Complexity of matching problems
Journal of Symbolic Computation
Opening the AC-unification race
Journal of Automated Reasoning
A catalog of complexity classes
Handbook of theoretical computer science (vol. A)
Handbook of theoretical computer science (vol. A)
Tight complexity bounds for term matching problems
Information and Computation
Handbook of logic in artificial intelligence and logic programming
Complexity of generalized satisfiability counting problems
Information and Computation
The complexity of counting problems in equational matching
Journal of Symbolic Computation
A Unification Algorithm for Associative-Commutative Functions
Journal of the ACM (JACM)
On the complexity of integer programming
Journal of the ACM (JACM)
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
An Overview of LP, The Larch Power
RTA '89 Proceedings of the 3rd International Conference on Rewriting Techniques and Applications
SPIKE-AC: A System for Proofs by Induction in Associative-Commutative Theories
RTA '96 Proceedings of the 7th International Conference on Rewriting Techniques and Applications
In Search of a Phase Transition in the AC-Matching Problem
CP '01 Proceedings of the 7th International Conference on Principles and Practice of Constraint Programming
Type inference for sublinear space functional programming
APLAS'10 Proceedings of the 8th Asian conference on Programming languages and systems
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The simultaneous elementary E-matching problem for an equational theory E is to decide whether there is an E-matcher for a given system of equations in which the only nonconstant function symbols occurring in the terms to be matched are the ones constrained by the equational axioms of E. We study the computational complexity of simultaneous elementary matching problems for the equational theories A of semigroups, AC of commutative semigroups, and ACU of commutative monoids. In each case, we delineate the boundary between NP-completeness and solvability in polynomial time by considering two parameters, the number of equations in the systems and the number of constant symbols in the signature. Moreover, we analyze further the intractable cases of simultaneous elementary AC-matching and ACU-matching by also taking into account the maximum number of occurrences of each variable. Using combinatorial optimization techniques, we show that if each variable is restricted to having at most two occurrences, then several cases of simultaneous elementary AC-matching and ACU-matching can be solved in polynomial time.