Efficiency of a Good But Not Linear Set Union Algorithm
Journal of the ACM (JACM)
An Efficient Unification Algorithm
ACM Transactions on Programming Languages and Systems (TOPLAS)
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
On equational theories, unification, and (Un)decidability
Journal of Symbolic Computation
Constraints in computational logics
Constraints in computational logics
Unification Modulo ACUI Plus Distributivity Axioms
Journal of Automated Reasoning
Cap unification: application to protocol security modulo homomorphic encryption
ASIACCS '10 Proceedings of the 5th ACM Symposium on Information, Computer and Communications Security
Unification modulo homomorphic encryption
FroCoS'09 Proceedings of the 7th international conference on Frontiers of combining systems
Type inference for sublinear space functional programming
APLAS'10 Proceedings of the 8th Asian conference on Programming languages and systems
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
Unification Modulo Homomorphic Encryption
Journal of Automated Reasoning
Unification modulo synchronous distributivity
IJCAR'12 Proceedings of the 6th international joint conference on Automated Reasoning
New algorithms for unification modulo one-sided distributivity and its variants
IJCAR'12 Proceedings of the 6th international joint conference on Automated Reasoning
An error-tolerant type system for variational lambda calculus
Proceedings of the 17th ACM SIGPLAN international conference on Functional programming
| Hi-index | 0.00 |
This work is a study of unification in some equational theories that have a one-sided distributivity axiom: x x (y + z) = x x y + x x z. First one-sided distributivity, the theory which has only this axiom, is studied. It is shown that, although one-sided distributivity is a simple theory in many ways, its unification problem is not trivial, and known universal unification procedures fail to provide a decision procedure for it. We give a unification procedure based on a process of decomposition combined with a generalized occurs check, which may be applied in any permutative theory, and another test. These tests together ensure termination. Next, we show that unification is undecidable if the laws of associativity x + (y + z) = (x + y) + z and a one-sided unit element x x 1 = x are added to one-sided distributivity. Unification under one-sided distributivity with (one-sided) unit element is shown to be as hard as Markov's problem (associative unification), whereas unification under two-sided distributivity, with or without unit element, is NP-hard. The study of these problems is motivated by possible applications in circuit synthesis and by the need for gaining insight in the problem of combining theories with overlapping sets of operator symbols.