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Lower and upper bounds of shortest paths in reachability graphs

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  • P. K. Mishra

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.

Suggested Citation

  • P. K. Mishra, 2004. "Lower and upper bounds of shortest paths in reachability graphs," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2004, pages 1-14, January.
    • Handle: RePEc:hin:jijmms:791535
    DOI: 10.1155/S0161171204403378
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