Priority as Extremal Probability

We extend the stratified model of probabilistic processes presented in [vGSS] to obtain a very general notion of process priority . The main idea is to allow probability guards of value 0 to be associated with alternatives of a probabilistic summation expression. Such alternatives can be chosen only if the non-zero alternatives are precluded by contextual constraints. We refer to this model as one of "extremal probability" and to its signature as PCCS i , where the i signifies the possibility of zero-probability alternatives. We provide PCCS i with a structural operational semantics and a notion of probabilistic bisimulation, which is shown to be a congruence. Of particular interest is the abstraction PCCS ß of PCCS i in which all non-zero probability guards are identified. Both the operational and bisimulation semantics of PCCS i easily adapt to this abstraction. PCCS ß represents a customized framework for reasoning about priority, and covers all features of process algebras propose..