Combining unification algorithms for confined regular equational theories
Proc. of the first international conference on Rewriting techniques and applications
Complete sets of unifiers and matchers in equational theories
Theoretical Computer Science
Sufficient completeness, term rewriting systems and “anti-unification”
Proc. of the 8th international conference on Automated deduction
Combination of unification algorithms
Proc. of the 8th international conference on Automated deduction
Proc. of the 8th international conference on Automated deduction
Some relationships between unification, restricted unification, and matching
Proc. of the 8th international conference on Automated deduction
Unification in many-sorted equational theories
Proc. of the 8th international conference on Automated deduction
Proceedings of the 7th International Conference on Automated Deduction
On equational theories, unification, and (Un)decidability
Journal of Symbolic Computation
Combining matching algorithms: The regular case
Journal of Symbolic Computation
On solving equations and disequations
Journal of the ACM (JACM)
Constraints in computational logics
FoSSaCS '01 Proceedings of the 4th International Conference on Foundations of Software Science and Computation Structures
Matching with Free Function Symbols - A Simple Extension of Matching?
RTA '01 Proceedings of the 12th International Conference on Rewriting Techniques and Applications
RTA '01 Proceedings of the 12th International Conference on Rewriting Techniques and Applications
Mathematical Service Trading Based on Equational Matching
Electronic Notes in Theoretical Computer Science (ENTCS)
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Unification is the problem to solve equations of first order terms by finding (all) substitutions into their variables that make these two terms equal. Matching is the problem to solve equations, where only one of the terms has to be instantiated by the substitution. Usually research in unification theory does not take care of the problems arising with matching, as it is considered as a special form of unification. We recall the various definitions of matching from the literature and we compare matching and unification in a more general framework called restricted unification. We show that matching and unification in collapse free cquational theories behave similar with respect to the existence and the cardinality of minimal complete sets of solutions. We present some counterexamples where matching and unification behave differently, especially we give an equational theory, in which the existence of solutions for unification problems is decidable, for matching problems, however, this is undecidable. Matching and restricted unification as defined here are equivalent to extending the given signature by free constants. Our counterexamples show that unification may become undecidable, if we add new free constants to the signature.