A criterion for the simplicity of finite Moore automata

Abstract

A Moore automaton A = (A, X,Y,S, A) can be obtained in two steps: first we consider the triplet (A, X, 6) - called a semiautomaton and denoted by S — and then we add the components Y and A which concern the output functioning. Our approach is: S is supposed to be fixed, we vary A in any possible way, and - among the resulting automata - we want to separate the simple and the nonsimple ones from each other. This task is treated by combinatorial methods. Concerning the efficiency of the procedure, we note that it uses a semiautomaton having |A|(|A| + l)/2 states