Fairness and conspiracies

We define a hierarchy of fairness postulates; k-fairness (∞-fairness) means the absence of any infinite execution in which some transition occurs only finitely often but is enabled infinitely often by some sequence of length ? k (of unrestricted length, respectively).We show (i) that for Petri nets in general, ∞-fairness equals k-fairness for all k, and (ii) that for a large subclass of nets, (k+1)-fairness equals k-fairness for all k. The transferral of these results to concurrent programs is also discussed.