On the sequential nature of unification
Journal of Logic Programming
Properties of substitutions and unifications
Journal of Symbolic Computation
A Machine-Oriented Logic Based on the Resolution Principle
Journal of the ACM (JACM)
Complete Sets of Reductions for Some Equational Theories
Journal of the ACM (JACM)
A Unification Algorithm for Associative-Commutative Functions
Journal of the ACM (JACM)
An Efficient Unification Algorithm
ACM Transactions on Programming Languages and Systems (TOPLAS)
A short survey on the state of the art in matching and unification problems
ACM SIGSAM Bulletin
Efficient solution of linear diophantine equations
Journal of Symbolic Computation
Adventures in associative-commutative unification
Journal of Symbolic Computation
Unification in Boolean Rings and Abelian Groups
Journal of Symbolic Computation
Rewriting of rules containing set terms in a logic data language LDL
Proceedings of the seventh ACM SIGACT-SIGMOD-SIGART symposium on Principles of database systems
Sets and constraint logic programming
ACM Transactions on Programming Languages and Systems (TOPLAS)
Journal of Automated Reasoning
On the Complexity of Counting the Hilbert Basis of a Linear Diophnatine System
LPAR '99 Proceedings of the 6th International Conference on Logic Programming and 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
Combining Pattern E-Unification Algorithms
RTA '01 Proceedings of the 12th International Conference on Rewriting Techniques and Applications
Theory and Practice of Logic Programming
Permutative rewriting and unification
Information and Computation
Unification and Matching Modulo Leaf-Permutative Equational Presentations
IJCAR '08 Proceedings of the 4th international joint conference on Automated Reasoning
CADE-22 Proceedings of the 22nd International Conference on Automated Deduction
UNIFICATION MODULO ACI + 1 + 0
Fundamenta Informaticae
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Unification in equational theories, that is, solving equations in varieties, is of special relevance to automated deduction. Major results in term rewriting systems, as in (Peterson & Stickel, 1981; Hsiang, 1982), depend on unification in presence of associative-commutative functions. (Stickel, 1975; Stickel, 1981) gave an associative-commutative unification algorithm, but its termination in the general case was still questioned. The first part of this paper is an introduction to unification theory, the second part concerns the solving of homogeneous linear diophantine equations, and the third contains a proof of termination and correctness of the associative-commutative unification algorithm for the general case.