Verification of Scenarios in Petri Nets Using Compact Tokenflows

In this paper we tackle the problem of verifying whether a scenario is executable in a Petri net. In contrast to sequentially ordered runs, a scenario includes both information about dependencies and independencies of events. Consequently, a scenario allows a precise and intuitive specification of a run of a concurrent or distributed system. In this paper we consider Petri nets with arc weights, namely marked place/transition-nets (p/t-nets) and p/t-nets with inhibitor arcs (pti-nets). A scenario of a p/t-net is a labelled partial order (lpo). A scenario of a pti-net is a labelled stratified order structure (lso). Accordingly, the question is either whether a given lpo is in the language of a given p/t-net or whether an lso is in the language of a given pti-net. Different approaches exist to define the partial language of a Petri net. Each definition yields a different verification algorithm, but existing algorithms perform quite poorly in terms of runtime for most examples. We introduce a new compact characterization of the partial language of a Petri net. This characterization is optimized with respect to the verification problem. The paper is a revised and extended version of the conference paper [10].