Synchronizations and General Repetitive Machines, with Applications to Ultimate Definite Automata

  • Authors:

  • R. G. Reynolds;W. F. Cutlip

  • Affiliations:

  • Michigan State University, Division of Engineering Research, East Lansing, Michigan;Michigan State University, Division of Engineering Research, East Lansing, Michigan

  • Venue:
  • Journal of the ACM (JACM)
  • Year:
  • 1969

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Abstract

Let s and t be states of a finite (deterministic) automaton A. t can be reached from s if there is a tape x such that, if A is in state s and receives x, A goes to state t.We consider (1) automata in which the initial state can be reached from any final state, and (2) automata which can be brought to a known state from any unknown state by applying a predetermined tape x.Necessary and sufficient conditions for an ultimate definite automaton to have the former property are obtained. Every ultimate definite automaton A is shown to have the latter property; and a characterization is obtained for all tapes which bring A to a known state. Finally, those ultimate definite automata having the former property are shown to be precisely those which can be brought to the start state from any state by some tape x.