Verifying concurrent probabilistic systems using probabilistic-epistemic logic specifications

摘要

In this paper, we address the problem of verifying probabilistic and epistemic properties in concurrent probabilistic systems expressed in PCTLK. PCTLK is an extension of the Probabilistic Computation Tree Logic (PCTL) augmented with Knowledge (K). In fact, PCTLK enjoys two epistemic modalities K i for knowledge and \(Pr_{\triangledown b}K_{i}\) for probabilistic knowledge. The approach presented for verifying PCTLK specifications in such concurrent systems is based on a transformation technique. More precisely, we convert PCTLK model checking into the problem of model checking Probabilistic Branching Time Logic (PBTL), which enjoys path quantifiers in the range of adversaries. We then prove that model checking a formula of PCTLK in concurrent probabilistic programs is PSPACE-complete. Furthermore, we represent models associated with PCTLK logic symbolically with Multi-Terminal Binary Decision Diagrams (MTBDDs), which are supported by the probabilistic model checker PRISM. Finally, an application, namely the NetBill online shopping payment protocol, and an example about synchronization illustrated through the dining philosophers problem are implemented with the MTBDD engine of this model checker to verify probabilistic epistemic properties and evaluate the practical complexity of this verification.