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Efficient ground completion

An O(n log n) algorithm for generating reduced sets of ground rewrite rules equivalent to a set of ground equations E
  • Wayne Snyder
Regular Papers
Part of the Lecture Notes in Computer Science book series (LNCS, volume 355)

Abstract

We give a fast method for generating reduced sets of rewrite rules equivalent to a given set of ground equations. Since, as we show, reduced ground rewrite systems are in fact canonical, this is essentially an efficient Knuth-Bendix procedure for the ground case. The method runs in O(n log n), where n is the number of occurrences of symbols in E. We also show how our method provides a precise characterization of the (finite) collection of all reduced sets of rewrite rules equivalent to a given ground set of equations E, and prove that our algorithm is complete in that it can enumerate every member of this collection. Finally, we show how to modify the method so that it takes as input E and a total precedence ordering on the symbols in E, and returns a reduced rewrite system contained in the lexicographic path ordering generated by the precedence.

Keywords

Word Problem Theorem Prove Ground Term Quotient Graph Equational Mating 
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

  • Wayne Snyder
    • 1
  1. 1.Department of Computer ScienceBoston UniversityBoston

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