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]

This page has been seen 36 times.

This article's PDF has been downloaded 132 times.