Groups of Automorphisms and Sets of Equivalence Classes of Input for Automata

Abstract

An investigation is presented which continues the work of Fleck and Weeg concerning the relationships between the equivalence classes of inputs and the group of automorphisms of a finite automaton. The principal result is that if for each state of a strongly connected automaton there exists a subset of the set of equiwfience classes of the input semigroup which constitute t~ group, then this group is isomorphic to a group of automorphisms of the automaton. The relationship between subautomata and subgroups of the group of autoraorphisms is also studied.