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Single Elementary Associative-Commutative Matching

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Abstract

A single elementary associative-commutative (AC) matching problem has a pattern term that consists of a single (variadic) AC function symbol with only variable symbols as arguments and a subject term that consists of a single (variadic) AC function symbol with only constant symbols as arguments. We show that even this very restricted formulation of AC matching has an NP-complete decision problem. We consider a number of methods to contain the growth in the search space, including a lookup table for the solubility of subproblems, a digraph reformulation of the problem, and a search tree pruning method that uses failure information together with a partial ordering on branches. We give empirical results for the method that seems to work best in practice, and we list some ‘hard’ problem instances.

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  1. Computer Science Laboratory, SRI International, Menlo Park, CA, 94025, USA. e-mail

    Steven Eker

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Eker, S. Single Elementary Associative-Commutative Matching. Journal of Automated Reasoning 28, 35–51 (2002). https://doi.org/10.1023/A:1020122610698

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