Synchronizing generalized monotonic automata

Dedicated to Academician Arto Salomaa on the occasian of his 70th birthday
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Abstract

In an earlier paper, we have studied reset words for synchronizing automata whose states admit a stable linear order. Here we show that the same bound on the length of the shortest reset word persists for synchronizing automata satisfying much weaker stability restriction. This result supports our conjecture concerning the length of reset words for synchronizing automata accepting only star-free languages.

Keywords

Synchronizing automata
Order-preserving transformation
Monotonic automata
Congruence on an automaton
Generalized monotonic automata
Rank of a word with respect to an automaton
Rank of an automaton

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