Equivalence of Mealy and Moore automata

Abstract

It is proved here that every Mealy automaton is a liomomorphic image of a Moore automaton, and among these Moore automata (up to isomorphism) there exists a unique one which is a homomorphic image of the others. A unique simple Moore automaton M is constructed (up to isomorphism) in the set MO(A) of all Moore automata equivalent to a Mealy automaton A such that M is a homomorphic image of every Moore automaton belonging to MO{A). By the help of this construction, it can be decided in steps |X|k that automaton mappings inducing by states of a k-uniform finite Mealy [Moore] automaton are equal or not. The structures of simple k-uniform Mealy [Moore] automata are described by the results of [1]. It gives a possibility for us to get the k-uniform Mealy [Moore] automata from the simple k-uniform Mealy [Moore] automata. Based on these results, we give a construction for finite Mealy [Moore] automata.