Modeling fairness and starvation in concurrent systems

Abstract

Standard temporal logic is augmented and a new temporal quantifier viz., never is defined. This augmented logic is integrated in Dijkstra's weakest precondition calculus. Definitions for fairness and starvation for concurrent systems in terms of weakest precondition are presented. According to the existing concept fairness for a transition rule asserts that if a rule remains continuously enabled (weak fairness) or repeatedly enabled (strong fairness), then it must be executed., where in the proposed definition fairness is related to the permission for execution where starvation relies upon actual execution. This definition is used to prove fairness of a given concurrent system. Through different examples it is shown that fairness is not the only prerequisite for starvation freedom. Available techniques use 'leads to' operator that forecasts system behavior where the proposed proof technique moves backward in time.