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Substitution tree indexing

  • Peter Graf
Regular Papers
Part of the Lecture Notes in Computer Science book series (LNCS, volume 914)

Abstract

Sophisticated maintenance and retrieval of first-order predicate calculus terms is a major key to efficient automated reasoning. We present a new indexing technique, which accelerates the speed of the basic retrieval operations such as finding complementary literals in resolution theorem proving or finding critical pairs during completion. Subsumption and reduction are also supported. Moreover, the new technique not only provides maintenance and efficient retrieval of terms but also of idem-potent substitutions. Substitution trees achieve maximal search speed paired with minimal memory requirements in various experiments and outperform traditional techniques such as path indexing, discrimination tree indexing, and abstraction trees by combining their advantages and adding some new features.

Keywords

Leaf Node Retrieval Algorithm Tree Indexing Indexing Technique Variable Binding 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    L. Bachmair, T. Chen, and I.V. Ramakrishnan. Associative-commutative discrimination nets. In Proceedings TAPSOFT '93, LNCS 668, pages 61–74. Springer Verlag, 1993.Google Scholar
  2. 2.
    R. Butler and R. Overbeek. Formula databases for high-performance resolution/paramodulation systems. Journal of Automated Reasoning, 12:139–156, 1994.CrossRefGoogle Scholar
  3. 3.
    J. Christian. Flatterms, discrimination nets, and fast term rewriting. Journal of Automated Reasoning, 10(1):95–113, February 1993.MathSciNetGoogle Scholar
  4. 4.
    P. Graf. Extended path-indexing. In 12th Conference on Automated Deduction, pages 514–528. Springer LNAI 814, 1994.Google Scholar
  5. 5.
    P. Graf. Substitution tree indexing. Technical Report MPI-I-94-251, Max-Planck-Institut für Informatik, Saarbrücken, Germany, 1994. Full version of this paper.Google Scholar
  6. 6.
    D. Knuth and P. Bendix. Simple Word Problems in Universal Algebras. Computational Problems in Abstract Algebras. Ed. J. Leech, Pergamon Press, 1970.Google Scholar
  7. 7.
    E. Lusk and R. Overbeek. Data structures and control architectures for the implementation of theorem proving programs. In 5th International Conference on Automated Deduction, pages 232–249. Springer Verlag, 1980.Google Scholar
  8. 8.
    W. McCune. Otter 2.0. In 10th International Conference on Automated Deduction, pages 663–664. Springer Verlag, 1990.Google Scholar
  9. 9.
    W. McCune. Experiments with discrimination-tree indexing and path-indexing for term retrieval. Journal of Automated Reasoning, 9(2):147–167, October 1992.CrossRefGoogle Scholar
  10. 10.
    H.J. Ohlbach. Abstraction tree indexing for terms. In Proceedings of the 9th European Conference on Artificial Intelligence, pages 479–484. Pitman Publishing, London, August 1990.Google Scholar
  11. 11.
    J.A. Robinson. A machine-oriented logic based on the resolution principle. Journal of the ACM, 12(1):23–41, 1965.CrossRefGoogle Scholar
  12. 12.
    M. Stickel. The path-indexing method for indexing terms. Technical Note 473, Artificial Intelligence Center, SRI International, Menlo Park, CA, October 1989.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1995

Authors and Affiliations

  • Peter Graf
    • 1
  1. 1.Max-Planck-Institut für Informatik Im StadtwaldSaarbrückenGermany

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