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A Method to Prove Non-Reachability in Priority Duration Petri Nets

Werner M., Popova-Zeugmann L., Richling J.

Fundamenta Informaticae

2004

Vol. 61, nr 3,4

351--368

Times and priorities are important concepts that are frequently used to model real-world systems. Thus, there exist extensions for Petri nets which allow to model times and priorities. In contrast, many proof techniques are based on classical (time-less and priority-less) Petri nets. However, this approach fails frequently for timed and prioritized Petri nets. In this paper, we present an approach to prove non-reachability in a Priority Duration Petri net. We use for this proving technique a state equation as well as conditions for firing that include a priority rule and a maximal step rule. Our approach leads to a system of equations and inequalities, which provide us with a sufficient condition of non-reachability. We demonstrate the application of our approach with an example