Reachability Analysis of Communicating Pushdown Systems

The reachability analysis of recursive programs that communicate asynchronously over reliable FIFO channels calls for restrictions to ensure decidability. Our first result characterizes communication topologies with a decidable reachability problem restricted to eager runs (i.e., runs where messages are either received immediately after being sent, or never received). The problem is EXPTIME-complete in the decidable case. The second result is a doubly exponential time algorithm for bounded context analysis in this setting, together with a matching lower bound. Both results extend and improve previous work from La Torre et al

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

On the Boundedness Problem for Higher-Order Pushdown Vector Addition Systems

International audienceKarp and Miller's algorithm is a well-known decision procedure that solves the termination and boundedness problems for vector addition systems with states (VASS), or equivalently Petri nets. This procedure was later extended to a general class of models, well-structured transition systems, and, more recently, to pushdown VASS. In this paper, we extend pushdown VASS to higher-order pushdown VASS (called HOPVASS), and we investigate whether an approach à la Karp and Miller can still be used to solve termination and boundedness.We provide a decidable characterisation of runs that can be iterated arbitrarily many times, which is the main ingredient of Karp and Miller's approach. However, the resulting Karp and Miller procedure only gives a semi-algorithm for HOPVASS. In fact, we show that coverability, termination and boundedness are all undecidable for HOPVASS, even in the restricted subcase of one counter and an order 2 stack. On the bright side, we prove that this semi-algorithm is in fact an algorithm for higher-order pushdown automata

Qualitative Transition Systems for the Abstraction and Comparison of Transient Behavior in Parametrized Dynamic Models

International audienceQuantitative models in Systems Biology depend on a large number of free parameters, whose values completely determine behavior of models. These parameters are often estimated by fitting the system to observed experimental measurements and data. The response of a model to parameter variation defines qualitative changes of the system's behavior. The influence of a given parameter can be estimated by varying it in a certain range. Some of these ranges produce similar system dynamics, making it possible to define general trends for trajectories of the system (e.g. oscillating behavior) in such parameter ranges. Such trends can be seen as a qualitative description of the system's dynamics within a parameter range. In this work, we define an automata-based formalism to formally describe the qualitative behavior of systems' dynamics. Qualitative behaviors are represented by finite transition systems whose states contain predicate valuation and whose transitions are labeled by probabilistic delays. Biochemical system' dynamics are automatically abstracted in terms of these qualitative transition systems by a random sampling of trajectories. Furthermore, we use graph theoretic tools to compare the resulting qualitative behaviors and to estimate those parameter ranges that yield similar behaviors. We validate this approach on published biochemical models and show that it enables rapid exploration of models' behavior, that is estimation of parameter ranges with a given behavior of interest and identification of some bifurcation points