On Fairness Notions in Distributed Systems II. Equivalence-Completions and Their Hierarchies

AbstractThis is the second part of a two-part paper in which we discuss the implementability of fairness notions in distributed systems where asynchronous processes interact via multiparty interactions. We focus here on equivalence-robust fairness notions where equivalence computations are either all fair or all unfair. Francez et al. (1992, Formal Aspects Comput.4, 582–591) propose a notion of completion to transform a non-equivalence-robust fairness notion to an equivalence-robust one while maintaining several properties of the source. However, a completion may not preserve strong feasibility—a necessary and sufficient condition for a completion to be implementable. In this paper, we study the system requirement for a completion to be strongly feasible and determine the strongest implementable completion for every given fairness notion. Moreover, for most systems we obtain a fairness notion, which we refer to as SG+, such that SG+ is the strongest fairness notion that is both implementable and equivalence-robust. We also provide a comprehensive comparison of SG+ and several well-known fairness notions and their minimal and maximal completions. Finally, we show that if equivalence-robustness is dropped, then in general it is impossible to define a fairness notion that is implementable and stronger than all other implementable fairness notions, unless the system consists of only one interaction. This implies plenty of leeway in the design of fairness notions suitable for various applications