Synchronizing Automata and the Černý Conjecture
Language and Automata Theory and Applications
State complexity of prefix, suffix, bifix and infix operators on regular languages
DLT'10 Proceedings of the 14th international conference on Developments in language theory
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A synchronizing word w for a given synchronizing DFA is called minimal if no proper prefix or suffix of w is synchronizing. We characterize the class of synchronizing automata having finite language of minimal synchronizing words (such automata are called finitely generated ). Using this characterization we prove that any such automaton possesses a synchronizing word of length at most 3n *** 5. We also prove that checking whether a given DFA $\mathcal{A}$ is finitely generated is co-NP-hard, and provide an algorithm for this problem which is exponential in the number of states $\mathcal{A}.$