Paper Info
Title
Modifying the upper bound on the length of minimal synchronizing word
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.
Year
DOI
Venue
2011
10.1007/978-3-642-22953-4_15
Clinical Orthopaedics and Related Research
Keywords
DocType
Volume
synchronizing automaton,small size,n-state complete dfa,synchronizing word,unique state,deterministic finite automaton,complete dfa,minimal synchronizing word,word w,ˇ,upper bound,discrete mathematics
Conference
abs/1104.2409
Citations 
PageRank 
References 
25
1.83
10
Authors
1
Name
Order
Citations
PageRank
A. N. Trahtman19211.68