Search

Petri net (PN) is an effective modeling and analysis tool for discrete event systems. By attaching a first-order logic predicate logic formula to a transition in a PN, a high-level Petri net named Logic Petri Net (LPN) is obtained. LPN has been proved to have equivalent modeling capability with inhibition Petri nets but keeps simpler net structures than the latter. It has the advantage of modeling the cooperative systems with the function to process batch and indeterminate resources. This paper proposes a vector computational method for LPN compositional analysis. It studies the composition of LPNs with the shared P-type subnets. Each logical expression is transformed into a unique disjunctive normal one and then into a unique set of vectors. A vector computational method is proposed such that the properties of the composition of the shared P-type subnets such as liveness, boundedness, and reversibility are verified. An E-commerce system with customers, merchants, and a third-party is constructed to illustrate the method. This paper can improve the state of the art in the theory of LPNs.

Extended colored logic Petri nets (ECLPNs) are extensions of logic Petri nets (LPNs) and colored logic Petri nets (CLPNs). They are equivalent to LPNs and CLPNs, which can describe the batch processing and indeterminacy functions of resources in cooperative systems. The advantage of ECLPNs is that their net structures are much simpler than their equivalent CLPNs, and therefore, ECLPNs can be easily used to model and analyze cooperative systems. For systems containing several subsystems with the same function and structure, we can describe them by a single ECLPN. Then we propose a composition method of ECLPNs. We define the robustness of a system based on ECLPN which reflects the validity of the collaboration of subsystems. We define a strict conservativeness that guarantees data security. The robustness and strict conservativeness of composed ECLPNs are analyzed. An E-commerce example is presented to illustrate the modeling capacity and the advantage of ECLPNs.

Logic Petri Nets (LPNs) is a high-level Petri net, which have the capability to model the batch and indeterminate processing of resources in cooperative systems. Their modeling capability is equivalent to that of inhibition Petri nets (IPNs) but the former maintains simpler net structures. This paper presents a systematic LPN synthesis approach for cooperative systems. First, a normal/logic transition with its connected places is treated as a basic design module. Then, we synthesize the basic design modules firstly to construct LPN models by connecting with shared resource places. Finally, some control strategies are designed to guarantee the resulting LPNs with desirable properties such as boundedness, liveness, and reversibility. An example for constructing an E-commerce system is proposed to illustrate the proposed approach. The paper is of significance in the sense that it provides industrial engineers and academic researchers a methodology of applying LPNs to modeling and analysis of cooperative systems.