Nothing Special   »   [go: up one dir, main page]

Skip to main content

Place/Transition Systems

  • 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

In the 1970ies, Place/Transition Systems were certainly the most common and the most extensively studied class of nets. Often they have just been called Petri Nets.

We introduce their basic concepts, viz. the idea of places that carry any number of (identical) tokens. This introduces a dimension of infinity that implies a lot of interesting theoretical problems such as liveness, boundedness and the reachability of markings.

We especially stress the viewpoint of General Net Theory, considering such nets as shorthand notation for elementary net systems. In this way the rich body of theory for c/e systems is applicable also for place/ transition nets. Finally we will study net properties that can be derived from coverability trees.

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
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • 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. G. Berthelot: Transformations and Decompostitions of Nets. this volume

    Google Scholar 

  2. Eike Best: Concurrent Behaviour: Sequences, Processes and Axioms. Arbeitspapiere der GMD 118, November 1984, also: Lecture Notes in Computer Science vol. 197 (1985)

    Google Scholar 

  3. Eike Best: Structure Theory of Petri Nets: The Free Choice Hiatus. This volume

    Google Scholar 

  4. Eike Best, Raymond Devillers: Concurrent Behaviour: Sequences, Processes and Programming Languages. Studien der GMD No. 99 (1985)

    Google Scholar 

  5. Eike Best, Cesar Fernandez: Notations and Terminology of Petri Net Theory. Arbeitspapiere der GMD 195, Gesellschaft für Mathematik und Datenverarbeitung (1986)

    Google Scholar 

  6. G. W. Brams (nom collectif): Reseaux de Petri: Theorie et Pratique; Tome 1 and 2, Masson publ. comp. Paris (1983)

    Google Scholar 

  7. H. J. Genrich: Das Zollstationenproblem. GMD internal report ISF/69-01-15 (1969), revised version: GMD internal report ISF/71-10-13 (1971).

    Google Scholar 

  8. H. J. Genrich: Einfache nicht-sequentielle Prozesse. GMD-Bericht 37 (1971)

    Google Scholar 

  9. H. J. Genrich: Predicate/Transition Nets. this volume

    Google Scholar 

  10. Ursula Goltz, Wolfgang Reisig: The Non-Sequential Behaviour of Petri Nets. Information & Control 57, Nos. 2-3, pp. 125–147 (1983)

    Article  MathSciNet  MATH  Google Scholar 

  11. M. Hack: Analysis of Production Schemata by Petri Nets. Cambridge, Mass.: MIT, Dept. of Electrical Engineering, MS Thesis (1972). also: MIT Project MAC, Computation Structures Note 17(1974)

    Google Scholar 

  12. M. Hack: Decidability Questions for Petri Nets. MIT, Dept. of Electrical Engineering (1975), also: MIT, Technical Report TR-159 (1976)

    Google Scholar 

  13. A. W. Holt et al: Information System Theory Project, Final Report. Princeton, N. J.: Applied Data Research Inc., RADC-TR-68-305, N TIS AD 679972 (1986)

    Google Scholar 

  14. Mathias Jantzen: Complexity of Place/Tansition Nets. This volume

    Google Scholar 

  15. Mathias Jantzen: Language Theory of Nets. This volume

    Google Scholar 

  16. K. Jensen: Coloured Petri Nets. this volume

    Google Scholar 

  17. R. M. Keller: Vector Replacement Systems: A Formalism for Modelling Asynchronous Systems. TR 117, Computer Science Lab., Dept. of Electrical Engineering, Princeton University, December 1972 (revised Jan. 1974)

    Google Scholar 

  18. S. R. Kosaraju: Decidability of Reachability in Vector Addition Systems. Proceedings of the Fourteenth Annual ACM Symposium on Theory of Computing, San Francisco, California, pp. 267-281 (1982)

    Google Scholar 

  19. K. Lautenbach: Exakte Bedingungen der Lebendigkeit für eine Klasse von Petri-Netzen. GMD-Bericht 82(1973)

    Google Scholar 

  20. Kurt Lautenbach: Linear Algebraic Techniques for Place/Transition Nets. This volume

    Google Scholar 

  21. Gerard Memmi: Advanced Algebraic Techniques of Nets. This volume

    Google Scholar 

  22. Horst Müller: private communication

    Google Scholar 

  23. J. Noe: A Petri Net Model for the CDC 6400. Proceedings of the ACM SIGOPS Workshop on System Performance Evaluation, New York, ACM, pp. 362-378 (1971)

    Google Scholar 

  24. Wolfgang Reisig: Petri Nets. EATCS Monographs on Theoretical Computer Science, Springer Verlag (1985)

    Google Scholar 

  25. Wolfgang Reisig: On the Semantics of Petri Nets. in: Neuhold, Chroust (eds.), Formal Models in Programming. North Holland Publ. Company, IFIP, (1985)

    Google Scholar 

  26. Grzegorz Rozenberg: Behaviour of Condition/Event Systems. This volume

    Google Scholar 

  27. G. Rozenberg, R. Verraedt: Subset Languages of Petri Nets. Theoretical Computer Science Vol. 26, pp. 301–326, and Vol. 27, pp. 85-108, (1983)

    Article  MathSciNet  MATH  Google Scholar 

  28. R. Shapiro, H. Saint: A New Approach to Optimization of Sequencing Decisions. Annual Review in Automatic Programming. Vol. 6, Part 5, pp. 257–288 (1970)

    Article  Google Scholar 

  29. Einar Smith, Wolfgang Reisig: The Semantics of a Net in a Net: A Exercise in General Net Theory. To appear in: K. Voss, HJ. Genrich, G. Rozenberg (eds.): Concurrency and Nets, Springer-Verlag (1987)

    Google Scholar 

  30. I. Suzuki, T. Murata: A Method for Hierarchically Representing Large Scale Petri Nets. Proc. of the 1980 Int. Cof. on Circuits and Computers, pp. 620-623 (1980)

    Google Scholar 

  31. P. S. Thiagarajan: Elementary Net Systems. This volume

    Google Scholar 

  32. R. Valette: Analysis of Petri Nets by Stepwise Refinements. Journal of Computer and System Sciences, Vol. 18, pp. 35–46 (1979)

    Article  MathSciNet  MATH  Google Scholar 

  33. Rüdiger Valk: Infinite Behaviour and Fairness of P/T-Systems. This volume

    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

Reisig, W. (1987). Place/Transition Systems. 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_6

Download citation

  • DOI: https://doi.org/10.1007/978-3-540-47919-2_6

  • 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