Synchronization of some DFA

A. N. Trahtman

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

3 Scopus citations


A word ω is called synchronizing (recurrent, reset, directable) word of deterministic finite automaton (DFA) if ω brings all states of the automaton to an unique state. Černý conjectured in 1964 that every nstate synchronizable automaton possesses a synchronizing word of length at most (n - 1)2. The problem is still open. It will be proved that the minimal length of synchronizing word is not greater than (n - 1)2/2 for every n-state (n > 2) synchronizable DFA with transition monoid having only trivial subgroups (such automata are called aperiodic). This important class of DFA accepting precisely star-free languages was involved and studied by Schützenberger. So for aperiodic automata as well as for automata accepting only star-free languages, the Černý conjecture holds true. Some properties of an arbitrary synchronizable DFA and its transition semigroup were established.

Original languageEnglish
Title of host publicationTheory and Applications of Models of Computation - 4th International Conference, TAMC 2007, Proceedings
PublisherSpringer Verlag
Number of pages10
ISBN (Print)3540725032, 9783540725039
StatePublished - 2007
Event4th International Conference on Theory and Applications of Models of Computation, TAMC 2007 - Shanghai, China
Duration: 22 May 200725 May 2007

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume4484 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Conference4th International Conference on Theory and Applications of Models of Computation, TAMC 2007


  • Aperiodic semigroup
  • Deterministic finite automata
  • Synchronization
  • Černý conjecture


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