IWWERT 1991: Word Equations and Related Topics pp 197-214 | Cite as

A solution of the complement problem in associatiue-commutatiue theories

  • Kounalis Emmanuel
  • Lugiez Denis
  • Pottier Loic
Conference paper
First Online:
Part of the Lecture Notes in Computer Science book series (LNCS, volume 677)

Abstract

We show in this paper that the problem of checking whether there are ground instances of a term t which are not instances of the terms t1, ..., tn modulo sets of associativity and commutativity axioms is decidable. This question belongs to the the well-known class of complement problems.

Its solution provides a formal basis for automating the process of learning from examples, verifying the sufficient-completeness property of algebraic specifications, designing associative-commutative compilation algorithms, finding solutions of systems of equations and disequations in associative and commutative theories, etc.

Keywords

The Subsumption Lattice of First-Order terms Associative and Commutative Reasoning AC-Disunification Inductive Learning Pattern-Matching Sufficient-Completeness 
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Copyright information

© Springer-Verlag Berlin Heidelberg 1993

Authors and Affiliations

  • Kounalis Emmanuel
    • 1
  • Lugiez Denis
    • 2
  • Pottier Loic
    • 3
  1. 1.Laboratoire d'Informatique de RouenMont-Saint-AignantFrance
  2. 2.INRIAVandoeuvre-lès-Nancy cedexFrance
  3. 3.INRIAValbonneCedexFrance

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