Modifying the upper bound on the length of minimal synchronizing word release_cbegzyooabe2hp5bi7lsqmozua

by A. N. Trahtman

Released as a article .

2012  

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 (n^3-n)/6 was found almost 30 years ago. We reduce the upper bound on the length of the minimal synchronizing word to n(7n^2+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.
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Type  article
Stage   submitted
Date   2012-12-10
Version   v5
Language   en ?
arXiv  1104.2409v5
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