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Structure theory of choice-free Petri nets based on eigenvalues.

Amer-Yahia, C.; Zerhouni, N.

In: Journal of the Franklin Institute, Engineering and Applied mathematics, Vol. 336, No. 5, pages 833-849. 1999.

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.

Keywords: Petri nets, concurrent systems, eigenvalues, net analysis, structural properties.

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