Copyright © 2004 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We prove the following property for safe marked graphs, safe conflict-free Petri nets, and live and safe extended free-choice Petri nets. We prove the following three results. If the Petri net is a marked graph, then the length of the shortest path is at most (|T|−1)⋅|T|/2. If the Petri net is conflict free, then the length of the shortest path is at most (|T|+1)⋅|T|/2. If the petrinet is live and extended free choice, then the length of the shortest path is at most |T|⋅|T+1|⋅|T+2|/6, where T is the set of transitions of the net.