On the Verification of Qualitative Properties of Probabilistic Processes under Fairness Constraints

We consider sequential and concurrent probabilistic processes and propose a general notion of fairness with respect to probabilistic choice, which allows to express various notions of fairness such as process fairness and event fairness. We show the soundness of proving the validity of qualitative properties of probabilistic processes under fairness constraints in the sense that whenever all fair executions of a probabilistic process fullll a certain linear time property E then E holds for almost all executions (i.e. E holds with probability 1). It follows that in order to verify probabilistic processes w.r.t. linear time speciications, it suuces to establish that { for some instance of our general notion of fairness { all fair executions satisfy the speciication. This generalizes the soundness results for extreme and-fairness established in 25] and 27] respectively. Furthermore, we show that-fairness of 27] is the only fairness notion which is complete for validity of qualitative linear time properties.