Section: Scientific Foundations

Statistical Model Checking

Complex systems pose two particular challenges to formal verification: (i) the non-determinism caused by concurrency and unpredictable environmental conditions and (ii) the size of the state space. Our interest is probabilistic model checking, that can verify intricate details of a system's dynamical behavior and where non-determinism is handled by assigning probabilistic distributions to unknowns and quantifying results with a probability. Exact probabilistic model checking quantifies these probabilities to the limit of numerical precision by an exhaustive exploration of the state space, but is restricted by what can be conveniently stored in memory. Our focus is therefore statistical model checking (SMC), that avoids an explicit representation of the state space by building a statistical model of the executions of a system and giving results within confidence bounds. The key challenges of this approach are to reduce the length (simulation steps and cpu time) and number of simulation traces necessary to achieve a result with given confidence. Rare properties pose a particular problem in this respect, since they are not only difficult to observe but their probability is difficult to bound. A further goal is to make a tool where the choice of modeling language and logic are flexible.