Analysis of Structural Liveness and Boundedness in Weighted Free-Choice Net Based on Circuit Flow Values

A Petri net is a mathematical method that can be used to represent and analyze discrete event systems. Although research on structural liveness and safety in ordinary free-choice (FC) nets has been reported, analysis methods for weighted Petri nets have not yet been developed. In this study, we propose a method for determining the structural liveness and safety of strongly connected FC nets. The flow rate of tokens for strongly connected marked graphs is defined as the \(circuit\ flow\ value\). In addition, the circuit flow value of a strongly connected FC net is obtained by calculating the superposition of the circuit flow value.