Contraintes Diophantiennes Linéaires : résolution et coopération inter-résolveurs

Abstract : The emergency of deduction with constraints as a new programming paradigm, which incorporates declarativity and efficiency, has intensified the need for the design of new efficient constraint solvers and the integration of various computation domains. Until now, most of the available constraint solvers are incomplete because they compute some solutions, but not all the solution set. We are first interested in complete solving of linear diophantine constraints. Afterwards, we investigate the combination of unification and built-in constraints. Complete solvers of linear diophantine equations do exist. However, there was no solver which directly provides the solution set basis of an equational and inequational system without turning inequations to equations by introducing slack variables. We present the first solver of a system of equations and inequations, which computes the solution set basis and avoids the adding of slack variables. Like most of the available complete solving methods, our solver does not dynamically exploit constraints in order to efficiently prune the se arch space. We cooperate our solver with propagation techniques. This cooperation aims at integrating local information based reasoning which is able to anticipate some failures and to exploit pruning opportunities. Our result is a new solver over finite domains. Finally, we propose a framework for the combination of built-in and equational unification constraints in presence of functions from terms to built-ins. The study of an instance of the framework where only homomorphisms are allowed shows how to filter information through cooperating solvers in order to reach the so-called quasi-solved forms.
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Theses
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http://docnum.univ-lorraine.fr/prive/SCD_T_1998_0025_AJILI.pdf
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https://hal.univ-lorraine.fr/tel-01747057
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Submitted on : Thursday, March 29, 2018 - 10:50:16 AM
Last modification on : Monday, April 16, 2018 - 10:40:34 AM

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Farid Ajili. Contraintes Diophantiennes Linéaires : résolution et coopération inter-résolveurs. Autre [cs.OH]. Université Henri Poincaré - Nancy 1, 1998. Français. ⟨NNT : 1998NAN10025⟩. ⟨tel-01747057⟩

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