2000 character limit reached
On the probability of being synchronizable (1304.5774v23)
Published 21 Apr 2013 in cs.FL, cs.DM, and math.CO
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random automaton with $n$ states and any fixed non-singleton alphabet is synchronizing with high probability (modulo an unpublished result about unique highest trees of random graphs).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.