On the structure of abelian automata

摘要

The structure of an abelian automaton is studied in connection with the notion of the stage and the transition structure of an automaton introduced in [6].The transition structure of an abelian automaton and the commutativity of its automorphism group are investigated.Each stage of an abelian automaton is a perfect automaton with a subset of input symbols related to the stage, and if stages S and S′ are in the relation S>S′, then the stage S′, is decomposed into a disjoint union of perfect automata that are homomorphic images of the perfect automaton defined by the stage S and isomorphic to each other.