Advertisement

Petri Net Theory — Problems Solved by Commutative Algebra

  • Christoph Schneider
  • Joachim Wehler
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1639)

Abstract

The paper deals with the computation of flows in coloured nets and with the potential reachability of markings over the integers in p/t nets. We introduce Artin nets as a subclass of coloured nets, which can be handled by methods from Commutative Algebra. As a first result we develop an algorithm for the explicit computation of flows in Artin nets, which is supported by existing tools. Concerning reachability in p/t nets we prove a refined rank condition as a second result.

Keywords

Coloured Petri net Artin net commutative net flow reachability Gröbner theory 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Bibliography

  1. [AM1969]
    Atiyah, Michael; Macdonald, I. G.: Introduction to Commutative Algebra. Addison-Wesley, Reading, Mass. 1969zbMATHGoogle Scholar
  2. [Bou1981]
    Bourbaki, Nicolas: Éléments de mathématique. Algèbre, Chapitre 7, Modules sur les anneaux principaux. Masson, Paris 1981Google Scholar
  3. [Bou1972]
    Bourbaki, Nicolas: Elements of mathematics. Commutative Algebra, Chapter I, Flat modules. Hermann, Paris 1972Google Scholar
  4. [BW1998]
    Buchberger, Bruno; Winkler, Franz (Eds.): Gröbner Bases and Applications. London Mathematical Society Lecture Note Series 251. Cambridge University Press 1998Google Scholar
  5. [BWK1998]
    Becker, Thomas; Weispfenning, Volker; Kredel, Heinz: Gröbner Bases: A computational approach to Commutative Algebra. Springer, Berlin et al. 1998Google Scholar
  6. [CLO1998]
    Cox, David; Little, John; O’Shea, Donal: Using Algebraic Geometry. Springer, Berlin et al. 1998zbMATHGoogle Scholar
  7. [CM1990]
    Couvreur, Jean-Michel; Martinez, J.: Linear invariants in commutative high level Petri nets. In: Rozenberg, G. (ed.): Advances in Petri Nets 1990. Lecture notes in Computer science, vol. 483. Springer, Berlin et al. 1990Google Scholar
  8. [DNR1996]
    Desel, Jörg; Neuendorf, Klaus-Peter; Radola, M.-D.: Proving nonreachability by modulo-invariants. Theoretical Computer Science 153 (1996), p. 49–64zbMATHCrossRefMathSciNetGoogle Scholar
  9. [GS1996]
    Grayson, Daniel.; Stillman, Michael: Macaulay 2. Available at “http://www.math.uiuc.edu
  10. [Jen1992]
    Jensen, Kurt: Coloured Petri nets. Basis Concepts, Analysis Methods and Practical Use. Springer, Berlin et al. 1992Google Scholar
  11. [Vas1998]
    Vasconcelos, Wolmer: Computational Methods in Commutative Algebra and Algebraic Geometry. Springer, Berlin et al. 1998Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1999

Authors and Affiliations

  • Christoph Schneider
    • 1
  • Joachim Wehler
    • 2
  1. 1.cke-schneider.de data serviceBerlinGermany
  2. 2.MünchenGermany

Personalised recommendations