Skip to main content

Infinite Behaviour and Fairness

  • Conference paper
Petri Nets: Central Models and Their Properties (ACPN 1986)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 254))

Included in the following conference series:

Abstract

Specification techniques for the infinite behaviour of a P/T-system are introduced and their expressive power is compared. In particular, fair behaviour is related to the wellknown liveness problem. Finally, the problem is studied how to implement fair behaviour using a fair occurrence rule for transitions.

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

Access this chapter

Subscribe and save

Springer+ Basic
$34.99 /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
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever

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. E. Best: Fairness and Conspiracies, Information Processing Letters 18 (1983), 215–220

    Article  MathSciNet  Google Scholar 

  2. L. Boasson and M. Nivat: Adherences of Languages, J. Comput. System Sci. 20 (1980), 285–309

    Article  MathSciNet  MATH  Google Scholar 

  3. P. Brinch Hansen: Operating System Principles, Englewood Cliffs: Prentice-Hall 1973

    MATH  Google Scholar 

  4. H. Carstensen: Fairness bei Petrinetzen mit unendlichem Verhalten, Univ. Hamburg, FB Informatik, Bericht Nr. 93, IFI-HH-B-93/82, 1982

    Google Scholar 

  5. H. Carstensen: Fairness in Deadlockfree Petri Nets with the Finite Delay Property, Proc. 5th European Workshop on Applications and Theory of Petri Nets, Arhus 1984, pp 234-253

    Google Scholar 

  6. H. Carstensen, R. Valk: Infinite Behaviour and Fairness in Petri Nets, in G. Rozenberg (ed.): Advances in Petri Nets 1984, Lect. Notes in Computer Sci. 188, Springer, Berlin, 1985, pp 83-100

    Google Scholar 

  7. H. Carstensen: Fairness bei nebenläufigen Systemen, eine Untersuchung am Modell der Petrinetze, Bericht des FB Informatik, Univ. Hamburg, 1986

    Google Scholar 

  8. R. S. Cohen, A. Y. Gold: Theory of ω-languages, Journ. Computer Syst. Sciences 15 (1977), 169–208

    Article  MathSciNet  MATH  Google Scholar 

  9. E. W. Dijkstfa: Co-operating sequential processes, in F. Genuys (ed.): Programming Languages, Academic Press, London, 1968, pp 43–112

    Google Scholar 

  10. E. W. Dijkstra: Hierarchical Ordering of Sequential Processes, Acta Informatica 1 (1971), pp 115–138

    Article  MathSciNet  Google Scholar 

  11. S. Eilenberg: Automata, Languages and Machines, Vol. A., Academic Press, New York 1974

    MATH  Google Scholar 

  12. D. Hauschildt, R. Valk: Safe States in Banker like Resource Allocation Problems, in: G. Rozenberg (ed.), Advances in Petri Nets 1985, Lecture Notes in Computer Science 222, Springer, Berlin, 1986

    Google Scholar 

  13. E. Jessen, R. Valk: Rechensysteme, Springer-Verlag, Berlin, 1986

    Google Scholar 

  14. M. Jantzen: Language Theory of Petri Nets (this volume)

    Google Scholar 

  15. L. H. Landweber: Decision problems for ω-automata, Math. Systems Theory 3 (1969), 376–384

    Article  MathSciNet  MATH  Google Scholar 

  16. K. Lautenbach: Ein kombinatorischer Ansatz zur Erreichung von Fairness in Scheduling Problemen, Applied Computer Sci. 8, Verlag C. Hauser, München, 1977

    Google Scholar 

  17. A. Merceron: Fair Processes, Proc. 7th Europ. Workshop on Application and Theory of Petri Nets, Oxford, 1986

    Google Scholar 

  18. T. Murata, Z. Wu: Fair Relation and Modified Synchronie Distances in a Petri Net, Journ. Franklin Institute, 320 (1985) 2, 68–82

    MathSciNet  Google Scholar 

  19. E. Pelz: ω-languages of Petri Nets and logical sentences, Proc. 7th Europ. Workshop on Application and Theory of Petri Nets, Oxford, 1986

    Google Scholar 

  20. W. Reisig: Coexistence: A Refinement of Concurrency, Proc. 7th Europ. Workshop on Application and Theory of Petri Nets, Oxford, 1986

    Google Scholar 

  21. M. Raynal: Algorithmes Distribués et Protocoles, Eyrolles, Paris, 1985

    Google Scholar 

  22. M. Raynal: An Optimal Algorithm for Mutual Exclusion in Computer Networks, Comm. ACM, 24 (1981), 9–17

    Article  MathSciNet  Google Scholar 

  23. G. Roucairol: FIFO-Nets (this volume)

    Google Scholar 

  24. R. Valk: Infinite Behaviour of Petri Nets, Theor. Comput. Sci. 25, (1983), 311–341

    Article  MathSciNet  MATH  Google Scholar 

  25. R. Valk, M. Jantzen: The Residue of Vector Sets with Applications to Decidability Problems in Petri Nets, Acta Informatica 21 (1985), 643–674

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 1987 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Valk, R. (1987). Infinite Behaviour and Fairness. In: Brauer, W., Reisig, W., Rozenberg, G. (eds) Petri Nets: Central Models and Their Properties. ACPN 1986. Lecture Notes in Computer Science, vol 254. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-47919-2_14

Download citation

  • DOI: https://doi.org/10.1007/978-3-540-47919-2_14

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-17905-4

  • Online ISBN: 978-3-540-47919-2

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics