Isomorphism Groups of Automata

  • Authors:

  • A. C. Fleck

  • Affiliations:

  • Michigan State University, East Lansing, Michigan

  • Venue:
  • Journal of the ACM (JACM)
  • Year:
  • 1962

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Abstract

This paper persues a discussion of certain algebraic properties of automata and their relationship to the structure (i.e., properties of the next state function) of automata. The device which is used for this study is the association of a group with each automaton. We introduce functions on automata and study the group of an automaton, a representation for the group elements and the direct product of automata. Finally, for a certain class of automata a necessary and sufficient condition, in terms of the group of the automaton, is given for insuring that an automaton can be represented as a direct product.