Summary: Finitary Fairness \Lambda
Rajeev Alur y Thomas A. Henzinger z
Department of Electrical Engineering and Computer Science
University of California, Berkeley, CA 94720.
Fairness is a mathematical abstraction: in a multiprogramming environment, fairness ab
stracts the details of admissible (``fair'') schedulers; in a distributed environment, fairness ab
stracts the independent processor speeds. 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 computation of a system there is an un
known 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
!regular safety properties contained in F .
The adequacy of the proposed abstraction is shown in two ways. Suppose we prove a program
property under the assumption of finitary fairness. In a multiprogramming environment, the
program then satisfies the property for all fair finitestate schedulers. In a distributed environ
ment, the program then satisfies the property for all choices of lower and upper bounds on the
speeds (or timings) of processors.