Synchronization of some DFA

A. N. Trahtman

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

3 Scopus citations

Abstract

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. http://www.cs.biu.ac.il/~trakht/syn.html

Original languageEnglish
Title of host publicationTheory and Applications of Models of Computation - 4th International Conference, TAMC 2007, Proceedings
PublisherSpringer Verlag
Pages234-243
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

Conference

Conference4th International Conference on Theory and Applications of Models of Computation, TAMC 2007
Country/TerritoryChina
CityShanghai
Period22/05/0725/05/07

Keywords

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

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