Structure theory of choice-free Petri nets based on eigenvalues

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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.

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Amer-Yahia, C., & Zerhouni, N. (1999). Structure theory of choice-free Petri nets based on eigenvalues. Journal of the Franklin Institute, 336(5), 833–849. https://doi.org/10.1016/S0016-0032(99)00008-3

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