Synchronizing Automata with Finitely Many Minimal Synchronizing Words

Abstract

A synchronizing word for a given synchronizing DFA is called minimal if none of its proper factors is synchronizing. We characterize the class of synchronizing automata having only finitely many minimal synchronizing words (the class of such automata is denoted by FG). 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 A is in FG is co-NP-hard and provide an algorithm for this problem which is exponential in the number of states A. © 2010 Elsevier Inc. All rights reserved.Author acknowledges support from the Federal Education Agency of Russia, Grant 2.1.1/3537, and from the Russian Foundation for Basic Research, Grants 09-01-12142 and 10-01-00793. This research was initiated with the partial support of GNSAGA during the visit of the author to the Ural State University, Russia