Ce travail s'inscrit dans le cadre de la vérification formelle de programmes. La vérification de modèle permet de s'assurer qu'une propriété est vérifiée par le modèle du système. Cette thèse étudie la vérification paramétrée de réseaux composés d'un nombre non borné de processus identiques où le nombre de processus est considéré comme un paramètre. Concernant les réseaux de protocoles probabilistes temporisés nous montrons que les problèmes de l'accessibilité et de synchronisation sont indécidables pour des topologies de communication en cliques. Cependant, en considérant des pertes et créations probabiliste de processus ces problèmes deviennent décidables. Pour ce qui est des réseaux dans lequel les messages n'atteignent qu'une sous partie des composants choisie de manière non-déterministe, nous prouvons que le problème de l'accessibilité paramétrée est décidable grâce à une réduction à un nouveau modèle de jeux à deux joueurs distribué pour lequel nous montrons que l'on peut décider de l'existence d'une stratégie gagnante en coNP. Finalement, nous considérons des stratégies locales qui permettent d'assurer que les processus effectuent leurs choix non-déterministes uniquement par rapport a leur connaissance locale du système. Sous cette hypothèse de stratégies locales, nous prouvons que les problèmes de l'accessibilité et de synchronisation paramétrées sont NP-complet. / This thesis deals with formal verification of distributed systems. Model checking is a technique for verifying that the model of a system under study fulfills a given property. This PhD investigates the parameterized verification of networks composed of many identical processes for which the number of processes is the parameter. Considering networks of probabilistic timed protocols, we show that the parameterized reachability and synchronization problems are undecidable when the communication topology is a clique. However, assuming probabilistic creation and deletion of processes, the problems become decidable. Regarding selective networks, where the messages only reach a subset of the components, we show decidability of the parameterized reachability problem thanks to reduction to a new model of distributed two-player games for which we prove decidability in coNP of the game problem. Finally, we consider local strategies that enforce all processes to resolve the non-determinism only according to their own local knowledge. Under this assumption of local strategy, we were able to show that the parameterized reachability and synchronization problems are NP-complete.

<p> </p> <p>Distributed agreement-based systems use common distributed agreement protocols such as leader election and consensus as building blocks for their target functionality—processes in these systems may need to agree on a leader, on the members of a group, on owners of locks, or on updates to replicated data. Such distributed agreement-based systems are common and potentially permit modular, scalable verification approaches that mimic their modular design. Interestingly, while there are many verification efforts that target agreement protocols themselves, little attention has been given to distributed agreement-based systems that build on top of these protocols. </p> <p>In this work, we aim to develop a fully-automated, modular, and usable parameterized verification approach for distributed agreement-based systems. To do so, we need to overcome the following challenges. First, the fully automated parameterized verification problem, i.e, the problem of algorithmically checking if the system is correct for any number of processes, is a well-known <em>undecidable </em>problem. Second, to enable modular verification that leverages the inherently-modular nature of these agreement-based systems, we need to be able to support <em>abstractions </em>of agreement protocols. Such abstractions can replace the agreement protocols’ implementations when verifying the overall system; enabling modular reasoning. Finally, even when the verification is fully automated, a system designer still needs assistance in <em>modeling </em>their distributed agreement-based systems. </p> <p>We systematically tackle these challenges through the following contributions. </p> <p>First, we support efficient, decidable verification of distributed agreement-based systems by developing a computational model—the GSP model—for reasoning about distributed (agreement-based) systems that admits decidability and <em>cutoff </em>results. Cutoff results enable practical verification by reducing the parameterized verification problem to the verification problem of a system with a fixed, finite number of processes. The GSP model supports generalized communication primitives and global guards, both of which are essential to enable abstractions of agreement protocols. </p> <p>Then, we address the usability and modularity aspects by developing a framework, QuickSilver, tailored for modeling and modular parameterized verification of distributed agreement-based systems. QuickSilver provides an intuitive domain-specific language, called Mercury, that is equipped with two agreement primitives capable of abstracting away agreement protocols when modeling agreement-based systems; enabling modular verification. QuickSilver extends the decidability and cutoff results of the GSP model to provide fully automated, efficient parameterized verification for a large class of systems modeled in Mercury. </p> <p>Finally, we leverage synthesis techniques to further enhance the usability of our approach and propose Cinnabar, a tool that supports synthesis of distributed agreement-based systems with efficiently-decidable parameterized verification. Cinnabar allows a system de- signer to provide a sketch of their Mercury model and uses a counterexample-guided synthesis procedure to search for model completions that both belong to the efficiently-decidable fragment of Mercury and are correct. </p> <p>We evaluate our contributions on various interesting distributed agreement-based systems adapted from real-world applications, such as a data store, a lock service, a surveillance system, a pathfinding algorithm for mobile robots, and more. </p>

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