Representing Nondeterministic and Probabilistic Behaviour in Reactive Processes

In this paper we investigate ways of modelling communicating processes that display both nondeterministic and probabilistic behaviour. We present an operational model for a probabilistic version of CSP, and describe a number of ways of abstracting a denotational semantics from such a model, so as to represent a process by a set of probability functions, one function for each way of resolving the nondeterministic choices. We then prove an interesting| although disappointing|result, which shows that no such denotational model can be compositional. We end by identifying a problem with the operational model, which is shared by all similar models known to us, and brieey give some indications as to how this problem might be overcome.