On Weak Persistency of Petri Nets

The reachability set of a special type of Petri net, called a persistent net, has been shown to be semilinear by Landweber and Robertson [2]. Recently Gr; bowsky [ 1 ] has given an algorithm to decide whether a given Petri net is persistent or not, and if so to compute the reachability set in the form of a semilinear set. Thus, the persistency is a decidable property of Petri nets, and for the class of persistent nets, the reachability problem and the equivalence problem of the reachability sets are decidable. Mayr [3] and Miiller [4] also have obtained these result:; independently. In this paper, we show that their ideas especially those in [ 1 ] and [2] can be extended to a wider class of Petri nets. More specifically, we define weakly per. sistent nets, and show that it is decidable whether a given Petri net is weakly persistent or not, and that the reachability set of a weakly persistent net is a semi&rear set which is effectively computable. In passing we present a characlterization of semilinear sets as the projective images of the reachability sets of weakllf persistent nets. Finally, some means which may be practically useful to compute the reachability sets are also provided.