Skip to main content

On the Compatibility of Model and Model-Class Transformations

  • Conference paper
  • First Online:

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2267))

Abstract

The incremental approach to stepwise development of models requires the ability to transform models (by replacing a submodel with another one) and to change the class of models (by adding features previously ignored). In the context of Petri Nets, this paper provides rigorous foundations for model transformations and net class transformations in the framework of high level replacement systems. We define net class transformations between elementary nets, place/transition nets and a new notion of algebraic high level nets and prove, among other results, that the two kinds of transformations are compatible. This is an important results for stepwise software development with Petri nets. The high abstraction level of the results allows an easy adaption to other specification techniques, such as e. g. Algebraic Specifications.

This work is part of the joint research project “DFG-Forschergruppe PETRINETZ- TECHNOLOGIE” supported by the German Research Council (DFG). This research was also supported in part by the TMR network “General Theory of Graph Transformation Systems” (GETGRATS) and by the Esprit Working Group APPLIGRAPH.

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

Buying options

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

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. J. Adamek, H. Herrlich, and G. Strecker. Abstract and Concrete Categories. Series in Pure and Applied Mathematics. John Wiley and Sons, 1990.

    Google Scholar 

  2. B. Baumgarten. Petrinetze, Grundlagen und Anwendungen. BI, 1990.

    Google Scholar 

  3. E. Best, R. Devillers, and J. Esparza. General refinement and recursion operators for the Petri Box Calculus. In P. Enjalbert et al., editors, STACS’ 93, volume 665 of Lecture Notes in Computer Science, pages 130–140. Springer Verlag, 1993.

    Google Scholar 

  4. E. Best, R. Devillers, and J. Hall. The Box Calculus: a new causal algebra with multi-label communication. In Advances in Petri Nets, volume 609 of Lecture Notes in Computer Science, pages 21–69. Springer Verlag, 1992.

    Google Scholar 

  5. C. Brown and D. Gurr. Refinement and Simulation of Nets-a categorical characterization. In K. Jensen, editor, 13th International Conference on Application and Theory of Petri Nets, volume 616 of Lecture Notes in Computer Science, pages 76–92. Springer Verlag, 1992.

    Google Scholar 

  6. E.K. Blum and F. Parisi-Presicce. Tha Semantics of Shared submodle Specifications. In TAPSOFT 85, volume 185 of Lecture Notes in Computer Science, pages 359–373. Springer Verlag,1985.

    Google Scholar 

  7. J. Desel and A. Merceron. Vicinity Respecting Net Morphisms. In Advances in Petri Nets, volume 483 of Lecture Notes in Computer Science, pages 165–185. Springer Verlag, 1990.

    Google Scholar 

  8. H. Ehrig, M. Gajewsky, and F. Parisi-Presicce. High-Level Replacement Systems with Applications to Algebraic Specifications and Petri Nets, volume 3: Concurrency, Parallelism, and Distribution, chapter 6, pages 341–400. World Scientific, Handbook of Graph Grammars and Computing by Graph Transformations, 1999.

    MathSciNet  Google Scholar 

  9. H. Ehrig, A. Habel, H.-J. Kreowski, and F. Parisi-Presicce. From graph grammars to high level replacement systems. In 4th Intern. Workshop on Graph Grammars, volume 532 of Lecture Notes in Computer Science, pages 269–291. Springer Verlag, 1991.

    Google Scholar 

  10. H. Ehrig and B. Mahr. Fundamentals of Algebraic Specification 1: Equations and Initial Semantics, volume 6 of EATCS Monographs on Theoretical Computer Science. Springer Verlag, Berlin, 1985.

    Google Scholar 

  11. C. Ermel. Anforderungsanalyse eines medizinischen Informationssystems mit Algebraischen High-Level-Netzen. Technical Report 96-15, TU Berlin, 1996.

    Google Scholar 

  12. M. Gajewsky and F. Parisi-Presicce. Formal Transformations of Petri Nets. Technical Report 2000-12, Technical University Berlin, 2000.

