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arXiv · 1304.5774

On the probability of being synchronizable

Mikhail V. Berlinkov
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Abstract

We prove that a random automaton with $n$ states and any fixed non-singleton alphabet is synchronizing with high probability (modulo an unpublished result about unique highest trees of random graphs). Moreover, we also prove that the convergence rate is exactly $1-\Theta(\frac{1}{n})$ as conjectured by [Cameron, 2011] for the most interesting binary alphabet case. Finally, we present a deterministic algorithm which decides whether a given random automaton is synchronizing in linear in $n$ expected time and prove that it is optimal.

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Mikhail V. Berlinkov. 2013-04-21. On the probability of being synchronizable. https://arxiv.org/abs/1304.5774

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