## Abstract

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 synchrvnizable. Černý 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 Černý conjecture holds true.

Original language | English |
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Pages (from-to) | 3-10 |

Number of pages | 8 |

Journal | Discrete Mathematics and Theoretical Computer Science |

Volume | 9 |

Issue number | 2 |

State | Published - 2007 |

## Keywords

- Deterministic finite automaton
- Star-free language
- Synchronizing word