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Deterministic one-counter automata

  • Automatentheorie
  • Conference paper
  • First Online:
GI Gesellschaft für Informatik e. V. 1. Fachtagung über Automatentheorie und Formale Sprachen

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2))

Abstract

The class of deterministic one-counter automata is a natural extension of the class of finite-state machines. We have shown that in contrast with the inclusion and nullity of intersection problems, which become undecidable under this generalisation the equivalence problem remains decidable.

We have established that these automata have certain periodic structural properties, and have derived an upper bound for the associated period that is asymptotically achievable. The resulting bound on the time complexity of the derived decision procedure is exponential in about the square root of the number of states of the tested machines. Whether a polynomial time test exists, remains open.

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References

  1. Hopcroft, J. E., and Ullman, J. D., Formal Languages and their Relation to Automata, Addison-Wesley, Reading, Mass., (1969).

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  2. Minsky, M. L., Computation: Finite and Infinite Machines, Prentice-Hall, Englewood Cliffs, N.J., (1967).

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  3. Paterson, M.S. Decision Problems in Computational Models, Proc. ACM Conference on Proving Assertions about Programs, Las Cruces, New Mexico, (1972).

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  4. Rosenkrantz, D. J., and Stearns, R. E., Properties of Deterministic Top-Down Grammars, Inf. and Control, 17, 226–256, (1970).

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  5. Valiant, L.G., Decision Procedures for Families of Deterministic Pushdown Automata, Ph.D. Thesis (to be submitted), University of Warwick, (1973).

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Authors
  1. L. G. Valiant
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  2. M. S. Paterson
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© 1973 Springer-Verlag

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Valiant, L.G., Paterson, M.S. (1973). Deterministic one-counter automata. In: GI Gesellschaft für Informatik e. V. 1. Fachtagung über Automatentheorie und Formale Sprachen. Lecture Notes in Computer Science, vol 2. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0039144

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  • DOI: https://doi.org/10.1007/BFb0039144

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-06527-2

  • Online ISBN: 978-3-540-37826-6

  • eBook Packages: Springer Book Archive

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