Polynomial function intervals for floating-point software verification

The focus of our work is the verification of tight functional properties of numerical programs, such as showing that a floating-point implementation of Riemann integration computes a close approximation of the exact integral. Programmers and engineers writing such programs will benefit from verification tools that support an expressive specification language and that are highly automated. Our work provides a new method for verification of numerical software, supporting a substantially more expressive language for specifications than other publicly available automated tools. The additional expressivity in the specification language is provided by two constructs. First, the specification can feature inclusions between interval arithmetic expressions. Second, the integral operator from classical analysis can be used in the specifications, where the integration bounds can be arbitrary expressions over real variables. To support our claim of expressivity, we outline the verification of four example programs, including the integration example mentioned earlier. A key component of our method is an algorithm for proving numerical theorems. This algorithm is based on automatic polynomial approximation of non-linear real and real-interval functions defined by expressions. The PolyPaver tool is our implementation of the algorithm and its source code is publicly available. In this paper we report on experiments using PolyPaver that indicate that the additional expressivity does not come at a performance cost when comparing with other publicly available state-of-the-art provers. We also include a scalability study that explores the limits of PolyPaver in proving tight functional specifications of progressively larger randomly generated programs

Some future challenges in the validation of control systems

International audienceStarting with our work on the characterization of the imprecision error in programs using floating-point-numbers, by abstract interpretation, this paper shows that there are numerous perspectives, if one wants to fully qualify the numerical quality of control systems, as found in the aeronautical and automotive industry, for instance. Some very common functions (e.g. integrators) are hard to statically analyse, because their numerical correctness depend on a fine-grained specification of the classes of input signals they handle. This gets even more complex in the case of e.g. PID controllers, which interact in closed loop with an external environment, since their input signals are in part the consequence of their own computation, similarly for the imprecision errors. We show examples of non-trivial bad and good numerical behaviours, discuss the results of our methods, and present our current research directions, that should hopefully help characterize the imprecision error of such control systems

Effet bénéfique de la transfusion à la phase aiguë de l’infarctus du myocarde du sujet âgé : étude prospective de 3316 cas

IF 0.905International audienceIntroductionL’anémie est fréquente dans la population âgée à la phase aiguë d’un infarctus du myocarde (IDM) et est associée à une augmentation de la mortalité à long terme. Cependant, le bénéfice de la transfusion de concentrés de globules rouges (TCGR) dans ce contexte reste incertain.Patients et méthodesTous les patients de 65 ans et plus, hospitalisés pour un IDM dans notre centre hospitalier universitaire ont été inclus prospectivement. Ils ont été séparés en deux groupes d’âges : les plus jeunes (65–79 ans) et les plus âgés (80 ans et plus) et trois sous-groupes de nadir de taux d’hémoglobine (NH) (≤ 8,8–10 et > 10 g/dL). Nous avons étudié l’association entre la TCGR durant l’hospitalisation et la mortalité à un an en analyse multivariée.RésultatsParmi les 3316 patients inclus, 1906 (57 %) avaient entre 65 et 79 ans et 1410 (42 %) 80 ans ou plus. Mille cent quinze (34 %) étaient anémiés à l’admission et 2329 (70 %) durant l’hospitalisation. Trois cent cinquante-neuf (19 %) avaient un taux d’hémoglobine à 10 g/dL ou moins chez les plus jeunes et 443 (31 %) chez les plus âgés (p 10 g/dL, la TCGR était associée à une augmentation de la mortalité à un an dans les deux groupes d’âge (HR = 7,44 [3,28–16,87], p < 0,001). Quand le NH était entre 8 et 10 g/dL, la transfusion n’avait pas d’effet significatif sur la mortalité à un an dans les deux groupes d’âge (HR = 1,42 [0,97–2,07], p = 0,07).ConclusionIl s’agit, à notre connaissance, de la première étude prospective comparant l’impact de la transfusion en fonction de l’âge sur la mortalité à un an à la phase aiguë de l’IDM. Elle retrouve une diminution nette de la mortalité à un an après transfusion chez les patients les plus âgés les plus anémiés et un effet neutre voire délétère pour les patients plus jeunes et moins anémiés. Des études randomisées interventionnelles sont nécessaires pour confirmer ces résultats

Autonomous racecar control in head-to-head competition using Mixed-Integer Quadratic Programming

International audienceThis work deals with the control of an autonomous racecar that should perform the fastest lap time on a track, while in presence of an opponent vehicle. Controlling the vehicle at its physical limit while ensuring collision-freeness is a challenging problem. We propose a Nonlinear Model Predictive Control (NMPC) model under a minimum time objective, which integrates the opponent vehicle's trajectory as a collision-avoidance constraint. By using a curvilinear coordinates system, progress time can be set as a direct optimization objective. The approximation of vehicle's shape is proposed and collision-avoidance constraints can therefore be represented efficiently. A safe control strategy is finally generated by a method based on Mixed-Integer Quadratic Programming (MIQP). We perform several experiments on our prototype implementation and discuss its performance issues

Autonomous racecar control in head-to-head competition using Mixed-Integer Quadratic Programming

International audienceThis work deals with the control of an autonomous racecar that should perform the fastest lap time on a track, while in presence of an opponent vehicle. Controlling the vehicle at its physical limit while ensuring collision-freeness is a challenging problem. We propose a Nonlinear Model Predictive Control (NMPC) model under a minimum time objective, which integrates the opponent vehicle's trajectory as a collision-avoidance constraint. By using a curvilinear coordinates system, progress time can be set as a direct optimization objective. The approximation of vehicle's shape is proposed and collision-avoidance constraints can therefore be represented efficiently. A safe control strategy is finally generated by a method based on Mixed-Integer Quadratic Programming (MIQP). We perform several experiments on our prototype implementation and discuss its performance issues

Computing DOI 10.1007/s00607-011-0182-8 A generalization of p-boxes to affine arithmetic

Abstract We often need to deal with information that contains both interval and probabilistic uncertainties. P-boxes and Dempster–Shafer structures are models that unify both kind of information, but they suffer from the main defect of intervals, the wrapping effect. We present here a new arithmetic that mixes, in a guaranteed manner, interval uncertainty with probabilities, while using some information about variable dependencies, hence limiting the loss from not accounting for correlations. This increases the precision of the result and decreases the computation time compared to standard p-box arithmetic