Matrix Mortality and the Černý-Pin Conjecture

Authors:
Jorge Almeida;Benjamin Steinberg
Affiliations:
Departamento de Matemática Pura, Faculdade de Ciências, Universidade do Porto, Porto, Portugal 4169-007;School of Mathematics and Statistics, Carleton University, Ottawa, Canada K1S 5B6
Venue:
DLT '09 Proceedings of the 13th International Conference on Developments in Language Theory
Year:
2009

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Abstract

In this paper, we establish the Černý-Pin conjecture for automata with the property that their transition monoid cannot recognize the language {a,b}* ab{a,b}*. For the subclass of automata whose transition monoids have the property that each regular -class is a subsemigroup, we give a tight bound on lengths of reset words for synchronizing automata thereby answering a question of Volkov.