Lower and upper bounds of shortest paths in reachability graphs
نویسنده
چکیده
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 Petri net 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.
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ورودعنوان ژورنال:
- Int. J. Math. Mathematical Sciences
دوره 2004 شماره
صفحات -
تاریخ انتشار 2004