International audienceQuantitative properties of stochastic systems are usually specified in logics that allow one to compare the measure of executions satisfying certain temporal properties with thresholds. The model checking problem for stochastic systems with respect to such logics is typically solved by a numerical approach [31,8,35,22,21,5] that iteratively computes (or approximates) the exact measure of paths satisfying relevant subformulas; the algorithms themselves depend on the class of systems being analyzed as well as the logic used for specifying the properties. Another approach to solve the model checking problem is to simulate the system for finitely many executions, and use hypothesis testing to infer whether the samples provide a statistical evidence for the satisfaction or violation of the specification. In this tutorial, we survey the statistical approach, and outline its main advantages in terms of efficiency, uniformity, and simplicity

Abstract. We study property preserving transformations for reactive systems. The main idea is the use of simulationsparameterized by Galois connections( ), relating the lattices of properties of two systems. We propose and study a notion of preservation of properties expressed by formulas of a logic, by a function mapping sets of states of a system S into sets of states of a system S'. We g i v e results on the preservation of properties expressed in sublanguages of the branching time -calculus when two systems S and S' are related via h i-simulations. They can be used to verify a property for a system by v erifying the same property on a simpler system which i s a n abstraction of it. We s h o w also under which conditions abstraction of concurrent systems can be computed from the abstraction of their components. This allows a compositional application of the proposed veri cation method. This is a revised version of the papers 2] and 16] the results are fully developed in 27].

Abstract. D-Finder tool implements a compositional method for the verification of component-based systems described in BIP language encompassing multi-party interaction. For deadlock detection, D-Finder applies proof strategies to eliminate potential deadlocks by computing increasingly stronger invariants.