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Trim Strongly Connected Synchronizing Automata and Ideal Languages

Maslennikova M., Rodaro E.

Fundamenta Informaticae

2018

Vol. 162, nr 2/3

183--203

We follow language theoretic approach to synchronizing automata and Černý’s conjecture initiated in a series of recent papers. We prove that for every ideal language there exists a strongly connected synchronizing automaton from some special class for which given language serves as the language of reset words. This class is formed by trim automata recognizing left quotients of principal left ideal languages. We show that the minimal automaton recognizing a left quotient of a principal left ideal can be viewed as a synchronizing automaton for which given finitely generated ideal serves as the language of reset words.