Structure theory of choice-free Petri nets based on eigenvalues (Q5926828)

By establishing a certain relation between the incidence matrix of choice-free Petri nets (CfPn) and the eigenvalues of an \(M\)-matrix, the authors use some theorems on \(M\)-matrices to prove structural boundedness, liveness, repetitiveness, conservativeness, consistency, and well-formedness of CfPn. This new approach circumvents the application of the existing complex methods such as the classic incidence matrix analysis, the reachability tree approach, and the reduction techniques which become prohibitive when large systems are analyzed. Three examples illustrate some relevant results and at the same time the computational simplicity (based on Matlab) is ensured by the eigenvalues method.