Linear invariants in commutative high level nets

  • Jean Michel Couvreur
  • Javier Martínez
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 483)


Commutative nets are a subclass of colored nets whose color functions belong to a ring of commutative diagonalizable endomorphisms. Although their ability to describe models is smaller than that of colored nets, they can handle a broad range of concurrent systems. Commutative nets include net subclasses such as regular homogeneous nets and ordered nets, whose practical importance has already been shown.

Mathematical properties of the color functions of commutative nets allow a symbolic computation of a family of generators of flows. The method proposed decreases the number of non-null elements in a given color function matrix, without adding new columns. By iteration, the entire matrix is annulled and a generative family of flows is obtained. The interpretation of the invariants associated with each flow is straightforward.


Linear invariants flow computation structural analysis methods subclasses of Petri nets colored nets 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. (Alla et al. 85)
    H.Alla, P.Ladet, J. Martínez, M. Silva. Modelling and validation of complex systems by coloured Petri nets. Advances in Petri nets 1984. L.N.C.S. 188, Springer-Verlag, pp.15–31Google Scholar
  2. (Blyth,Robertson 86).
    T.S.Blyth, E.F.Robertson. Linear Algebra (Vol. 4). Chapman and Hall. London.Google Scholar
  3. (Bourbaki 81).
    N.Bourbaki. Algèbre (Chapitres 4 à 7). Masson. Paris.Google Scholar
  4. (Brams 83).
    G.W.Brams. Réseaux de Petri:théorie et pratique. Masson. ParisGoogle Scholar
  5. (Chambalad 72).
    L. Chambalad. Algèbre multilinaire. Dunod. ParisGoogle Scholar
  6. (Genrich 88).
    H.J.Genrich.Equivalence transformations of PrT-Nets. 9th European Workshop on Application and Theory of Petri Nets. Vol. II. Venice (Italy). June. pp. 229–248Google Scholar
  7. (Genrich,Lautenbach 83).
    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. 98–111Google Scholar
  8. (Jensen 81).
    K.Jensen. Coloured Petri nets and the invariant method. Theoretical Computer Science 14. North Holland Publ. Co. pp.317–336Google Scholar
  9. (Haddad 87).
    S.Haddad. Une catégorie régulière de réseau de Petri de haut niveau: définition, propietés et reductions. Application à la validation des systèmes distribués. Ph.D. University Paris VI. June.Google Scholar
  10. (Haddad, Couvreur 88).
    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. II. Venice (Italy). June.Google Scholar
  11. (Reisig 85).
    W.Reisig. Petri nets. EATCS Monographs on Theoretical Computer Science, Vol. 4. Springer Publ. Co.Google Scholar
  12. (Silva 85).
    M.Silva. Las redes de Petri en la automática y la informática. Ed. AC. Madrid.Google Scholar
  13. (Silva et al. 85)
    M.Silva, J.Martínez, P.Ladet, H.Alla. Generalized inverses and the calculation of invariants for coloured Petri nets. Technique et science informatique. Vol.4 no1, pp. 113–126Google Scholar
  14. (Vautherin,Memmi 85).
    J. Vautherin, G. Memmi. Computation of flows for unary predicates transition nets. Advances in Petri nets 1984. L.N.C.S. 188, Springer-Verlag. pp.455–467Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1991

Authors and Affiliations

  • Jean Michel Couvreur
    • 1
  • Javier Martínez
    • 2
  1. 1.Université Paris VI-C.N.R.S. MASI - C3Paris Cedex 05France
  2. 2.Dpto. de Ingeniería Eléctrica e InformáticaUniversidad de ZaragozaZaragozaSpain

Personalised recommendations