Modifying the upper bound on the length of minimal synchronizing word

A. N. Trahtman

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

36 Scopus citations

Abstract

A word w is called synchronizing (recurrent, reset, magic, directable) word of deterministic finite automaton (DFA) if w sends all states of the automaton to a unique state. In 1964 Jan Černy found a sequence of n-state complete DFA possessing a minimal synchronizing word of length (n - 1)2. He conjectured that it is an upper bound on the length of such words for complete DFA. Nevertheless, the best upper bound (n3 - n)/6 was found almost 30 years ago. We reduce the upper bound on the length of the minimal synchronizing word to n(7n2 + 6n - 16)/48. An implemented algorithm for finding synchronizing word with restricted upper bound is described. The work presents the distribution of all synchronizing automata of small size according to the length of an almost minimal synchronizing word.

Original languageEnglish
Title of host publicationFundamentals of Computation Theory - 18th International Symposium, FCT 2011, Proceedings
Pages173-180
Number of pages8
DOIs
StatePublished - 2011
Event18th International Symposium on Fundamentals of Computation Theory, FCT 2011 - Oslo, Norway
Duration: 22 Aug 201125 Aug 2011

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume6914 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference18th International Symposium on Fundamentals of Computation Theory, FCT 2011
Country/TerritoryNorway
CityOslo
Period22/08/1125/08/11

Keywords

  • deterministic finite automaton
  • synchronizing word
  • Černy conjecture

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