Executability of scenarios in Petri nets

In this paper we show that it can be tested in polynomial time whether a scenario is an execution of a Petri net. This holds for a wide variety of Petri net classes, ranging from elementary nets to general inhibitor nets. Scenarios are given by causal structures expressing causal dependencies and concurrency among events. In the case of elementary nets and of place/transition nets, such causal structures are partial orders among transition occurrences. For several extended Petri net classes, the extension of partial orders to stratified order structures is considered. The algorithms are based on the representation of the non-sequential behaviour of Petri nets by so called token flow functions and a characterization of Petri net executions called token flow property. This property allows nontrivial transformations into flow optimization problems which can be solved in polynomial time. The paper is a revised, consolidated and extended version of the conference papers [1,2] and includes parts of the habilitation thesis [3].