%0 Journal Article
%T The  erny Conjecture for Aperiodic Automata
%A Avraham N. Trahtman
%J Discrete Mathematics & Theoretical Computer Science
%D 2007
%I Discrete Mathematics & Theoretical Computer Science
%X A 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.
%U http://www.dmtcs.org/dmtcs-ojs/index.php/dmtcs/article/view/649