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On Structural Conditions for Weak Persistency and Semilinearity of Petri Nets.

Hiraishi, Kunihiko

iias, Research Report No. 100, pages 1-17 pp.. Numazu, Japan: International Institute for Advanced Study of Social Information Science, February 1990.

Abstract: The author obtains a necessary and suffucient condition for a Petri net to be weakly persistent for every initial marking. A necessary and sufficient condition for reachability can also be obtained for this class of Petri nets. The reachability set of a weakly persistent Petri net has been shown to be semilinear. The class of normal Petri nets has been proposed as a class of Petri nets which have semilinear reachability sets. Normality of Petri nets is a structural condition for sinklessness. The author shows that the reachability set is semilinear if the total number of times that sinklessness is violated is finite during each firing.

Keywords: weak persistency; semilinearity (of) reachability set; reachability condition; normal net; sinklessness.

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