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arXiv · 1404.6962

Fast Synchronization of Random Automata

Cyril Nicaud
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Abstract

A synchronizing word for an automaton is a word that brings that automaton into one and the same state, regardless of the starting position. Cerny conjectured in 1964 that if a n-state deterministic automaton has a synchronizing word, then it has a synchronizing word of size at most (n-1)^2. Berlinkov recently made a breakthrough in the probabilistic analysis of synchronization by proving that with high probability, an automaton has a synchronizing word. In this article, we prove that with high probability an automaton admits a synchronizing word of length smaller than n^(1+ε), and therefore that the Cerny conjecture holds with high probability.

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Cyril Nicaud. 2014-09-01. Fast Synchronization of Random Automata. https://arxiv.org/abs/1404.6962

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