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.