Complexity of matching problems
Journal of Symbolic Computation
Efficient solution of linear diophantine equations
Journal of Symbolic Computation
UMIST OBJ: a language for executable program specifications
The Computer Journal - Special issue: formal aspects of computing systems
Compilation of pattern matching with associative-commutative functions
TAPSOFT '91 Proceedings of the international joint conference on theory and practice of software development on Colloquium on trees in algebra and programming (CAAP '91): vol 1
Handbook of theoretical computer science (vol. B)
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Solution of the Robbins Problem
Journal of Automated Reasoning
Computational Complexity of Simultaneous Elementary Matching Problems (Extended Abstract)
MFCS '95 Proceedings of the 20th International Symposium on Mathematical Foundations of Computer Science
A Compiler for Rewrite Programs in Associative-Commutative Theories
PLILP '98/ALP '98 Proceedings of the 10th International Symposium on Principles of Declarative Programming
Associative-Commutative Discrimination Nets
TAPSOFT '93 Proceedings of the International Joint Conference CAAP/FASE on Theory and Practice of Software Development
An Overview of LP, The Larch Power
RTA '89 Proceedings of the 3rd International Conference on Rewriting Techniques and Applications
STORM: A MAny-to-One Associative-Commutative Matcher
RTA '95 Proceedings of the 6th International Conference on Rewriting Techniques and Applications
Experiments with associative-commutative discrimination nets
IJCAI'95 Proceedings of the 14th international joint conference on Artificial intelligence - Volume 1
Compilation techniques for associative-commutative normalisation
Algebraic'97 Proceedings of the 2nd international conference on Theory and Practice of Algebraic Specifications
Associative-commutative rewriting on large terms
RTA'03 Proceedings of the 14th international conference on Rewriting techniques and applications
Tactics for reasoning modulo AC in coq
CPP'11 Proceedings of the First international conference on Certified Programs and Proofs
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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.