Some aspects of synchronization of DFA

Avraham Trahtman

Research output: Contribution to journalArticlepeer-review

5 Scopus citations


A word w is called synchronizing (recurrent, reset, directable) word of deterministic finite automata (DFA) if w brings all states of the automaton to a unique state. According to the famous conjecture of Černý from 1964, every n-state synchronizing automaton possesses a synchronizing word of length at most (n-1) 2. The problem is still open. It will be proved that the Černý conjecture holds good for synchronizing DFA with transition monoid having no involutions and for every n-state (n > 2) synchronizing DFA with transition monoid having only trivial subgroups the minimal length of synchronizing word is not greater than (n-1) 2/2. The last important class of DFA involved and studied by Schǔtzenberger is called aperiodic; its automata accept precisely star-free languages. Some properties of an arbitrary synchronizing DFA were established. See .

Original languageEnglish
Pages (from-to)719-727
Number of pages9
JournalJournal of Computer Science and Technology
Issue number5
StatePublished - Sep 2008


  • Aperiodic semigroup
  • Deterministic finite automata (DFA)
  • Synchronization
  • Černý conjecture


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