Automorphism groups and factor automata of strongly connected automata

摘要

Structures of strongly connected automata are investigated in connection with their automorphism groups, input sets, and factor automata. First, detailed considerations are given concerning group-matrix type automata introduced by M. Ito which give a representation of strongly connected automata. By using these results, we study the following condition for a given finite group G and a given strongly connected automaton B:P(G, B): There exists a strongly connected automaton A such that the automorphism group of A is isomorphic to G and the factor automaton of A by its automorphism group is isomorphic to B.