Nous proposons dans cette thèse plusieurs contributions relatives à la vérification quantitative des systèmes. Cette discipline vise à évaluer les propriétés fonctionnelles et les performances d'un système. Une telle vérification requiert deux ingrédients : un modèle formel de représentation d'un système et une logique temporelle pour exprimer la propriété considérée. L'évaluation est alors faite par une méthode statistique ou numérique. La complexité spatiale des méthodes numériques, proportionnelle à la taille de l'espace d'états, les rend impraticables si les systèmes présentent une combinatoire importante. La méthode de comparaison stochastique basée sur les chaînes de Markov censurées réduit la mémoire occupée en restreignant l'analyse à un sous-ensemble des états de la chaîne originale. Dans cette thèse nous fournissons de nouvelles bornes dépendant de l'information disponible relative à la chaîne. Nous introduisons une nouvelle logique temporelle quantitative appelée Hybrid Automata Stochastic Logic (HASL), pour la vérification des processus stochastiques à événements discrets (DESP).HASL emploie les automates linéaires hybrides (LHA) pour sélectionner des préfixes de chemins d'exécution d'un DESP. LHA permet de collecter des informations élaborées durant la génération des chemins, fournissant ainsi à l'utilisateur un moyen d'exprimer des mesures sophistiquées. HASL supporte donc des raisonnements temporels mixés avec une analyse à base de récompenses. Nous avons aussi développé COSMOS, un outil qui implémente la vérification statistique de formules HASL pour des réseaux de Petri stochastiques. Les ateliers flexibles (FMS) ont souvent été modélisés par des réseaux de Petri. Cependant le modélisateur doit avoir une bonne connaissance de ce formalisme. Afin de faciliter cette modélisation nous proposons une méthodologie de modélisation compositionnelle orientée vers les applications qui ne requiert aucune connaissance des réseaux de Petri. / We propose in this thesis several contributions related to the quantitative verification of systems. This discipline aims to evaluate functional and performance properties of a system. Such a verification requires two ingredients: a formal model to represent the system and a temporal logic to express the desired property. Then the evaluation is done with a statistical or numerical method. The spatial complexity of numerical methods which is proportional to the size of the state space of the model makes them impractical when the state space is very large. The method of stochastic comparison with censored Markov chains is one of the methods that reduces memory requirements by restricting the analysis to a subset of the states of the original Markov chain. In this thesis we provide new bounds that depend on the available information about the chain. We introduce a new quantitative temporal logic named Hybrid Automata Stochastic Logic (HASL), for the verification of discrete event stochastic processes (DESP). HASL employs Linear Hybrid Automata (LHA) to select prefixes of relevant execution paths of a DESP. LHA allows rather elaborate information to be collected on-the-fly during path selection, providing the user with a powerful mean to express sophisticated measures. In essence HASL provides a unifying verification framework where temporal reasoning is naturally blended with elaborate reward-based analysis. We have also developed COSMOS, a tool that implements statistical verification of HASL formulas over stochastic Petri nets. Flexible manufacturing systems (FMS) have often been modelized by Petri nets. However the modeler should have a good knowledge of this formalism. In order to facilitate such a modeling we propose a methodology of compositional modeling that is application oriented and does not require any knowledge of Petri nets by the modeler.

We propose in this thesis several contributions related to the quantitative verification of systems. This discipline aims to evaluate functional and performance properties of a system. Such a verification requires two ingredients: a formal model to represent the system and a temporal logic to express the desired property. Then the evaluation is done with a statistical or numerical method. The spatial complexity of numerical methods which is proportional to the size of the state space of the model makes them impractical when the state space is very large. The method of stochastic comparison with censored Markov chains is one of the methods that reduces memory requirements by restricting the analysis to a subset of the states of the original Markov chain. In this thesis we provide new bounds that depend on the available information about the chain. We introduce a new quantitative temporal logic named Hybrid Automata Stochastic Logic (HASL), for the verification of discrete event stochastic processes (DESP). HASL employs Linear Hybrid Automata (LHA) to select prefixes of relevant execution paths of a DESP. LHA allows rather elaborate information to be collected on-the-fly during path selection, providing the user with a powerful mean to express sophisticated measures. In essence HASL provides a unifying verification framework where temporal reasoning is naturally blended with elaborate reward-based analysis. We have also developed COSMOS, a tool that implements statistical verification of HASL formulas over stochastic Petri nets. Flexible manufacturing systems (FMS) have often been modelized by Petri nets. However the modeler should have a good knowledge of this formalism. In order to facilitate such a modeling we propose a methodology of compositional modeling that is application oriented and does not require any knowledge of Petri nets by the modeler.