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Generative families of positive invariants in Coloured nets sub-classes

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Advances in Petri Nets 1993 (ICATPN 1991)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 674))

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Abstract

In Petri nets and high-level nets, positive flows provide additional informations to the ones given by the flows. For instance with the help of positive flows one decides the structural boundeness of the nets and one detects the structural implicit places. Up to now, no computation of positive flows has been developed for coloured nets. In this paper, we present a computation of positive flows for two basic families of coloured nets: unary regular nets and unary predicate/transition nets. At first we show that these two computations are reducible to the resolution of the parametrized equation A.X 1 = ... = A.X n where A is a matrix, Xi, the unknowns are vectors and n is the parameter. Then we present an algorithm to solve this equation. At last we show how the solutions of the parametrized equation can be used to solve the complete equations system for unary regular nets and unary predicate/transition nets.

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References

  1. J.ABADIE Méthode de Fourier et méthode duale pour les systèmes d'inéquations linéaires”, communication invitée au ”Mathematical Programming Symposium, Londres 64. Note E.D.F. N. HR 5.759/3, June 5 1964.

    Google Scholar 

  2. G.W. BRAMS Réseaux de Petri. Théorie et pratique. Masson éditeur, Paris, 1983.

    Google Scholar 

  3. J.M. COUVREUR, S. HADDAD, J.F. PEYRE Résolution paramétrée de familles de systèmes linéaires, RAIRO-Operations Research, vol. 26, n∘2, AFCET-Gauthier-Villars, Paris 1992, p. 183–206.

    Google Scholar 

  4. J.M. COLOM, M. SILVA Improving the linearly based Characterization of P/T nets. Advances in Petri nets 1990. L.N.C.S. 483, G.Rozenberg (eds.). Springer-Verlag, pp. 113–145

    Google Scholar 

  5. J.M. Colom, M. Silva Convex geometry and semiflows in P/T nets. A comparative study of algorithms for computation of minimal P-semiflows. Advances in Petri nets 1990. L.N.C.S. 483, G.Rozenberg (eds.). Springer-Verlag, pp. 79–112

    Google Scholar 

  6. J.M. COUVREUR The general computation of flows for coloured nets. Proceeding of the 11th International Conference on Application and Theory of Petri Nets. Paris. June 90. pp 204–223

    Google Scholar 

  7. J.FARKAS Theorie der einfachen Ungleichungen Journal fur die reine und andgewandte Mathematik, 124, pp. 1–27 1902.

    Google Scholar 

  8. J.FOURIER Histoire de l'Académie Royale des Sciences, Analyse des travaux pendant l'année 1824, Partie Mathématique, Paris 1827 pp. xlvij–lv.

    Google Scholar 

  9. H.J. GENRICH, K. LAUTENBACH System modelling with high-level Petri nets, Theoretical Computer Science 13, 1981,pp 103–136.

    Google Scholar 

  10. H.J. GENRICH, K. LAUTENBACH S-Invariance in predicate transition nets. Informatik Fachberichte 66: Application and Theory of Petri Nets. A.Pagnoni, G.Rozenberg (eds.). Springer-Verlag, pp. 98–111

    Google Scholar 

  11. S. HADDAD, C. GIRAULT Algebraic structure of flows of a regular net, Oxford England, June 1986, Advances in Petri nets, G.Rozenberg ed., L.N.C.S. N. 266, G.Rozenberg ed., Springer Verlag, 1987, pp 73–88.

    Google Scholar 

  12. S. HADDAD Une catégorie régulière de réseau de Petri de haut niveau: définition, propriétés et réductions. Application à la validation de systèmes distribués, Thèse de l'Université Pierre et Marie Curie, Paris, juin 1987.

    Google Scholar 

  13. S. HADDAD, J.M. COUVREUR Towards a general and powerful computation of flows for parametrized coloured nets. 9th European Workshop on Application and Theory of Petri Nets. Vol.11. Venice (Italy). June 1988.

    Google Scholar 

  14. K. JENSEN Coloured Petri nets and the invariant method. Theorical Computer Science 14. North Holland Publ. Co.pp. 317–336

    Google Scholar 

  15. K. JENSEN Coloured Petri nets: Central models and their properties. Advances in Petri nets, G.Rozenberg ed.,L.N.C.S. N. 254, Springer-Verlag Part I. Bad Honnef, September 1986. pp 248–299.

    Google Scholar 

  16. G.MEMMI and G.ROUCAIROL Linear algebra in net theory. Proc. of Advanced course on general Net Theory of Processes and Systems Hambourg 1979, L.N.C.S. 84, W.Brauer (Ed.), Springer Verlag (1980)

    Google Scholar 

  17. G. MEMMI Méthodes d'analyse de réseaux de Petri, réseaux à files et applications aux systèmes temps réel, Thèse d'état, Université Pierre et Marie Curie, Paris, juin 1983.

    Google Scholar 

  18. M. SILVA, J. MARTINEZ, P. LADET, H. ALLA Generalized inverses and the calculation of symbolic invariants for coloured Petri nets, Technique et Science Informatiques, Vol.4 n1, 1985, pp 113–126.

    Google Scholar 

  19. N. TREVE Le calcul d'invariants dans les réseaux à prédicats/transistions unaires. Thèse de l'universitée Paris Sud, Paris 1986.

    Google Scholar 

  20. J. VAUTHERIN, G. MEMMI Computation of flows for unary predicates transitions nets, Advances in Petri nets, G.Rozenberg (eds.), L.N.C.S. 188, Springer-Verlag 1984, pp. 455–467.

    Google Scholar 

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Authors and Affiliations

  1. Université Paris VI - C.N.R.S. MASI, 4 Place Jussieu, 75252, Paris Cedex 05

    J. M. Couvreur, S. Haddad & J. F. Peyre

Authors
  1. J. M. Couvreur
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  2. S. Haddad
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  3. J. F. Peyre
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Grzegorz Rozenberg

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© 1993 Springer-Verlag Berlin Heidelberg

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Couvreur, J.M., Haddad, S., Peyre, J.F. (1993). Generative families of positive invariants in Coloured nets sub-classes. In: Rozenberg, G. (eds) Advances in Petri Nets 1993. ICATPN 1991. Lecture Notes in Computer Science, vol 674. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-56689-9_39

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  • DOI: https://doi.org/10.1007/3-540-56689-9_39

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  • Print ISBN: 978-3-540-56689-2

  • Online ISBN: 978-3-540-47631-3

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