A Machine-Oriented Logic Based on the Resolution Principle
Journal of the ACM (JACM)
A Unification Algorithm for Associative-Commutative Functions
Journal of the ACM (JACM)
Associative-Commutative Unification
Proceedings of the 7th International Conference on Automated Deduction
The algorithm description language ALDES (report)
ACM SIGSAM Bulletin
Associative commutative pattern matching
IJCAI'79 Proceedings of the 6th international joint conference on Artificial intelligence - Volume 1
History and basic features of the critical-pair/completion procedure
Journal of Symbolic Computation
Efficient solution of linear diophantine equations
Journal of Symbolic Computation
Unification in permutative equational theories is undecidable
Journal of Symbolic Computation
Journal of Automated Reasoning
A Nondeterministic Polynomial-Time Unification Algorithm for Bags, Sets and Trees
FoSSaCS '99 Proceedings of the Second International Conference on Foundations of Software Science and Computation Structure, Held as Part of the European Joint Conferences on the Theory and Practice of Software, ETAPS'99
Permutative rewriting and unification
Information and Computation
AC completion with termination tools
CADE'11 Proceedings of the 23rd international conference on Automated deduction
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From the work of Siekmann & Livesey, and Stickel it is known how to unify two terms in an associative and commutative theory: transfer the terms into Abelian strings, look for mappings which solve the problem in the Abelian monoid, and decide whether a mapping can be regarded as a unifier. Very often most of the mappings are thus eliminated, and so it is crucial for efficiency either to not create these unnecessary solutions or to remove them as soon as possible. The following work formalises the transformations between the free algebra and this monoid. This leads to an algorithm which uses maximal information for its search for solutions in the monoid. It is both very efficient and easily verifiable. Some applications of this algorithm are shown in the appendix.