Lower and upper bounds of shortest paths in reachability graphs

P. K. Mishra

International Journal of Mathematics and Mathematical Sciences, 2004, vol. 2004, 1-14

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.

Date: 2004
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:791535

DOI: 10.1155/S0161171204403378

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