On the Decidability of Soundness of Workflow Nets with an Unbounded Resource

In this work, we consider the modeling of workflow systems with Petri nets. A resource workflow net (RWF-net) is a workflow net supplied with an additional set of initially marked resource places. Resources can be consumed and/or produced by transitions. We constrain neither the intermediate nor final resource markings, hence a net can have an infinite number of different reachable states. An initially marked RWF-net is called sound if it properly terminates its work and, moreover, an increase of the initial resource does not violate its proper termination. An unmarked RWF-net is sound if it is sound for some initial resource. In this paper, we prove the decidability of both marked and unmarked soundness for a restricted class of RWF-nets with a single unbounded resource place (1-dim RWF-nets). We present an algorithm for computing the minimal sound resource for a given sound 1-dim RWF-net.