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Journal Articles Discrete Mathematics and Theoretical Computer Science Year : 2010

Synchronizing random automata


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.
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hal-00990454 , version 1 (13-05-2014)



Evgeny Skvortsov, Yulia Zaks. Synchronizing random automata. Discrete Mathematics and Theoretical Computer Science, 2010, Vol. 12 no. 4 (4), pp.95-108. ⟨10.46298/dmtcs.514⟩. ⟨hal-00990454⟩


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