    Google Scholar 

  13. K. Jensen. Computer tools for construction, modification and analysis of Petrinets. In W. Brauer, W. Reisig, and G. Rozenberg, editors, Petri Nets: Applications and Relationships to Other Models of Concurrency, pages 4–19. Springer Verlag, 1987.

    Google Scholar 

  14. K. Jensen. Coloured Petri Nets. Basic Concepts, Analysis Methods and Practical Use, volume 1: Basic Concepts. Springer Verlag, EATCS Monographs in Theoretical Computer Science, 1992.

    Google Scholar 

  15. J. Lilius. On the Structure of High-Level Nets. PhD thesis, Helsinki University of Technology, 1995. Digital Systems Laoratory, Research Report 33.

    Google Scholar 

  16. J. Padberg. Abstract Petri Nets: A Uniform Approach and Rule-Based Refinement. PhD thesis, Technical University Berlin, 1996. Shaker Verlag.

    Google Scholar 

  17. F. Parisi-Presicce. A rule-based approach to modular system design. In Proc. of 12th IEEE Internat. Conf. on Software Engineering, Nice (France), pages 202–211, 1990.

    Google Scholar 

  18. J. Padberg, H. Ehrig, and L. Ribeiro. Algebraic high-level net transformation systems. Mathematical Structures in Computer Science, 5:217–256, 1995.

    Article  MATH  MathSciNet  Google Scholar 

  19. J. Padberg, M. Gajewsky, and C. Ermel. Rule-Based Refinement of High-Level Nets Preserving Safety Properties. In E. Astesiano, editor, Fundamental Approaches to Software Engineering, volume 1382 of Lecture Notes in Computer Science, pages 221–238. Springer Verlag, 1998.

    Chapter  Google Scholar 

  20. J. Padberg, M. Gajewsky, and K. Hoffrmann. Incremental Development of Safety Properties in Petri Net Transformations. In G. Engels and G. Rozenberg, editors, Theory and Application of Graph Transformations(TAGT’98) volume 1764 of Lecture Notes in Computer Science, pages 410–425. Springer Verlag, 1999.

    Google Scholar 

  21. J. Padberg, K. Hoffrmann, and M. Gajewsky. Stepwise Introduction and Preservation of Safety Properties in Algebraic High-Level Net Systems. In T. Maibaum, editor, Fundamental Approaches to Software Engineering, volume 1783 of Lecture Notes in Computer Science, pages 249–265. Springer Verlag, 2000.

    Chapter  Google Scholar 

  22. G. Rozenberg and J. Engelfriet. Elementary net systems. In W. Reisig and G. Rozenberg, editors, Lectures on Petri Nets: Basic Models, volume 1491 of Lecture Notes in Computer Science, pages 12–121. Springer Verlag, 1998.

    Google Scholar 

  23. Wolfgang Reisig. Petrinetze. Eine Einführung. Springer Verlag, 1982.

    Google Scholar 

  24. W. Reisig. Petri Nets, volume 4 of EATCS Monographs on Theoretical Computer Science. Springer Verlag, 1985.

    Google Scholar 

  25. W. Reisig. Petri Nets and Algebraic Specifications. Theoretical Computer Science, 80:1–34, 1991.

    Article  MATH  MathSciNet  Google Scholar 

  26. J. Vautherin. Parallel System Specification with Coloured Petri Nets. In G. Rozenberg, editor, Advances in Petri Nets 87, volume 266 of Lecture Notes in Computer Science, pages293–308. Springer Verlag, 1987.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2002 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Gajewsky, M., Parisi-Presicce, F. (2002). On the Compatibility of Model and Model-Class Transformations. In: Cerioli, M., Reggio, G. (eds) Recent Trends in Algebraic Development Techniques. WADT 2001. Lecture Notes in Computer Science, vol 2267. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45645-7_6

Download citation

  • DOI: https://doi.org/10.1007/3-540-45645-7_6

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-43159-6

  • Online ISBN: 978-3-540-45645-2

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics