A compact topology for sand automata

In this paper, we exhibit a strong relation between the sand automata configuration space and the cellular automata configuration space. This relation induces a compact topology for sand automata, and a new context in which sand automata are homeomorphic to cellular automata acting on a specific subshift. We show that the existing topological results for sand automata, including the Hedlund-like representation theorem, still hold. In this context, we give a characterization of the cellular automata which are sand automata, and study some dynamical behaviors such as equicontinuity. Furthermore, we deal with the nilpotency. We show that the classical definition is not meaningful for sand automata. Then, we introduce a suitable new notion of nilpotency for sand automata. Finally, we prove that this simple dynamical behavior is undecidable

Syntactic Abstraction of B Models to Generate Tests

In a model-based testing approach as well as for the verification of properties, B models provide an interesting solution. However, for industrial applications, the size of their state space often makes them hard to handle. To reduce the amount of states, an abstraction function can be used, often combining state variable elimination and domain abstractions of the remaining variables. This paper complements previous results, based on domain abstraction for test generation, by adding a preliminary syntactic abstraction phase, based on variable elimination. We define a syntactic transformation that suppresses some variables from a B event model, in addition to a method that chooses relevant variables according to a test purpose. We propose two methods to compute an abstraction A of an initial model M. The first one computes A as a simulation of M, and the second one computes A as a bisimulation of M. The abstraction process produces a finite state system. We apply this abstraction computation to a Model Based Testing process.Comment: Tests and Proofs 2010, Malaga : Spain (2010

PLTL Partitioned Model Checking for Reactive Systems under Fairness Assumptions

We are interested in verifying dynamic properties of finite state reactive systems under fairness assumptions by model checking. The systems we want to verify are specified through a top-down refinement process. In order to deal with the state explosion problem, we have proposed in previous works to partition the reachability graph, and to perform the verification on each part separately. Moreover, we have defined a class, called Bmod, of dynamic properties that are verifiable by parts, whatever the partition. We decide if a property P belongs to Bmod by looking at the form of the Buchi automaton that accepts the negation of P. However, when a property P belongs to Bmod, the property f => P, where f is a fairness assumption, does not necessarily belong to Bmod. In this paper, we propose to use the refinement process in order to build the parts on which the verification has to be performed. We then show that with such a partition, if a property P is verifiable by parts and if f is the expression of the fairness assumptions on a system, then the property f => P is still verifiable by parts. This approach is illustrated by its application to the chip card protocol T=1 using the B engineering design language

A compact topology for sand automata

In this paper, we exhibit a strong relation between the sand automata configuration space and the cellular automata configuration space. This relation induces a compact topology for sand automata, and a new context in which sand automata are homeomorphic to cellular automata acting on a specific subshift. We show that the existing topological results for sand automata, including the Hedlund-like representation theorem, still hold. In this context, we give a characterization of the cellular automata which are sand automata, and study some dynamical behaviors such as equicontinuity. Furthermore, we deal with the nilpotency. We show that the classical definition is not meaningful for sand automata. Then, we introduce a suitable new notion of nilpotency for sand automata. Finally, we prove that this simple dynamical behavior is undecidable

Biological model of motion integration and segmentation based on form cues

Active vision is an essential part of every biological organism possessing an eye system: posture, eye movements, visual research, ... All require a motion percept to operate. At the basis of active vision lays the ability to calculate movements of objects in the scene, at least on a sufficient level to react correctly. In this report we present a model of motion integration and segmentation in the first visual cortex areas. Specifically we modeled the first two cortex areas involved in motion processing in the primate: V1 and MT. To be able to process motion correctly a visual system also need to deal with form information. We investigate how form cues coming from the ventral pathway can be used by the V1/MT dorsal pathway to solve some perception problems. By using a recurrent dynamical system between the V1 and MT layers we are able to find out psychophysical results such as motion integration and center-surround effects due to the feedback connections, or end-of-line and 2D features detectors thanks to the shunting inhibition. We propose to modulate this system by a form information coming from the ventral stream and are thus able to explain asymmetric center-surround effects as well as motion segmentation and segregation between extrinsic and intrinsic junctions

Parallelization of a relaxation scheme modelling the bedload transport of sediments in shallow water flow

In this work we are interested in numerical simulations for bedload erosion processes. We present a relaxation solver that we apply to moving dunes test cases in one and two dimensions. In particular we retrieve the so-called anti-dune process that is well described in the experiments. In order to be able to run 2D test cases with reasonable CPU time, we also describe and apply a parallelization procedure by using domain decomposition based on the classical MPI library.Comment: 19 page

B Model Slicing and Predicate Abstraction to Generate Tests

Accepted manuscript. Revised and extended version of a TAP'10 paper. To appear.International audienceIn a model-based testing approach as well as for the verification of properties, B models provide an interesting modeling solution. However, for industrial applications, the size of their state space often makes them hard to handle. To reduce the amount of states, an abstraction function can be used. The abstraction is often a domain abstraction of the state variables that requires many proof obligations to be discharged, which can be very time-consuming for real applications. This paper presents a contribution to this problem that complements an approach based on domain abstraction for test generation, by adding a preliminary syntactic abstraction phase, based on variable elimination. We define a syntactic transformation that suppresses some variables from a B event model, in addition to three methods that choose relevant variables according to a test purpose. In this way, we propose a method that computes an abstraction of a source model {\mathsf{M}} according to a set of selected relevant variables. Depending on the method used, the abstraction can be computed as a simulation or as a bisimulation of {\mathsf{M}}. With this approach, the abstraction process produces a finite state system. We apply this abstraction computation to a model-based testing process. We evaluate experimentally the impact of the model simplification by variables' elimination on the size of the models, on the number of proof obligations to discharge, on the precision of the abstraction and on the coverage achieved by the test generation

Génération de tests à partir de critères dynamiques de sélection et par abstraction

International audienceCet article présente une méthode de génération assistée de tests. Elle applique des critères dynamiques de sélection des tests (TP) sur un modèle formel comportemental (M) utilisé auparavant, par exemple par LTG, pour générer des tests fonctionnels à partir de critères statiques de sélection. On peut appliquer à M un critère dynamique de sélection TP mais ceci nécessite de représenter M par un automate. Pour des applications réelles, sa taille en nombre d'états et de transitions est beaucoup trop grande (voir infinie) pour être utilisable. Nous proposons une méthode pour extraire une abstraction de M à partir d'un objectif de test TP. Nous effectuons un produit synchronisé de cette abstraction avec TP afin de cibler les exécutions du système sous test qui satisfont TP. Puis nous générons des tests abstraits symboliques à partir de ce modèle réduit en appliquant les critères de couverture tous les états ou toutes les transitions. Cet ensemble de tests est valué à partir de M, concrétisé puis exécuté sur l'implémentation sous test. Cette méthode est proposée pour compléter la méthode BZ-TT de génération de tests à partir de critères statiques de sélection. L'utilisateur obtient des tests complémentaires en fournissant un critère dynamique de sélection. La méthode réutilise M, la couche de concrétisation des tests et l'infrastructure d'exécution des tests. L'originalité de l'approche est de construire une abstraction du modèle issue automatiquement de l'analyse statique d'un objectif de test formalisant des besoins de test d'une propriété dynamique du système