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Polynomial interpretations and the complexity of algorithms

  • Adam Cichon
  • Pierre Lescanne
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 607)

Abstract

The ability to use a polynomial iterpretation to prove termination of a rewrite system naturally prompts the question as to what restriction on complexity this imposes. The main result of this paper is that a polynomial interpretation termination proof of a rewrite system R which computes a number theoretic function implies a polynomial bound on that function's rate of growth.

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References

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    O. Geupel. Terminationbeweise bei Termersetzungssytem, 1988. Diplomarbeit.Google Scholar
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    G. Huet and D.C. Oppen. Equations and rewrite rules: A survey. In R. Book, editor, Formal Language Theory: Perspectives and Open Problems, pages 349–405. Academic Press, 1980.Google Scholar
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    D. Lankford. Canonical algebraic simplification in computational logic. Report ATP-25, University of Texas, 1975.Google Scholar
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    D. Lankford. On proving term rewriting systems are noetherian. Report MTP-3, Louisiana Tech. University, 1979.Google Scholar
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    C. Lautemann. A note on polynomial interpretation. In Bulletin of the European Association for Theoretical Computer Science, volume 4, pages 129–131, October 1988.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1992

Authors and Affiliations

  • Adam Cichon
    • 1
  • Pierre Lescanne
    • 1
  1. 1.CRIN & INRIA-LorraineVillers-lès-NancyFrance

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