Résolution de contraintes sur les flottants dédiée à la vérification de programmes

Abstract : The verification of programs with floating-point numbers computation is an important issue in the development of critical software systems. Computations over floating-point numbers are not accurate, and the results may be very different from the expected results over real numbers. The aim of this thesis is to design a constraint solver over floating-point numbers for program verification purposes. We introduce a new method for solving constraints over floating-point numbers. This method is based on an over-approximation of floating-point constraints using constraints over real numbers. This overapproximation is safe, that’s to say it doesn’t loose any solution over the floats. The generated constraints are then solved with a constraint solver over real numbers. We propose a new filtering algorithm using linear programming techniques, which takes advantage of these over-approximations of floating-point constraints. We introduce also new search methods and heuristics to find floating-point solutions of these constraints. Using our implementation, we show on a set of counter-examples the difference of the execution of programs over the floats with the specification over real numbers.
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Autre [cs.OH]. Université Nice Sophia Antipolis, 2013. Français. 〈NNT : 2013NICE4121〉
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Mohammed Belaid. Résolution de contraintes sur les flottants dédiée à la vérification de programmes. Autre [cs.OH]. Université Nice Sophia Antipolis, 2013. Français. 〈NNT : 2013NICE4121〉. 〈tel-00937667〉

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