It Usually Works: The Temporal Logic of Stochastic Systems

In this paper the branching time logic pCTL is deened. pCTL expresses quantitative bounds on the probabilities of correct behavior ; it can be interpreted over discrete Markov processes. A bisim-ulation relation is deened on nite 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 re-nement, 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.