On the Computation of Place Invariants for Algebraic Petri Nets | SpringerLink
Skip to main content

On the Computation of Place Invariants for Algebraic Petri Nets

  • Conference paper
Structures in Concurrency Theory

Part of the book series: Workshops in Computing ((WORKSHOPS COMP.))

Abstract

The paper is concerned with the computation of a generator set for the space of all place invariants for a given algebraic net. We will show that the problem can be divided into two major steps. First we trace back the problem to a set of equations between terms. Then we combine the solutions of these equations to obtain the solution of the original problem. For both steps we present a solution for a restricted class of algebraic nets, where the algebraic specification contains no equations and at most unary operation symbols.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Subscribe and save

Springer+ Basic
¥17,985 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Chapter
JPY 3498
Price includes VAT (Japan)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
JPY 5719
Price includes VAT (Japan)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
JPY 7149
Price includes VAT (Japan)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Similar content being viewed by others

References

  1. J.M. Couvreur. The general computations of flows for coloured nets. Proc. of the 11th Int. Workshop on Appl. and Theory of Petri Nets, 1990.

    Google Scholar 

  2. J.M. Couvreur, J. Martinez. Linear invariants in commutative high level nets. High-level Petri nets, Theory and Application, 1991.

    Google Scholar 

  3. H. Ehrig, B. Mahr. Fundamentals of Algebraic Specifications 1. EATCS Monographs on Theor. Comp. Science 6. Springer 1985.

    Google Scholar 

  4. H. Genrich, K. Lautenbach. S-invariance in Pr/T-nets. Informatik-Fachberichte, (66), 1983.

    Google Scholar 

  5. S. Haddad, J.M. Couvreur. Towards a general and powerful computation of flows for parameterized coloured nets. Proc. of the 9th European Workshop on Appl. and Theory of Petri Nets, 1988.

    Google Scholar 

  6. K. Jensen. Coloured Petri nets and the invariant-method. Theor. Comp. Science, 14: 317–336, 1981.

    Article  MATH  Google Scholar 

  7. K. Jensen. How to find invariants for coloured Petri nets. LNCS, 118: 327–338, 1981.

    Google Scholar 

  8. K. Lautenbach, A. Pagnoni. Invariance and duality in predicate/transition nets and in coloured nets. Arbeitspapiere der GMD, 132, 1985.

    Google Scholar 

  9. G. Memmi, J. Vautherin. Analysing nets by the invariant method. In: Rozenberg, Brauer, Reisig (eds.), Advances in Petri nets 1986, pages 300–336, 1987.

    Google Scholar 

  10. W. Reisig. Petri nets and algebraic specifications. Theor. Comp. Science, 80 (1991): 1–34.

    Article  MATH  MathSciNet  Google Scholar 

  11. K. Schmidt. T-invariants of algebraic petri nets. Informatik-Bericht der HU Berlin, 31, 1994.

    Google Scholar 

  12. M. Silva, J. Martinez, P. Ladet, H. Alia. Generalized inverses and the calculations of symbolic invariants for coloured nets. High-level Petri nets, Theory and Application, 1991.

    Google Scholar 

  13. J. Vautherin. Parallel systems specification with colored Petri nets and abstract data types. Proc. of the 7th European Workshop on ATPN Oxford 1986, 5–23.

    Google Scholar 

  14. J. Vautherin. Calculation of semi-flows for Pr/T-systems. In T. Murata, editor, Int. Workshop on Petri Nets and Performance Models. IEEE Computer Society Press, 1987.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 1995 British Computer Society

About this paper

Cite this paper

Schmidt, K. (1995). On the Computation of Place Invariants for Algebraic Petri Nets. In: Desel, J. (eds) Structures in Concurrency Theory. Workshops in Computing. Springer, London. https://doi.org/10.1007/978-1-4471-3078-9_21

Download citation

  • DOI: https://doi.org/10.1007/978-1-4471-3078-9_21

  • Publisher Name: Springer, London

  • Print ISBN: 978-3-540-19982-3

  • Online ISBN: 978-1-4471-3078-9

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics