Abstract
Boolean Petri net (BPN) and Crisp Boolean Petri net (CBPN) is a well-studied graph model since 2010 which has several applications in mathematical modeling of complex or tricky networks. Modeling any network with Petri net which can generate binary numbers as marking vectors in its reachability tree is still has much uses. In CBPN with a minimum number of transition and minimum number of steps of reachability tree, minimal execution time to run the machine has not been noted till date, thus it’s necessary to sort out this problem. Possibly it may occur due to some forbidden structure which hinders any 1-safe Petri net to be a CBPN. In this paper, we present some forbidden digraphs whose presence interrupts the generation of binary n-vectors exactly once. Any 1-safe Petri net is not a CBPN if it contains any of the subnet induced to the four forbidden structures discussed in this paper.
Highlights
In the field of modeling any real-world system, Petri net is one of the emerging theories from the early ‘90s
We propose the structure of some forbidden subnets which hinders any 1-safe Petri net to be a Crisp Boolean Petri net (CBPN)
In this paper, we have considered the family of crisp Boolean Petri net graphs and proposed four forbidden subnets for any 1-safe Petri net graph
Summary
In the field of modeling any real-world system, Petri net is one of the emerging theories from the early ‘90s. When for any Petri net if the possible number of reachable states does not follow a linear time algorithm, it may occur due to the existence of some forbidden structures in the model. By saying Crisp Boolean Petri nets, it means that a 1-safe Petri net that produces each binary n-vector only once in its reachability graph. We propose the structure of some forbidden subnets which hinders any 1-safe Petri net to be a CBPN These forbidden digraphs interrupt in the generation of all the binary n-vectors exactly once in its reachability tree as its marking vector (Pastor et al, 1994; Kansal et al, 2012). A Petri net is a Boolean Petri net if it generates all the binary vectors in its reachability graph (Kansal et al, 2011b) (see Figure 2)
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