A solution of the complement problem in associatiue-commutatiue theories

  • Kounalis Emmanuel
  • Lugiez Denis
  • Pottier Loic
Part of the Lecture Notes in Computer Science book series (LNCS, volume 520)


We show in this paper that the question 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.


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 1991

Authors and Affiliations

  • Kounalis Emmanuel
    • 1
    • 2
  • Lugiez Denis
    • 2
    • 1
  • Pottier Loic
    • 4
    • 3
  1. 1.CRIn-INRIAFrance
  2. 2.Vandoeuvre-lès-Nancy cedexFrance
  3. 3.INRIAFrance
  4. 4.ValbonneCedexFrance

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