Combining unification algorithms for confined regular equational theories
Proc. of the first international conference on Rewriting techniques and applications
Properties of substitutions and unifications
Journal of Symbolic Computation
Complete sets of unifiers and matchers in equational theories
Theoretical Computer Science
On unification: Equational theories are not bounded
Journal of Symbolic Computation
Unification in combinations of collapse-free theories with disjoint sets of function symbols
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
On equational theories, unification and decidability
on Rewriting techniques and applications
Unification under associativity and idempotence is of type nullary
Journal of Automated Reasoning
The theory of idempotent semigroups is of unification type zero
Journal of Automated Reasoning
History and basic features of the critical-pair/completion procedure
Journal of Symbolic Computation
Journal of Symbolic Computation
Unification in combinations of collapse-free regular theories
Journal of Symbolic Computation
Unification problems with one-sided distributivity
Journal of Symbolic Computation
Matching - A special case of unification?
Journal of Symbolic Computation
A Machine-Oriented Logic Based on the Resolution Principle
Journal of the ACM (JACM)
The Concept of Demodulation in Theorem Proving
Journal of the ACM (JACM)
An Efficient Unification Algorithm
ACM Transactions on Programming Languages and Systems (TOPLAS)
Symbolic Logic and Mechanical Theorem Proving
Symbolic Logic and Mechanical Theorem Proving
Introduction To Automata Theory, Languages, And Computation
Introduction To Automata Theory, Languages, And Computation
Canonical Forms and Unification
Proceedings of the 5th Conference on Automated Deduction
Proceedings of the 7th International Conference on Automated Deduction
A New Equational Unification Method: A Generalization of Martelli-Montanari's Algorithm
Proceedings of the 7th International Conference on Automated Deduction
Complete Sets of Unifiers and Matchers in Equational Theories
CAAP '83 Proceedings of the 8th Colloquium on Trees in Algebra and Programming
Unification for completely commutative theories
SAC '92 Proceedings of the 1992 ACM/SIGAPP Symposium on Applied computing: technological challenges of the 1990's
On solving equations and disequations
Journal of the ACM (JACM)
Constraints in computational logics
Journal of Automated Reasoning
UNIFICATION MODULO ACI + 1 + 0
Fundamenta Informaticae
Asymmetric unification: a new unification paradigm for cryptographic protocol analysis
CADE'13 Proceedings of the 24th international conference on Automated Deduction
CADE'13 Proceedings of the 24th international conference on Automated Deduction
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We investigate the following classes of equational theories which are important in unification theory: permutative, finite, Noetherian, simple, almost collapse free, collapse free, regular, and @W-free theories. We show some relationships between the particular classes and their connections to the unification hierarchy. Especially, we study conditions, under which minimal and complete sets of unifiers always exist. We have some undecidability results for the membership problem of equational theories to these classes (the 'class problem'): simplicity, almost collapse freeness, and @W-freeness are undecidable properties. Finiteness is known to be also undecidable, and the other investigated properties, permutativity, regularity, and collapse freeness, are known to be trivially decidable. We give an equational theory where every single equation has a minimal set of unifiers, however, for some systems of equations no minimal set of unifiers exists. This example suggests that the definition of a unification problem has to be modified and that the definitions of the unification types have to be adapted accordingly.