Skip to main content

Morphisms to Preserve Sructural Properties of Petri Nets

  • Chapter
Computer Science 2
  • 103 Accesses

Abstract

Petri net theory allows modeling and analysis of concurrent systems ([1], [2], [3] or [4] offer a broad introduction). To be able to draw mappings between nets is quite useful, in particular in the case of a top-down/bottom-up methodology. The classical definition of net morphism, see [5], [2], is the least restrictive definition which respects the topology of the source net. However it is too weak to respect other structural features that the source net may exhibit. Vicinity respecting morphisms restrict the classical morphism definition. They were defined in [6] where some of their properties are studied. The present paper is a continuity of [6] and shows that vicinity respecting morphisms preserve almost all relevant, structural properties of the source net.

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 169.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 219.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 219.99
Price excludes VAT (USA)
  • Durable hardcover 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.

References

  1. W. Reisig, ā€œPetri Nets An Introductionā€, EATCS Monograph on Computer Science, Springer Verlag, Berlin (1985).

    Google ScholarĀ 

  2. H.J. Genrich, K. Lautenbach and P.S. Thiagarajan, Elements of general net theory, in: ā€œNet Theory and Applicationsā€, W. Brauer, ed., Lecture Notes in Computer Science, Vol. 84, pp.21ā€“163, Springer Verlag, Berlin (1980).

    ChapterĀ  Google ScholarĀ 

  3. G. Rozenberg and P.S. Thiagarajan, Petri nets: basic notions, structure, behaviour, in: ā€œCurrent Trends in Concurrency Overviews and Tutorialsā€, Lecture Notes in Computer Science, J. W. de Baekker, W-P. Roever and G. Rozenberg, ed., Vol. 224, pp. 585ā€“668, Springer Verlag, Berlin (1986).

    ChapterĀ  Google ScholarĀ 

  4. W. Brauer, W. Reisig and G. Rozenberg G., ed., ā€œPetri Nets. Central Models and their Properties. Advances in Petri Nets 1986ā€, Part I, Proceedings of an Advanced Course, Bad Honnef, September 1986, Lecture Notes in Computer Science, Vol. 254, Springer Verlag, Berlin (1987).

    MATHĀ  Google ScholarĀ 

  5. C.A. Petri, Concepts of net theory, Mathematical Foundations of Computer Science, Proceedings of Symposium and Summer School, High Tatras, Sep. 3ā€“8, 1973, Mathematical Institute of the Slovak Academy of Sciences, pp. 137-146 (1973).

    Google ScholarĀ 

  6. J. Desel and A. Merceron, Vicinity respecting morphisms. in: ā€œAdvances in Petri Nets 1990ā€, G. Rozenberg, ed., Lecture Notes in Computer Science Vol. 483, pp. 165ā€“185, Springer Verlag, Berlin (1991).

    ChapterĀ  Google ScholarĀ 

  7. W. Reisig, Place/Transition nets, in: [4], pp.117ā€“141 (1987).

    MathSciNetĀ  Google ScholarĀ 

  8. J. Desel and J. Esparza, ā€œStructure and Analysis of Choice Netsā€, Monograph in preparation.

    Google ScholarĀ 

  9. E. Best and C. FernĆ”ndez C., Notation and terminology on Petri nets theory, Arbeitspapier der GMD Nr. 195, Gesellschaft fĆ¼r Mathematik und Datenverarbeitung, St. Augustin, FRG, (1987).

    Google ScholarĀ 

  10. E. Best, Structure theory of Petri nets: the Free Choice Hiatus. in: [4], pp. 168ā€“206 (1987).

    MathSciNetĀ  Google ScholarĀ 

  11. W. Brauer, R. Gold and W. Vogler, A survey of behaviour and equivalence preserving refinements of Petri nets, in: ā€œAdvances in Petri Nets 1990ā€, Rozenberg G., ed., Lecture Notes in Computer Science Vol. 483, pp. 1ā€“46, Springer Verlag, Berlin (1991).

    ChapterĀ  Google ScholarĀ 

  12. G. Winskel, Petri nets, algebras, morphisms and compositionality, Information and Computation 72, pp.197ā€“238 (1987).

    ArticleĀ  MathSciNetĀ  MATHĀ  Google ScholarĀ 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

Ā© 1994 Springer Science+Business Media New York

About this chapter

Cite this chapter

Merceron, A. (1994). Morphisms to Preserve Sructural Properties of Petri Nets. In: Baeza-Yates, R. (eds) Computer Science 2. Springer, Boston, MA. https://doi.org/10.1007/978-1-4757-9805-0_36

Download citation

  • DOI: https://doi.org/10.1007/978-1-4757-9805-0_36

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4757-9807-4

  • Online ISBN: 978-1-4757-9805-0

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics