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The complexity of equivalence and containment for free single variable program schemes

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Automata, Languages and Programming (ICALP 1978)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 62))

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Abstract

Non-containment for free single variable program schemes is shown to be NP-complete. A polynomial time algorithm for deciding equivalence of two free schemes, provided one of them has the predicates appearing in the same order in all executions, is given. However, the ordering of a free scheme is shown to lead to an exponential increase in size.

This research was supported in part by the office of Naval Research under contract N00014-76-0018 and by Aarhus University, Aarhus, Denmark.

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References

  1. A.V. Aho, J.E. Hopcroft, J.D. Ullman: "The Design and Analysis of Algorithms", Addison-Wesley Publishing Company, 1974.

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  2. A.V. Aho and J.D. Ullman: "The Theory of Parsing, Translation, and Compiling", Volume I: Parsing, Prentice-Hall, Inc., Englewood Cliffs, N.J. 1972.

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  3. R.L. Constable, H.B. Hunt III, S. Sahni: "On the Computational Complexity of Scheme Equivalence", Proc. Eights An. Princeton Conf. on Information Sciences and Systems, Princeton University, 1974. Also submitted to SIAM J. Computing.

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  4. S.A. Greibach: "Theory of Program Structures: Schemes, Semantics, Verification", Lecture Notes in Computer Science 36, Springer-Verlag, 1975.

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  5. Z. Manna: "Mathematical Theory of Computation", McGraw-Hill Inc. 1974.

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Author notes

  1. Erik Meineche Schmidt

    Present address: Computer Science Department, Aarhus University, Aarhus, Denmark

Authors and Affiliations

  1. Department of Computer Science, Cornell University, 14853, Ithaca, New York, USA

    Steven Fortune, John Hopcroft & Erik Meineche Schmidt

Authors
  1. Steven Fortune
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  2. John Hopcroft
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  3. Erik Meineche Schmidt
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Editor information

Giorgio Ausiello Corrado Böhm

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© 1978 Springer-Verlag Berlin Heidelberg

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Fortune, S., Hopcroft, J., Schmidt, E.M. (1978). The complexity of equivalence and containment for free single variable program schemes. In: Ausiello, G., Böhm, C. (eds) Automata, Languages and Programming. ICALP 1978. Lecture Notes in Computer Science, vol 62. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-08860-1_17

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  • DOI: https://doi.org/10.1007/3-540-08860-1_17

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-08860-8

  • Online ISBN: 978-3-540-35807-7

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