Summary
Coloured Petri Nets permit construction of more compact models than do generalized Petri Nets. In coloured Petri Nets the real parallelism can be considerable which leads to large sets of reachable markings. To analyse coloured Nets, the method of linear invariants of markings has been used successfully. In this paper, we present a systematic method for calculating symbolic invariants of a coloured Petri Net that is to say, invariant relations in terms of place markings, of functions associated to the arcs of the coloured net and, eventually, of generalised inverses of these functions.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
Bibliographie
H. Alu, P. Ladet, J. Martinezand Silva, M.: Modelling and Validation of Complex Systems by Coloured Petri Nets: Application to a Flexible Manufacturing System; and European Workshop on Petri Net Applications and Theory, Aarhus, June 1984, 122–140.
G. W. Brams: Réseaux de Petri: Théorie et Pratique. Masson, Paris. 1983.
S. L. Campbelland C. D. Meyer: Generalized Inverses of Linear Transformations; Pitman, London, 1979.
K. Jensen: Coloured Petri Nets and the Invariant Method; Theoretical Computer Science 14, North Holland. Publ. Co., 1981, 317–336.
K. Jensen: How to Find Invariants for Coloured Petri Nets; Mathematical Foundations of Computer Science, Lecture Notes in Computer Science 118, Springer Verlag, Berlin. 1981.
K. Lautenbach and H. A. Schmid: Use Of Petri Nets for Proving Correctness of Concurrent Process Systems; IFIP 74, North Holland Pub. Co., 1974, 187–191.
J. Martinez and M. Silva: A Simple and Fast Algorithm to Obtain all Invariants of a Generalized Petri Net; 2nd European Workshop on Petri Nets Theory and Applications, Informatik Fachberichte 52, Springer Verlag, Berlin, 1982 301–310.
J. Martinez:Contributionaland/isisymodelado de sistemas concurrentes mediante redes de Petri; Ph. D. Thesis, Universidad de Zaragoza. Spain. October 1984.
W. Basic: Petri Nets with Individual Tokens; 3th European Workshop on Applications and Theory of Petri Nets, Varenna, September 1982, 386–406.
M. Silva: Simplification des réseaux de Petri par élimination de places implicites; Digital Processes 6 (4), 1980, 245–256.
M. Silva: Las redes de Petri en la Automàtica y la Informàtica; Ed. AC, Madrid, 1985.
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1991 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Silva, M., Martinez, J., Ladet, P., Alla, H. (1991). Generalized Inverses and the Calculation of Symbolic Invariants for Coloured Petri Nets. In: Jensen, K., Rozenberg, G. (eds) High-level Petri Nets. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-84524-6_10
Download citation
DOI: https://doi.org/10.1007/978-3-642-84524-6_10
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-54125-7
Online ISBN: 978-3-642-84524-6
eBook Packages: Springer Book Archive