Abstract
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.
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Emmanuel, K., Denis, L., Loic, P. (1991). A solution of the complement problem in associatiue-commutatiue theories. In: Tarlecki, A. (eds) Mathematical Foundations of Computer Science 1991. MFCS 1991. Lecture Notes in Computer Science, vol 520. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-54345-7_72
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DOI: https://doi.org/10.1007/3-540-54345-7_72
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