Properties of substitutions and unifications
Journal of Symbolic Computation
On the Church-Rosser property for the direct sum of term rewriting systems
Journal of the ACM (JACM)
Complete sets of unifiers and matchers in equational theories
Theoretical Computer Science
Completion of a set of rules modulo a set of equations
SIAM Journal on Computing
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
A general complete E-unification procedure
on Rewriting techniques and applications
Journal of Automated Reasoning
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
Unification in combinations of collapse-free regular theories
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)
A Unification Algorithm for Associative-Commutative Functions
Journal of the ACM (JACM)
Simplification by Cooperating Decision Procedures
ACM Transactions on Programming Languages and Systems (TOPLAS)
An Efficient Unification Algorithm
ACM Transactions on Programming Languages and Systems (TOPLAS)
Proving termination with multiset orderings
Communications of the ACM
Rewrite Methods for Clausal and Non-Clausal Theorem Proving
Proceedings of the 10th Colloquium on Automata, Languages and Programming
Canonical Forms and Unification
Proceedings of the 5th Conference on Automated Deduction
A Progress Report on New Decision Algorithms for Finitely Prsented Abelian Groups
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
A complete unification algorithm for associative-commutative functions
IJCAI'75 Proceedings of the 4th international joint conference on Artificial intelligence - Volume 1
Combining matching algorithms: The regular case
Journal of Symbolic Computation
A multi-theory constraint satisfaction system
CSC '93 Proceedings of the 1993 ACM conference on Computer science
Higher-order equational logic programming
POPL '94 Proceedings of the 21st ACM SIGPLAN-SIGACT symposium on Principles of programming languages
On solving equations and disequations
Journal of the ACM (JACM)
Constraints in computational logics
Relative undecidability in term rewriting: II. the confluence hierarchy
Information and Computation
External Rewriting for Skeptical Proof Assistants
Journal of Automated Reasoning
Unions of non-disjoint theories and combinations of satisfiability procedures
Theoretical Computer Science
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
UNIMOK: A System for Combining Equational Unification Algorithm
RtA '99 Proceedings of the 10th International Conference on Rewriting Techniques and Applications
Matching with Free Function Symbols - A Simple Extension of Matching?
RTA '01 Proceedings of the 12th International Conference on Rewriting Techniques and Applications
Combining Pattern E-Unification Algorithms
RTA '01 Proceedings of the 12th International Conference on Rewriting Techniques and Applications
Combining Decision Procedures for Positive Theories Sharing Constructors
RTA '02 Proceedings of the 13th International Conference on Rewriting Techniques and Applications
Symbolic protocol analysis with an Abelian group operator or Diffie-Hellman exponentiation
Journal of Computer Security
Theory and Practice of Logic Programming
Information and Computation - Special issue: Combining logical systems
Hierarchical combination of intruder theories
Information and Computation
Combining Algorithms for Deciding Knowledge in Security Protocols
FroCoS '07 Proceedings of the 6th international symposium on Frontiers of Combining Systems
A Proof Theoretic Analysis of Intruder Theories
RTA '09 Proceedings of the 20th International Conference on Rewriting Techniques and Applications
Symbolic protocol analysis in the union of disjoint intruder theories: Combining decision procedures
Theoretical Computer Science
Protocol analysis in Maude-NPA using unification modulo homomorphic encryption
Proceedings of the 13th international ACM SIGPLAN symposium on Principles and practices of declarative programming
Protocol analysis modulo combination of theories: a case study in Maude-NPA
STM'10 Proceedings of the 6th international conference on Security and trust management
Fast sort computations for order-sorted matching and unification
Formal modeling
ICALP'05 Proceedings of the 32nd international conference on Automata, Languages and Programming
E-unification with Constants vs. General E-unification
Journal of Automated Reasoning
Assertion checking over combined abstraction of linear arithmetic and uninterpreted functions
ESOP'06 Proceedings of the 15th European conference on Programming Languages and Systems
Decidability and Combination Results for Two Notions of Knowledge in Security Protocols
Journal of Automated Reasoning
UNIFICATION MODULO ACI + 1 + 0
Fundamenta Informaticae
Building decision procedures in the calculus of inductive constructions
CSL'07/EACSL'07 Proceedings of the 21st international conference, and Proceedings of the 16th annuall conference on Computer Science Logic
Modularity in term rewriting revisited
Theoretical Computer Science
CADE'13 Proceedings of the 24th international conference on Automated Deduction
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The unification problem in a disjoint combination of equational theories, E"1+...+E"n, is reduced to a combination of two kinds of problems in the E"j's: the pure unification, problem with free (Uninterpreted) constants and the constant-elimination problem. The constant-elimination problem is to find, given terms t"i, 1@?i@?m and free constants c"i, 1@?i@?m, all substitutions @s such that for all i with 1@?i@?m, @st"i is equal to some t'"i that does not contain c"i. The soundness and completeness of the method shows, that a disjoint combination of theories is finitary, provided every theory is finitary and constant-elimination problems in every theory are finitary solvable. In particular, any combination of finitary unifying regular theories, of Boolean rings, of Abelian groups or of theories with terminating basic narrowing, is of unification-type finitary. As a special case, unification in a combination of a free Boolean ring with free function symbols is decidable and finitary; the same holds for Abelian groups. This paper extends the known results on unification in a combination of regular and collapse-free theories in two aspects: i) Arbitrary theories are admissable. ii) The described general procedure can be used for enumerating a complete set of unifiers, even if some unification procedure for a paticular theory produces an infinite complete set of unifiers. It is demonstrated that unifiability of unification problems is decidable in the general case E"1+...+E"n if for every i@?{1,...,n}, there is a method to decide unification problems in a combination of E"i with free function symbols.