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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|Ã¢ÂˆÂ’1)Ã¢Â‹Â…|T|/2. If the Petri net is conflict free, then the length  of the shortest path is at most (|T|+1)Ã¢Â‹Â…|T|/2. If the petrinet is live and extended free choice, then the length of the shortest path is at most |T|Ã¢Â‹Â…|T+1|Ã¢Â‹Â…|T+2|/6, where T is the set of transitions of the net

Lower and upper bounds of shortest paths in reachability graphs