Reactive, Generative and Strati ed Models of Probabilistic Processes

We introduce three models of probabilistic processes, namely, reactive, generative and strati ed. These models are investigated within the context of PCCS, an extension of Milner's SCCS in which each summand of a process summation expression is guarded by a probability and the sum of these probabilities is 1. For each model we present a structural operational semantics of PCCS and a notion of bisimulation equivalence which we prove to be a congruence. We also show that the models form a hierarchy: the reactive model is derivable from the generative model by abstraction from the relative probabilities of di erent actions, and the generative model is derivable from the strati ed model by abstraction from the purely probabilistic branching structure. Moreover the classical nonprobabilistic model is derivable from each of these models by abstraction from all probabilities.