On the construction of a family of automata that are generically non-minimal

Abstract

One way to generate an accessible deterministic finite automaton is to first generate a spanning tree and then complete it to an automaton. We introduce the ideas of a sequential automaton, that are automata with sequential trees as breadth-first spanning subtrees. We introduce the concept of elementary equivalent states and explore combinatorial properties of non-minimal sequential automata. We then show that minimality is negligible among sequential automata by calculating the probability that an automaton has two elementary equivalent states and showing that this probability approach 1 as the size of the automaton increases. © 2013 Springer-Verlag Berlin Heidelberg.