Observable Liveness

Abstract. Whereas the traditional liveness property for Petri nets guarantees that each transition can always occur again, observable liveness requires that, from any reachable marking, each observable transition can be forced to fire by choosing appropriate controllable transitions; hence it is defined for Petri nets with distinguished observable and controllable transitions. We introduce observable liveness and show this new notion generalizes liveness in the following sense: liveness of a net implies observable liveness, provided the only conflicts that can appear are between controllable transitions. This assumption refers to applications where the uncontrollable part models a deterministic machine (or several deterministic machines), whereas the user of the machine is modeled by the controllable part and can behave arbitrarily.