Forward Analysis and Model Checking for Trace Bounded WSTS

We investigate a subclass of well-structured transition systems (WSTS), the bounded---in the sense of Ginsburg and Spanier (Trans. AMS 1964)---complete deterministic ones, which we claim provide an adequate basis for the study of forward analyses as developed by Finkel and Goubault-Larrecq (Logic. Meth. Comput. Sci. 2012). Indeed, we prove that, unlike other conditions considered previously for the termination of forward analysis, boundedness is decidable. Boundedness turns out to be a valuable restriction for WSTS verification, as we show that it further allows to decide all $\omega$-regular properties on the set of infinite traces of the system

Verification of Flat FIFO Systems

The decidability and complexity of reachability problems and model-checking for flat counter systems have been explored in detail. However, only few results are known for flat FIFO systems, only in some particular cases (a single loop or a single bounded expression). We prove, by establishing reductions between properties, and by reducing SAT to a subset of these properties that many verification problems like reachability, non-termination, unboundedness are NP-complete for flat FIFO systems, generalizing similar existing results for flat counter systems. We construct a trace-flattable counter system that is bisimilar to a given flat FIFO system, which allows to model-check the original flat FIFO system. Our results lay the theoretical foundations and open the way to build a verification tool for (general) FIFO systems based on analysis of flat subsystems

Extrapolation-based Path Invariants for Abstraction Refinement of Fifo Systems

Rapport de Recherche RR-1459-09 LaBRIThe technique of counterexample-guided abstraction refinement (Cegar) has been successfully applied in the areas of software and hardware verification. Automatic abstraction refinement is also desirable for the safety verification of complex infinite-state models. This paper investigates Cegar in the context of formal models of network protocols, in our case, the verification of fifo systems. Our main contribution is the introduction of extrapolation-based path invariants for abstraction refinement. We develop a range of algorithms that are based on this novel theoretical notion, and which are parametrized by different extrapolation operators. These are utilized as subroutines in the refinement step of our Cegar semi-algorithm that is based on recognizable partition abstractions. We give suffcient conditions for the termination of Cegar by constraining the extrapolation operator. Our empirical evaluation confirms the benefit of extrapolation-based path invariants

Abstract Interpretation of FIFO channels

We address the analysis and the verification of communicating systems, which are systems built from sequential processes communicating via unbounded FIFO channels. We adopt the Abstract Interpretation approach to this problem, by defining approximate representations of sets of configuration of FIFO channels. In this paper we restrict our attention to the case where processes are finite-state processes and the alphabet of exchanged messages is finite. We first focus on systems with only one queue, for which we propose an abstract lattice based on regular languages, and we then generalize our proposal to systems with several queues. In particular, we define for these systems two abstract lattices, which are resp. non-relational and relational abstract lattices. We use those lattices for computing an over-approximation of the reachability set of a CFSM. Our experimental evaluation shows that, for some protocols, we obtain results that are as good as those obtained by exact methods founded on acceleration techniques. \\ Nous nous intéressons à l'analyse et à la vérification de systèmes communiquants, qui sont des systèmes formés de processus séquentiels communiquant par des files de communication non bornées. Nous proposons de suivre l'approche de l'interprétation abstraite, en définissant des représentations approchées pour les ensembles de configuration de files de communication. Dans le cadre de cet article, nous nous restreignons au cas où les processus sont d'état fini et l'alphabet des messages échangés est également fini. Nous étudions d'abord les systèmes avec une seule file de communication, pour lesquels nous proposons un treillis abstrait fondé sur les langages réguliers, puis généralisons notre proposition aux systèmes avec plusieurs files. En particulier nous définissons pour ces derniers deux treillis abstraits, le premier non-relationel et le second relationel, c'est-à-dire capable de représenter des propriétés liant deux files de communication différentes. Nous utiliserons ces treillis pour calculer une sur-approximation de l'ensemble d'atteignabilité d'un CFSM. Notre évaluation expérimentale montre que nous obtenons, sur certains protocoles, des résultats aussi bons que ceux obtenus par des méthodes exactes fondées sur des techniques d'accélération

On (Omega-)regular model checking

peer reviewedChecking infinite-state systems is frequently done by encoding infinite sets of states as regular languages. Computing such a regular representation of, say, the set of reachable states of a system requires acceleration techniques that can finitely compute the effect of an unbounded number of transitions. Among the acceleration techniques that have been proposed, one finds both specific and generic techniques. Specific techniques exploit the particular type of system being analyzed, for example, a system manipulating queues or integers, whereas generic techniques only assume that the transition relation is represented by a finite-state transducer, which has to be iterated. In this article, we investigate the possibility of using generic techniques in cases where only specific techniques have been exploited so far. Finding that existing generic techniques are often not applicable in cases easily handled by specific techniques, we have developed a new approach to iterating transducers. This new approach builds on earlier work, but exploits a number of new conceptual and algorithmic ideas, often induced with the help of experiments, that give it a broad scope, as well as good performances