MICHEL , Claude

Program verification is a key issue for critical applications such as aviation, aerospace, or embedded systems. Bounded model checking (BMC) and constraint programming (CBMC, CBPV, ...) approaches are based on counterexamples that violate a property of the program to verify. Searching for such counterexamples can be very long and costly when...

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Ce papier présente un nouvel algorithme pour la résolution d'une sous-classe de problèmes contraints quantifiés sur le continu (QCSP) pour lesquels les quantificateurs existentiels précèdent les quantificateurs universels. Cette classe de QCSPs possède un remarquable potentiel d'applications dans les domaines de l'ingénierie et de la...

Static value analysis is a classical approach for verifying programs with floating-point computations. Value analysis mainly relies on abstract interpretation and over-approximates the possible values of program variables. State-of-the-art tools may however compute over-approximations that can be rather coarse for some very usual program...

Programs with floating-point computations are tricky to develop because floating-point arithmetic differs from real arithmetic and has many counterintuitive properties. A classical approach to verify such programs consists in estimating the precision of floating-point computations with respect to the same sequence of operations in an idealized...

This paper introduces a new algorithm for solving a sub-class of quantified constraint satisfaction problems (QCSP) where existential quantifiers precede universally quantified inequalities on continuous domains. This class of QCSPs has numerous applications in engineering and design. We propose here a new generic branch and prune algorithm for...

Static value analysis is a classical approach for verifying programs with floating-point computations. Value analysis mainly relies on abstract interpretation and over-approximates the possible values of program variables. State-of-the-art tools may however compute over-approximations that can be rather coarse for some very usual program...

Abstract interpretation based value analysis is a classical approach for verifying programs with floating-point computations. However, state-of-the-art tools compute an over-approximation of the variable values that can be very coarse. In this paper, we show that constraint solvers can significantly refine the approximations computed with...

Programs with floating-point computations are often derived from mathematical models or designed with the semantics of the real numbers in mind. However, for a given input, the computed path with floating-point numbers may differ from the path corresponding to the same computation with real numbers. A common practice when validating such...

Programs with floating-point computations are often derived from mathematical models or designed with the semantics of the real numbers in mind. However, for a given input, the computed path with floating-point numbers may significantly differ from the path corresponding to the same computation with real numbers. As a consequence, developers do...

La réduction basé sur l'optimalité (ou RBO) est une technique qui a été proposée pour améliorer les algorithmes d'optimisation globale. Elle cherche à profiter des bornes connues du domaine de la fonction objectif pour tenter de réduire les bornes des domaines des variables et, ainsi, accélérer le processus de recherche d'un optimum global....

Interval methods have shown their ability to locate and prove the existence of a global optima in a safe and rigorous way. Unfortunately, these methods are rather slow. Efficient solvers for optimization problems are based on linear relaxations. However, the latter are unsafe, and thus may overestimate, or, worst, underestimate the very global...

Mes recherches ont principalement porté sur la programmation par contraintes, avec deux thèmes de prédilection, les contraintes sur les réels et les contraintes sur les flottants.Sur les réels, ces travaux se caractérisent principalement par l'utilisation rigoureuse de relaxations linéaires pour la résolution de systèmes de contraintes sur les...

Solving constraints over floating-point numbers is a critical issue in numerous applications notably in program verification. Capabilities of filtering algorithms for constraints over the floating-point numbers have been so far limited to 2b-consistency and its derivatives. Though safe, such filtering techniques suffer from the well known...

Solving constraints over oating-point numbers is a critical issue in numerous applications notably in program veri cation. Capabilities of ltering algorithms over the oating-point numbers have been so far limited to 2b-consistency and its derivatives. Though safe, such ltering techniques su er from the well known pathological problems of local...

Solving constraints over oating-point numbers is a critical issue in numerous applications notably in program verication. Capa-bilities of ltering algorithms over the oating-point numbers (F) have been so far limited to 2b-consistency and its derivatives. Though safe, such ltering techniques suer from the well known pathological prob-lems of...

La mise en oeuvre effective de méthodes de vérification de programmes comportant des calculs sur les nombres à virgule flottante reste encore problématique. Cela est en partie dû aux difficultés inhérentes à l'arithmétique des nombres à virgule flottante dont la pauvreté des propriétés rend souvent impossible la transposition de résultats...

We investigate the capabilities of constraints programming techniques in rigor- ous global optimization methods. We introduce different constraint programming techniques to reduce the gap between efficient but unsafe systems like Baron1, and safe but slow global optimization approaches. We show how constraint program- ming filtering techniques...

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We investigate the capabilities of constraints programming techniques in rigorous global optimization methods. We introduce different constraint programming techniques to reduce the gap between efficient but unsafe systems like Baron, and safe but slow global optimization approaches. We show how constraint programming filtering techniques can...

Finding feasible points for which the proof succeeds is a critical issue in safe Branch and Bound algorithms which handle continuous problems. In this paper, we introduce a new strategy to compute very accurate approximations of feasible points. This strategy takes advantage of the Newton method for under-constrained systems of equations and...