Abstract
This paper introduces a new flow calculation theory for a wide subclass of coloured nets : the regular nets (R.N.). Their parametrization allows to study at the same time the flows for all nets differing only by the sizes of the colour sets. The algebraic structure of the flows subspace provides a fundamental decomposition theorem leading to an algorithm computing a flow basis for a parametrized regular net. The modelling of a significant classical example is presented with the computation of a basis of flows.
C.N.R.S : Unite Associee de Methodologie et Architecture des Systemes Informatiques et Greco C3-Semantique et Evaluation
This is a preview of subscription content, log in via an institution.
Preview
Unable to display preview. Download preview PDF.
References
H. ALLA, P. LADET, J. MARTINEZ, M. SILVA: Modelling and validation of complex systems by coloured Petri nets. Fifth european workshop on applications and theory of Petri nets. Aarhus, Denmark (1984)
G. BERTHELOT: Transformation et analyse de réseaux de Petri, applications aux protocoles. Thèse d'etat. Université Pierre et Marie Curie. Paris (1983)
G.W. BRAMS: Réseaux de Petri. Théorie et pratique. Masson editeur, Paris (1983)
H.J. GENRICH, K. LAUTENBACH: System modelling with high-level Petri nets, Theoretical computer science 13 (1981)
H.J. GENRICH, K. LAUTENBACH: S-invariance in predicate transition nets. Third european workshop on applications and theory of Petri nets. Varenne Italy (1982)
S. HADDAD, J-M. BERNARD: Les réseaux réguliers, specification et validation par le logiciel ARP. Troisieme colloque de génie logiciel Afcet. Versailles (1986)
S. HADDAD: Thesis to appear in march 1987. Université P. et. M. Curie.
P. HUBER, A.M. JENSEN, L.O. JEPSEN, K. JENSEN: Towards reachability trees for high-level Petri nets. Fifth european workshop on applications and theory of Petri nets. Aarhus, Denmark (1984)
K. JENSEN: How to find invariants for coloured Petri nets. Mathematical foundations of computer science. Lectures notes in computer science 118. Springer-Verlag (1981)
K. JENSEN: High-level Petri nets. Third european workshop on applications and theory of Petri nets. Varenne Italy (1982)
R. KUJANSUU, M. LINDQVIST: Efficient algorithms for computing S-invariants for predicate transition nets. Fifth european workshop on applications and theory of Petri nets. Aarhus, Denmark (1984)
K. LAUTENBACH, A. PAGNONI: Invariance and duality in predicate transition nets and in coloured nets. Arbeitspapiere der G.M.D. 132
S. LANG: Algebra. Addison-Wesley (seventh printing) 1977
G. MEMMI: Méthodes d'analyse de réseaux de Petri, réseaux à files et applications aux systèmes temps réel. Thèse d'etat. Université Pierre et Marie Curie. Paris (1983)
M. SILVA, J. MARTINEZ, P. LADET, H. ALLA: Generalized inverses and the calculation of symbolic invariants for coloured Petri nets. Technique et science informatique Vol. 4 No 1 (1985)
J. VAUTHERIN, G. MEMMI: Computation of flows for unary predicates transitions nets. Advances in Petri net (p. 455–467). Lecture notes in computer science 188. Springer-Verlag 1984
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1987 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Haddad, S., Girault, C. (1987). Algebraic structure of flows of a regular coloured net. In: Rozenberg, G. (eds) Advances in Petri Nets 1987. APN 1986. Lecture Notes in Computer Science, vol 266. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-18086-9_20
Download citation
DOI: https://doi.org/10.1007/3-540-18086-9_20
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-18086-9
Online ISBN: 978-3-540-47743-3
eBook Packages: Springer Book Archive