Abstract
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.
Highlights
INTRODUCTIONLogic Petri net (LPN) is such a model that describes and analyzes the batch and indeterminate processing of data [12]
This paper proposes a vector computational method for analyzing the compositional properties of logic Petri net (LPN). It studies the composition of LPNs with the shared P-type subnets
A vector computational method is proposed such that the properties of the composition of LPN models with two types such as liveness, boundedness, and reversibility are verified
Summary
Logic Petri net (LPN) is such a model that describes and analyzes the batch and indeterminate processing of data [12]. It is obtained by attaching a first-logic predicate logic formula to a transition in a classical PN in [13]. Sanders and Meyer propose stochastic activity networks that have predicates and functions on markings of places [15] They can describe the processing of batch and indeterminate data. A vector computational method is proposed such that the properties of the composition of LPN models with two types such as liveness, boundedness, and reversibility are verified.
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