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

M3 - ???researchoutput.researchoutputtypes.contributiontobookanthology.conference???

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 -