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Journal of Automated Reasoning

, Volume 28, Issue 1, pp 35–51 | Cite as

Single Elementary Associative-Commutative Matching

  • Steven Eker
Article

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.

congruence class rewriting diophantine equations poset searching 

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Copyright information

© Kluwer Academic Publishers 2002

Authors and Affiliations

  • Steven Eker
    • 1
  1. 1.Computer Science LaboratorySRI InternationalMenlo ParkUSA. e-mail

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