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  • 标题:Lower and upper bounds of shortest paths in reachability graphs
  • 本地全文:下载
  • 作者:P. K. Mishra
  • 期刊名称:International Journal of Mathematics and Mathematical Sciences
  • 印刷版ISSN:0161-1712
  • 电子版ISSN:1687-0425
  • 出版年度:2004
  • 卷号:2004
  • 期号:57
  • 页码:3023-3036
  • DOI:10.1155/S0161171204403378
  • 出版社:Hindawi Publishing Corporation
  • 摘要:

    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.

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