Composing fair objects

When specifying large systems, we would like to be able to specify small components independently, and to be able to compose them in such a way that their specified properties are preserved. We have previously proposed the concept of a fair object, which incorporates the specification o f both safety and liveness properties, as a suitable such unit of specification. Unfortunately, however, liveness proper ties of fair objects are often not preserved under composition. In this paper, we define a simple test to determine whether the liveness properties of fair objects are preserved under composition. We then show how liveness properties can be restored in some cases when they are broken, through the addition of fairness constraints.