Structure theory of choice-free Petri nets based on eigenvalues

Abstract

Choice-free are a class of Petri nets where structural conflicts are forbidden. They are well-suited for modeling concurrent systems with bulk services and arrivals. A new approach, based on eigenvalues, for the study of some structural properties of Choice-free Petri nets is given in this paper. The structural results follow from the computation of eigenvalues of a square matrix with nonnegative off-diagonal elements, known as an M-matrix, obtained by a transformation of the classical incidence matrix. Theorems on M-matrices are used in this paper to prove structural boundedness, liveness, repetitiveness, conservativeness, consistency, and well-formedness of Choice-free Petri nets.