Geodesic
Analysis of structural properties of Petri nets based on product incidence matrix
Kybernetika, Tome 49 (2013) no. 4, pp. 601-618

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This paper presents some structural properties of a generalized Petri net (PN) with an algorithm to determine the (partial) conservativeness and (partial) consistency of the net. A product incidence matrix $A=CC^T$ or $\tilde{A}=C^TC$ is defined and used to further improve the relations among PNs, linear inequalities and matrix analysis. Thus, based on Cramer's Rule, a new approach for the study of the solution of a linear system is given in terms of certain sub-determinants of the coefficient matrix and an efficient algorithm is proposed to compute these sub-determinants. The paper extends the common necessary and/or sufficient conditions for conservativeness and consistency in previous papers and some examples are designed to explain the conclusions finally.
Classification : 93A15, 93C65
Keywords: Petri net; structural property; linear inequality; product incidence matrix 
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     author = {Ji, Guangyou and Wang, Mingzhe},
     title = {Analysis of structural properties of {Petri} nets based on product incidence matrix},
     journal = {Kybernetika},
     pages = {601--618},
     publisher = {mathdoc},
     volume = {49},
     number = {4},
     year = {2013},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/KYB_2013__49_4_a6/}
}
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Ji, Guangyou; Wang, Mingzhe. Analysis of structural properties of Petri nets based on product incidence matrix. Kybernetika, Tome 49 (2013) no. 4, pp. 601-618. http://geodesic.mathdoc.fr/item/KYB_2013__49_4_a6/