Finitary fairness

Fairness is a mathematical abstraction: in a multiprogramming environment, fairness abstracts the details of admissible (“fair”) schedulers; in a distributed environment, fairness abstracts the speeds of independent processors. We argue that the standard definition of fairness often is unnecessarily weak and can be replaced by the stronger, yet still abstract, notion of finitary fairness. While standard weak fairness requires that no enabled transition is postponed forever, finitary weak fairness requires that for every run of a system there is an unknown bound k such that no enabled transition is postponed more than k consecutive times. In general, the finitary restriction fin(F) of any given fairness assumption F is the union of all w-regular safety properties that are contained in F. The adequacy of the proposed abstraction is demonstrated in two ways. Suppose that we prove a program property under the assumption of finitary fairness. In a multiprogramming environment, the program then satisfies the property for all fair finite-state schedulers. In a distributed environment, the program then satisfies the property for all choices of lower and upper bounds on the speeds (or timings) of processors