From Fairness to Chance

Fairness is a mathematical abstraction used in the modeling of a wide range of phenomena, including concurrency, scheduling, and probability. In this paper, we study fairness in the context of probabilistic systems, and we introduce probabilistic fairness, a novel notion of fairness that is itself deened in terms of probability. The deenition of probabilistic fairness makes it invariant with respect to synchronous composition, and facilitates the design of model-checking algorithms for quantitative properties of probabilistic systems. We compare probabilistic fairness with other notions of fairness for probabilistic systems, and we provide algorithms that solve the veriication problem for various classes of probabilistic properties on nite-state systems with fairness.