Splitting forward simulations to cope with liveness

In the literature, the conditions on history variables or forward simulations that are related to liveness are expressed in terms of behaviours, and are stronger than convenient and necessary. In this paper, we propose alternative conditions on the simulation relation, which are expressed in terms of the next state relation, and are closely tied to the weak or strong fairness conditions of the specifications. The proof of soundness of this proposal is based on a new theorem that asserts the existence of a strongly fair scheduler for infinitely many alternatives. The theory is extended to simulations in which the concrete specification (occasionally) does fewer steps than the abstract specification it implements.