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Consider only general superpositions in completion procedures

  • Hantao Zhang
  • Deepak Kapur
Regular Papers
Part of the Lecture Notes in Computer Science book series (LNCS, volume 355)

Abstract

Superposition or critical pair computation is one of the key operations in the Knuth-Bendix completion procedure and its extensions. We propose a practical technique which can save computation of some critical pairs where the most general unifiers used to generate these critical pairs are less general than the most general unifiers used to generate other joinable critical pairs. Consequently, there is no need to superpose identical subterms at different positions in a rule more than once and there is also no need to superpose symmetric subterms in a rule more than once. The combination of this technique with other critical pair criteria proposed in the literature is also discussed. The technique has been integrated in the completion procedures for ordinary term rewriting systems as well as term rewriting systems with associative-commutative operators implemented in RRL, Rewrite Rule Laboratory. Performance of the completion procedures with and without this technique is compared on a number of examples.

Keywords

Theorem Prove Associative Ring Critical Pair Canonical System Automate Deduction 
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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Copyright information

© Springer-Verlag Berlin Heidelberg 1989

Authors and Affiliations

  • Hantao Zhang
    • 1
  • Deepak Kapur
    • 2
  1. 1.Department of Computer ScienceThe University of IowaIowa City
  2. 2.Department of Computer ScienceState University of New York at AlbanyAlbany

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