Synchronizing monotonic automata

Authors:
Dimitry S. Ananichev;Mikhail V. Volkov
Affiliations:
Department of Mathematics and Mechanics, Ural State University, Ekaterinburg, Russia;Department of Mathematics and Mechanics, Ural State University, Ekaterinburg, Russia
Venue:
DLT'03 Proceedings of the 7th international conference on Developments in language theory
Year:
2003

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Abstract

We show that if the state set Q of a synchronizing automaton A = 〈Q, Σ, δ〉 admits a linear order such that for each letter a ∈ Σ the transformation δ(-, a) of Q preserves this order, then A possesses a reset word of length |Q|-1. We also consider two natural generalizations of the notion of a reset word and provide for them results of a similar flavour.