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Elementary lower bounds for the lengths of refutations

  • Hai-Ping Ko
  • Mark E. Nadel
Session 6: Theorem Proving and Complexity
Part of the Lecture Notes in Computer Science book series (LNCS, volume 624)

Abstract

This paper presents some lower bounds for the lengths of refutations in logic programming. These lower bounds will immediately imply corresponding lower bounds for pure Prolog. For programs without free variables, we present the Special Linear Lower Bounds. For goals whose ground solutions would generate a discrete data-type, we present the Asymptotic log(n) Lower Bound.

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References

  1. 1.
    Ko, H-P, and Nadel, M.E., Substitution and Refutation Revisited, Proceedings of the Eighth International Conference on Logic Programming, 1991.Google Scholar
  2. 2.
    Ko, H-P, and Nadel, M.E., Lower Bounds for the Lengths of Refutations, submitted for publication, 1991.Google Scholar
  3. 3.
    Lassez, J-L, Maher, M.J., and Marriott, K., Unification Revisited, in M. Boscarol, L. Carlucci Aiello, and G. Levi (eds), Foundations of Logic and Functional Programming, LNCS 306 (1987), pp. 67–113.Google Scholar
  4. 4.
    Lloyd, J.W., Foundations of Logic Programming, 2nd edition, Springer-Verlag, 1987.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1992

Authors and Affiliations

  • Hai-Ping Ko
    • 1
  • Mark E. Nadel
    • 1
  1. 1.The MITRE CorporationBedford

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