On the computational complexity of algebra on lattices
SIAM Journal on Computing
Constrained equational reasoning
ISSAC '89 Proceedings of the ACM-SIGSAM 1989 international symposium on Symbolic and algebraic computation
The complexity of very simple Boolean formulas with applications
SIAM Journal on Computing
Unification in free distributive lattices
Theoretical Computer Science
Unification in the union of disjoint equational theories: combining decision procedures
Journal of Symbolic Computation
Unification modulo ACI + 1 + 0
Fundamenta Informaticae
Combination of constraint solvers for free and quasi-free structures
Theoretical Computer Science - Special issue: rewriting systems and applications
A decision algorithm for distributive unification
Theoretical Computer Science - Special issue on rewriting techniques and applications
Unification of concept terms in description logics
Journal of Symbolic Computation
Chaff: engineering an efficient SAT solver
Proceedings of the 38th annual Design Automation Conference
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Lemma and Model Caching in Decision Procedures for Quantified Boolean Formulas
TABLEAUX '02 Proceedings of the International Conference on Automated Reasoning with Analytic Tableaux and Related Methods
Model-Theoretic Aspects of Unification
IWWERT '90 Proceedings of the First International Workshop on Word Equations and Related Topics
Theorem Proving with Ordering Constrained Clauses
CADE-11 Proceedings of the 11th International Conference on Automated Deduction: Automated Deduction
CADE-13 Proceedings of the 13th International Conference on Automated Deduction: Automated Deduction
QUBE: A System for Deciding Quantified Boolean Formulas Satisfiability
IJCAR '01 Proceedings of the First International Joint Conference on Automated Reasoning
On Unification for Bonded Distributive Lattices
CADE-17 Proceedings of the 17th International Conference on Automated Deduction
Journal of Symbolic Computation
ISMVL '04 Proceedings of the 34th International Symposium on Multiple-Valued Logic
Unifiability and admissibility in finite algebras
CiE'12 Proceedings of the 8th Turing Centenary conference on Computability in Europe: how the world computes
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We give a method for deciding unifiability in the variety of bounded distributive lattices. For this, we reduce the problem of deciding whether a unification problem S has a solution to the problem of checking the satisfiability of a set ΦS of ground clauses. This is achieved by using a structure-preserving translation to clause form. The satisfiability check can then be performed by either a resolution-based theorem prover or a SAT checker. We apply the method to unification with free constants and to unification with linear constant restrictions, and show that, in fact, it yields a decision procedure for the positive theory of the variety of bounded distributive lattices. We also consider the problem of unification over (i.e., in an algebraic extension of) the free lattice. Complexity issues are also addressed.