The černý conjecture for aperiodic automata

A. N. Trahtman

Research output: Contribution to journalArticlepeer-review

67 Scopus citations


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 languageEnglish
Pages (from-to)3-10
Number of pages8
JournalDiscrete Mathematics and Theoretical Computer Science
Issue number2
StatePublished - 2007


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


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