Communications of the ACM
A decision procedure for term algebras with queues
ACM Transactions on Computational Logic (TOCL)
A Categorial Approch to the Theory of Lists
Proceedings of the International Conference on Mathematics of Program Construction, 375th Anniversary of the Groningen University
An Improved Lower Bound for the Elementary Theories of Trees
CADE-13 Proceedings of the 13th International Conference on Automated Deduction: Automated Deduction
Essentials of Constraint Programming
Essentials of Constraint Programming
Essentials of Constraint Programming
Essentials of Constraint Programming
Principles of Constraint Programming
Principles of Constraint Programming
Theory and Practice of Logic Programming
Theory of finite or infinite trees revisited
Theory and Practice of Logic Programming
Solving first-order constraints in the theory of the evaluated trees
CSCLP'06 Proceedings of the constraint solving and contraint logic programming 11th annual ERCIM international conference on Recent advances in constraints
About the combination of trees and rational numbers in a complete first-order theory
FroCoS'05 Proceedings of the 5th international conference on Frontiers of Combining Systems
Extension of first-order theories into trees
AISC'06 Proceedings of the 8th international conference on Artificial Intelligence and Symbolic Computation
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Over the last decade, first-order constraints have been efficiently used in the artificial intelligence world to model many kinds of complex problems such as: scheduling, resource allocation, computer graphics and bio-informatics. Recently, a new property called decomposability has been introduced and many first-order theories have been proved to be decomposable: finite or infinite trees, rational and real numbers, linear dense order,...etc. A decision procedure in the form of five rewriting rules has also been developed. This latter can decide if a first-order formula without free variables is true or not in any decomposable theory. Unfortunately, this decision procedure is not enough when we want to express the solutions of a first-order constraint having free variables. These kind of problems are generally known as first-order constraint satisfaction problems. We present in this paper, not only a decision procedure but a full first-order constraint solver for decomposable theories. Our solver is given in the form of nine rewriting rules which transform any first-order constraint 驴 (which can possibly contain free variables) into an equivalent formula 驴 which is either the formula true, or the formula false or a simple solved formula having at least one free variable and being equivalent neither to true nor to false. We show the efficiency of our solver by solving complex first-order constraints over finite or infinite trees containing a huge number of imbricated quantifiers and negations and compare the performances with those obtained using the most recent and efficient dedicated solver for finite or infinite trees. This is the first full first-order constraint solver for any decomposable theory.