” Lecture Notes in Computer Science, 5583, 67–80 (2009).
I. K. Rystsov, “Representation of regular ideals in finite automata,” Cybernetics and Systems Analysis, 39, No. 5, 668–675 (2003).
A. H. Clifford and G. B. Preston, The Algebraic Theory of Semigroups [Russian translation], Vol. 1, Mir, Moscow (1972).
E. B. Vinberg, Linear Representations of Groups [in Russian], Nauka, Moscow (1985).
G. Lallement, Semigroups and Combinatorial Applications [Russian translation], Mir, Moscow (1985).
J. Kari, “A counter example to a conjecture concerning synchronizing words in finite automata,” in: EATCS Bull, 73 (2001), p. 146.
B. Steinberg, “A theory of transformation monoids: Combinatorics and representation theory,” The Electronic Journal of Combinatorics, 17, #R164, 1–56 (2010).
Author information
Authors and Affiliations
Corresponding author
Additional information
Translated from Kibernetika i Sistemnyi Analiz, No. 4, pp. 19–27, July–August, 2015.
