Progress, Justness, and Fairness

Abstract

Fairness assumptions are a valuable tool when reasoning about systems. In this paper, we classify several fairness properties found in the literature and argue that most of them are too restrictive for many applications. As an alternative we introduce the concept of justness.

Justness

“…For the infinite path that loops in the first state is complete. Nevertheless, as nothing stops Cataline from making progress, in reality t will occur [16].…”

“…The criterion of justness aims to ensure the liveness property occurring in these examples. In [16] it is formulated as follows:…”

“…As we argued in [10,15,16], a progress assumption as above is too strong in the context of reactive systems, meaning that it rules out as incomplete too many paths. There, a transition typically represents an interaction between the distributed system being modelled and its environment.…”

“…Such a property holds for a distributed system if the [good] thing happens in each of its possible runs. One of the ways to formalise this in terms of transition systems is to postulate a set of good states G , and say that the liveness property G holds for the process P if all complete paths starting in P pass through a state of G [16]. Without a completeness criterion the concept of a liveness property appears to be meaningless.…”

“…In [10,15,16] we worked with transition systems that are equipped with a partitioning of the transitions into blocking and non-blocking ones, and reformulated the progress assumption as follows: a (transition) system in a state that admits a non-blocking transition will eventually progress, i.e., perform a transition.…”