https://hal.inria.fr/hal-00966534Trahtman, Avraham N.Avraham N.TrahtmanDepartment of Mathematics [Israël] - Bar-Ilan University [Israël]The Černý conjecture for aperiodic automataHAL CCSD2007[INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM]Inria Sophia Antipolis-Méditerranée / I3s, Service Ist2014-03-26 17:01:532017-11-29 10:26:222014-03-27 13:58:42enJournal articleshttps://hal.inria.fr/hal-00966534/document10.46298/dmtcs.395application/pdf1A word w is called a synchronizing (recurrent, reset, directable) word of a deterministic finite automaton (DFA) if w brings all states of the automaton to some specific state; a DFA that has a synchronizing word is said to be synchronizable. Cerny conjectured in 1964 that every n-state synchronizable DFA possesses a synchronizing word of length at most (n-1)2. We consider automata with aperiodic transition monoid (such automata are called aperiodic). We show that every synchronizable n-state aperiodic DFA has a synchronizing word of length at most n(n-1)/2. Thus, for aperiodic automata as well as for automata accepting only star-free languages, the Cerny conjecture holds true.