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Reducing the complexity of the Knuth-Bendix completion algorithm: A "unification" of different approaches

  • Franz Winkler
Rewrite Rules And The Completion Procedure
Part of the Lecture Notes in Computer Science book series (LNCS, volume 204)

Abstract

The Knuth-Bendix completion procedure for rewrite rule systems is of wide applicability in symbolic and algebraic computation. Attempts to reduce the complexity of this completion algorithm are reported in the literature. Already in their seminal 1967 paper D.E. Knuth and P.B. Bendix have suggested to keep all the rules interreduced during the execution of the algorithm. G. Huet has presented a version of the completion algorithm in which every rewrite rule is kept in reduced form with respect to all the other rules in the system. Borrowing an idea of Buchberger's for the completion of bases of polynomial ideals the author has proposed in 1983 a criterion for detecting "unnecessary" critical pairs. If a critical pair is recognized as unnecessary then one need not apply the costly process of computing normal forms to it. It has been unclear whether these approaches can be combined. We demonstrate that it is possible to keep all the rewrite rules interreduced and still use a criterion for eliminating unnecessary critical pairs.

Keywords

Normal Form Induction Hypothesis Theorem Prove Polynomial Ideal Critical Pair 
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 1985

Authors and Affiliations

  • Franz Winkler
    • 1
  1. 1.Department of Computer and Information SciencesUniversity of DelawareNewarkUSA

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