Groups of Automorphisms and Sets of Equivalence Classes of Input for Automata
Bruce H. Barnes · Journal of the ACM · 1965
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.