Priority as extremal probability

We extend the stratified model of probabilistic processes to obtain a very general notion ofprocess 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 asPCCS . We providePCCS with a structural operational semantics and a notionof probabilistic bisimulation, which is shown to be a congruence. Of particular interest is the abstractionPCCS ofPCCS in which all non-zero probability guards are identified.PCCS represents a customized framework for reasoning about priority, and covers all features of process algebras proposed for reasoning about priority that we know of.A preliminary version of this paper appeared inProceedings of CONCUR '90 — First International Conference on Concurrency Theory, Vol. 458 of the Springer-Verlag seriesLecture Notes in Computer Science, pp. 456–466, Aug. 1990. The research of Scott Smolka was supported in part by NSF Grants CCR-9120995, CCR-9208585 and CCR-9505562; and AFOSR Grants F49620-93-1-0250, F49620-95-1-0508 and F49620-96-1-0087.