Testing the executability of scenarios in general inhibitor nets

In this paper we introduce executions of place/transition Petri nets with weighted inhibitor arcs (PTI-net) as enabled labeled stratified order structures (LSOs) and present a polynomial algorithm to decide, whether a scenario given by an LSO is an execution of a given PTI-net. The algorithm is based on an equivalent characterization of enabled LSOs called token flow property. Although the definition of the token flow property involves exponentially many objects in the size of the LSO, there is a nontrivial transformation into a flow optimization problem which can be solved in polynomial time.