The Černý Conjecture and 1-Contracting Automata

  • Henk Don
Keywords: Deterministic finite automaton, Synchronizing word

Abstract

A deterministic finite automaton is synchronizing if there exists a word that sends all states of the automaton to the same state. Černý conjectured in 1964 that a synchronizing automaton with $n$ states has a synchronizing word of length at most $(n-1)^2$. We introduce the notion of aperiodically 1-contracting automata and prove that in these automata all subsets of the state set are reachable, so that in particular they are synchronizing. Furthermore, we give a sufficient condition under which the Černý conjecture holds for aperiodically 1-contracting automata. As a special case, we prove some results for circular automata.

Published
2016-07-22
Article Number
P3.12