Lower and upper bounds of shortest paths in reachability graphs

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|

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