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Solving Word Problems in Free Algebras Using Complexity Functions

  • Alex Pelin
  • Jean H. Gallier
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 170)

Abstract

We present a new method for solving word problems using complexity functions. Complexity functions are used to compute normal forms. Given a set of (conditional) equations E, complexity functions are used to convert these equations into reductions (rewrite rules decreasing the complexity of terms). Using the top-down reduction extension Rep induced by a set of equations E and a compIexity function, we investigate properties which guarantee that any two (ground) terms t1 and t2 are congruent modulo the congruence ≌E if and only if Rep(t1)=Rep ( t2). Our method actually consists in computing Rep incrementally, as the composition of a sequence of top-down reduction extensions induced by possibly different complexity functions. This method relaxes some of the restrictions imposed by the Cburch-Rosser property.

Keywords

Normal Form Complexity Function Word Problem Free Algebra Conditional Equation 
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 1984

Authors and Affiliations

  • Alex Pelin
    • 1
  • Jean H. Gallier
    • 2
  1. 1.Department of Computer and Information ScienceTemple UniversityPhiladelphia
  2. 2.Department of Computer and Information ScienceUniversity of PennsylvaniaPhiladelphia

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