Abstract
A necessary and sufficient condition for a Petri net to be weakly persistent for every initial marking is obtained. Moreover, a necessary and sufficient condition for reachability is obtainable for this class of Petri nets. As a sufficient condition for a Petri net to have a semilinear reachability set the notion of sinklessness has been proposed, where a marked Petri net is said to be sinkless if the total number of tokens in each minimal circuit is not decreased to 0 by firing transitions. We show that the reachability set is semilinear if the total number of times that sinklessness is violated is finite during each firing, and define a new subclass of Petri nets which have this property for every initial marking.
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