Skvortsov, Evgeny and Zaks, Yulia - Synchronizing random automata

dmtcs:514 - Discrete Mathematics & Theoretical Computer Science, January 1, 2010, Vol. 12 no. 4
Synchronizing random automata

Authors: Skvortsov, Evgeny and Zaks, Yulia

Conjecture that any synchronizing automaton with n states has a reset word of length (n - 1)(2) was made by. Cerny in 1964. Notwithstanding the numerous attempts made by various researchers this conjecture hasn't been definitively proven yet. In this paper we study a random automaton that is sampled uniformly at random from the set of all automata with n states and m(n) letters. We show that for m(n) > 18 ln n any random automaton is synchronizing with high probability. For m(n) > n(beta), beta > 1/2 we also show that any random automaton with high probability satisfies the. Cerny conjecture.


Source : oai:HAL:hal-00990454v1
Volume: Vol. 12 no. 4
Published on: January 1, 2010
Submitted on: March 26, 2015
Keywords: Synchronizing DFA,Random DFA,Wormald's Theorem,Cerny problem,[INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM]


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