Synchronizing groups and automata

Authors:
Fredrick Arnold;Benjamin Steinberg
Affiliations:
School of Mathematics and Statistics, Carleton University, Ottawa, ON, Canada;School of Mathematics and Statistics, Carleton University, Ottawa, ON, Canada
Venue:
Theoretical Computer Science
Year:
2006

Citing 2
Cited 3

Sur un Cas Particulier de la Conjecture de Cerny

Proceedings of the Fifth Colloquium on Automata, Languages and Programming
Synchronizing finite automata on Eulerian digraphs

Theoretical Computer Science - Mathematical foundations of computer science

Černý's conjecture and group representation theory

Journal of Algebraic Combinatorics: An International Journal
The averaging trick and the Černý conjecture

DLT'10 Proceedings of the 14th international conference on Developments in language theory
Groups synchronizing a transformation of non-uniform kernel

Theoretical Computer Science

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Abstract

Pin showed that every p-state automaton (p a prime) containing a cyclic permutation and a non-permutation has a synchronizing word of length at most (p - 1)2. In this paper, we consider permutation automata with the property that adding any nonpermutation will lead to a synchronizing word and establish bounds on the lengths of such synchronizing words. In particular, we show that permutation groups whose permutation character over the rationals splits into a sum of only two irreducible characters have the desired property.