Analysis of structural properties of Petri nets based on product incidence matrix

Guangyou Ji; Mingzhe Wang

Kybernetika (2013)

  • Volume: 49, Issue: 4, page 601-618
  • ISSN: 0023-5954

Abstract

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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 = C C T or A ˜ = C T C 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.

How to cite

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Ji, Guangyou, and Wang, Mingzhe. "Analysis of structural properties of Petri nets based on product incidence matrix." Kybernetika 49.4 (2013): 601-618. <http://eudml.org/doc/260636>.

@article{Ji2013,
abstract = {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.},
author = {Ji, Guangyou, Wang, Mingzhe},
journal = {Kybernetika},
keywords = {Petri net; structural property; linear inequality; product incidence matrix; Petri net; structural property; linear inequality; product incidence matrix},
language = {eng},
number = {4},
pages = {601-618},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Analysis of structural properties of Petri nets based on product incidence matrix},
url = {http://eudml.org/doc/260636},
volume = {49},
year = {2013},
}

TY - JOUR
AU - Ji, Guangyou
AU - Wang, Mingzhe
TI - Analysis of structural properties of Petri nets based on product incidence matrix
JO - Kybernetika
PY - 2013
PB - Institute of Information Theory and Automation AS CR
VL - 49
IS - 4
SP - 601
EP - 618
AB - 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.
LA - eng
KW - Petri net; structural property; linear inequality; product incidence matrix; Petri net; structural property; linear inequality; product incidence matrix
UR - http://eudml.org/doc/260636
ER -

References

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