Journal of Logic Programming
Equational problems anddisunification
Journal of Symbolic Computation
Communications of the ACM
A Machine-Oriented Logic Based on the Resolution Principle
Journal of the ACM (JACM)
An Efficient Unification Algorithm
ACM Transactions on Programming Languages and Systems (TOPLAS)
A decision procedure for term algebras with queues
ACM Transactions on Computational Logic (TOCL)
Incremental Algorithms for Constraint Solving and Entailment over Rational Trees
Proceedings of the 13th Conference on Foundations of Software Technology and Theoretical Computer Science
Solving Disequations in Equational Theories
Proceedings of the 9th International Conference on Automated Deduction
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
Proceedings of the 2006 ACM symposium on Applied computing
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
Proceedings of the 2007 ACM symposium on Applied computing
Proceedings of the 2008 ACM symposium on Applied computing
Theory of finite or infinite trees revisited
Theory and Practice of Logic Programming
A Full First-Order Constraint Solver for Decomposable Theories
Proceedings of the 9th AISC international conference, the 15th Calculemas symposium, and the 7th international MKM conference on Intelligent Computer Mathematics
From exponential to almost linear decomposability of finite or infinite trees
Proceedings of the 2009 ACM symposium on Applied Computing
A full first-order constraint solver for decomposable theories
Annals of Mathematics and Artificial Intelligence
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
Complexity of a CHR solver for existentially quantified conjunctions of equations over trees
CSCLP'06 Proceedings of the constraint solving and contraint logic programming 11th annual ERCIM international conference on Recent advances in constraints
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We present in this paper a general algorithm for solvingfirst-order formulas in particular theories called decomposabletheories. First of all, using special quantifiers, we give aformal characterization of decomposable theories and show some oftheir properties. Then, we present a general algorithm for solvingfirst-order formulas in any decomposable theory T. Thealgorithm is given in the form of five rewriting rules. Ittransforms a first-order formula Φ, which can possibly containfree variables, into a conjunction φ of solved formulas easilytransformable into a Boolean combination of existentiallyquantified conjunctions of atomic formulas. In particular, if Φhas no free variables then φ is either the formula trueor ¬true. The correctness of our algorithm proves thecompleteness of the decomposable theories. Finally, we show thatthe theory 𝑻 of finite or infinite trees is a decomposabletheory and give some benchmarks realized by an implementation ofour algorithm, solving formulas on two-partner games in 𝓣with more than 160 nested alternated quantifiers.