TY - GEN
T1 - Modifying the upper bound on the length of minimal synchronizing word
AU - Trahtman, A. N.
PY - 2011
Y1 - 2011
N2 - 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.
AB - 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.
KW - deterministic finite automaton
KW - synchronizing word
KW - Černy conjecture
UR - http://www.scopus.com/inward/record.url?scp=80052419722&partnerID=8YFLogxK
U2 - 10.1007/978-3-642-22953-4_15
DO - 10.1007/978-3-642-22953-4_15
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AN - SCOPUS:80052419722
SN - 9783642229527
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 173
EP - 180
BT - Fundamentals of Computation Theory - 18th International Symposium, FCT 2011, Proceedings
T2 - 18th International Symposium on Fundamentals of Computation Theory, FCT 2011
Y2 - 22 August 2011 through 25 August 2011
ER -