Chapitre 1 Detailed scientific report : TEMPO team

ion Technique The use of abstractions and compositional reasoning to tackle the state explosion problem was investigated in [Fre06] where a simulation relation between a complex component was computed. To overcome some inherent problems in this approach we shifted our attention to generating abstractions as part of the analysis itself. Counterexample guided abstraction refinement (CEGAR) automatically refines an abstraction using spurious counterexamples and in [FJK08] we extended it to hybrid systems and to parameter synthesis. Predicate abstraction is a powerful technique for extracting finite-state models from infinite-state discrete programs. We have extended it for hybrid system by computing finite discrete quotient with based on the satisfaction of user-provided predicates. The algorithm of [ADI06b]. performs an on-the-fly exploration of the abstract system. In [ADI06a] we focused on identifying such predicates automatically by analyzing spurious counter-examples generated by the search in the abstract state-space. We developed a number of techniques for discovering new predicates that will rule out closely-related spurious counter-examples, implemented them and demonstrating the promise of the approach on case studies. Simulation-based Approaches Simulation which will always remain an important part of the evaluation process for large and complex systems can be made more rigorous and systematic by improving and guaranteeing its coverage of the space of trajectories. Sensitivity analysis is the study of how the behaviors of a dynamical systems depends on its initial conditions and parameters. Efficient techniques exist to provide local sensitivity information around simulated trajectories with a small overhead in the computational cost. In [DM07], we observed that this information could be used to estimate reachable sets for nonlinear and hybrid systems using a finite number of numerical simulations. Thus it can be applied for systems with a high number of state variables, due to the scalability of simulation, and is limited only by the number of uncertain parameters. This technique was further developed in [Don07] and applied in particular to nonlinear oscillating analog circuits. In [DKR09] it was extended to work on Simulink models of embedded systems and in [DCLL09] it was applied to biological models from immunology. These ideas have been used for statistical model checking [CDL08, CDL09]. For the hard problem of sampling the input space we proposed a combination with the exploration technique technique described in Section 1.2.2 [DMS08].