A solution of the complement problem in associatiue-commutatiue theories
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.
KeywordsThe Subsumption Lattice of First-Order terms Associative and Commutative Reasoning AC-Disunification Inductive Learning Pattern-Matching Sufficient-Completeness
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