It Usually Works: The Temporal Logic of Stochastic Systems

In this paper the branching time logic pCTL* is defined. pCTL* expresses quantitative bounds on the probabilities of correct behavior; it can be interpreted over discrete Markov processes. A bisimulation relation is defined on finite Markov processes, and shown to be sound and complete with respect to pCTL*. We extend the universe of models to generalized Markov processes in order to support notions of refinement, abstraction, and parametrization. Model checking pCTL* over generalized Markov processes is shown to be elementary by a reduction to RCF. We conclude by describing practical and theoretical avenues for further work.