Worst-case Analysis of Set Union Algorithms
Journal of the ACM (JACM)
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
Extending arbitrary solvers with constraint handling rules
Proceedings of the 5th ACM SIGPLAN international conference on Principles and practice of declaritive programming
Optimal union-find in Constraint Handling Rules
Theory and Practice of Logic Programming
Principles of Constraint Programming
Principles of Constraint Programming
Proceedings of the 2007 ACM symposium on Applied computing
Theory and Practice of Logic Programming
Proceedings of the 2008 ACM symposium on Applied computing
Theory of finite or infinite trees revisited
Theory and Practice of Logic Programming
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First-order constraints are first-order formulas built on a set of function and relation symbols using the following logical symbols: =, true, false, ¬, ∧, ∨, →, ↔, ∀, ∃, (,). 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, configuration, temporal and spatial reasoning, computer graphics, bio-informatics. While theory of finite or infinite trees T has played a fundamental role for both modeling and solving these problems, the complexity of solving first-order constraints with nested quantifiers and negations in T has been proved to be inherently huge (a tower of powers of two). However, a new property called decomposability has been recently introduced and used as a black-box to build many efficient first-order constraint solvers over T. We show in this paper that the algorithm which is used in this black-box (i.e. the algorithm which performs decomposability) has an exponential time and space complexity. We then present a much more efficient algorithm in the form of four rewriting rules which can perform the same decomposability in an almost-linear time and space complexity.