Experimental study of the shortest reset word of random automata

Abstract

In this paper we describe an approach to finding the shortest reset word of a finite synchronizing automaton by using a SAT solver. We use this approach to perform an experimental study of the length of the shortest reset word of a finite synchronizing automaton. The largest automata we considered had 100 states. The results of the experiments allow us to formulate a hypothesis that the length of the shortest reset word of a random finite automaton with n states and 2 input letters with high probability is sublinear with respect to n and can be estimated as 1.95n0.55. © 2011 Springer-Verlag.