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A solution of the complement problem in associatiue-commutatiue theories

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Word Equations and Related Topics (IWWERT 1991)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 677))

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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.

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Authors and Affiliations

  1. Laboratoire d'Informatique de Rouen, BP 118 Place Emile Blondel, B.P. 118, 76134, Mont-Saint-Aignant, France

    Kounalis Emmanuel

  2. INRIA, Campus scientifique, BP. 239, 54506, Vandoeuvre-lès-Nancy cedex, France

    Lugiez Denis

  3. INRIA, 2004 route des Lucioles, Sophia Antipolis, 06565, ValbonneCedex, France

    Pottier Loic

Authors
  1. Kounalis Emmanuel
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  2. Lugiez Denis
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  3. Pottier Loic
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Habib Abdulrab Jean-Pierre Pécuchet

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© 1993 Springer-Verlag Berlin Heidelberg

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Emmanuel, K., Denis, L., Loic, P. (1993). A solution of the complement problem in associatiue-commutatiue theories. In: Abdulrab, H., Pécuchet, JP. (eds) Word Equations and Related Topics. IWWERT 1991. Lecture Notes in Computer Science, vol 677. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-56730-5_39

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  • DOI: https://doi.org/10.1007/3-540-56730-5_39

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-56730-1

  • Online ISBN: 978-3-540-47636-8

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