CSL Model Checking of Deterministic and Stochastic Petri Nets

Deterministic and Stochastic Petri Nets (DSPNs) are widely used for modeling discrete-event systems where events may occur either without consuming time, after a deterministic time, or after an exponentially distributed time. The underlying process defined by DSPNs, under certain restrictions, corresponds to a class of Markov Regenerative Processes (MRGP). In this paper, we investigate the use of CSL (Continuous Stochastic Logic) to express probabilistic properties, such as time-bounded until and time-bounded next, at the DSPN level. The verification of such properties requires the solution of the steady-state and transient probabilities of the underlying MRGP. We also address a number of semantic issues regarding the application of CSL for MRGP and provide numerical model checking algorithms for this logic. A prototype model checker, based on SPNica, is also described.