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Solving disequations in equational theories

  • Hans-Jürgen Bürckert
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 310)

Abstract

Disunification is the problem to solve a system < s i = t i : 1 ≤ in, p j q j : 1 ≤jm〉 of equations and disequations. Solutions are substitutions for the variables of the problem that make the two terms of each equation equal, but let those of the disequations different. We investigate this in the case, where equality is defined by an equational theory E. We show how E-disunification can be reduced to E-unification, that is solving equations only, and give a disunification algorithm for equational theories provided there is a unification algorithm. In fact this result shows that for theories, where the solutions of all unification problems can be represented by finitely many substitutions, there is also a finite representation of the solutions of all disunification problems. As an application we discuss how AC1-disunification can be used as a method to represent many AC-unifiers by a few AC1-disunifiers.

Keywords

Equational theories E-unification E-disunification solving equations and disequations 

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Copyright information

© Springer-Verlag Berlin Heidelberg 1988

Authors and Affiliations

  • Hans-Jürgen Bürckert
    • 1
  1. 1.FB Informatik, Universität KaiserslauternKaiserslauternFR Germany

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