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Formules booléennes quantifiées : transformations formelles et calculs parallèles

Abstract : Many problems of artificial intelligence and formal verification can be reduced to a validity test of a quantified boolean formula (QBF). But, to perform this test, current QBF solvers need a formula in a restrictive syntactic form, as conjunctive normal form or negation normal form. The goal of our work is to get rid of these strong syntactic constraints in order to use the QBF language in its whole expressivity and we treat this subject in formal and computational manner. Our first contribution is a set of equivalences and algorithms that can process a particular pattern, the intermediate results. This pattern provides an effective alternative in space and in time resolution, at the naive suppression of bi-implications and exclusive-or during the conversion in prenex form. It also offers new opportunities of transformations in different fragments of the QBF language. Our second contribution is computational and its goal is to use the power of parallel computing architectures to deal with QBF without syntactic restriction. So we are developing an innovative architecture for parallelizing the QBF validity problem. Its originality lies in its architecture of “syntactic parallelization” versus parallelization based on the semantics of quantifiers.
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Submitted on : Friday, March 18, 2011 - 12:03:43 PM
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  • HAL Id : tel-00578083, version 1

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Benoit da Mota. Formules booléennes quantifiées : transformations formelles et calculs parallèles. Informatique [cs]. Université d'Angers, 2010. Français. ⟨tel-00578083⟩

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