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Conceptual Modeling of Concurrent Systems through Stepwise Abstraction and Refinement Using Petri Net Morphisms

  • Boleslaw Mikolajczak
  • Zuyan Wang
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2813)

Abstract

Development of complex concurrent systems is very often performed in a top-down or bottom-up approach depending on design circumstances. Such design reflects vertical conceptual modeling of concurrent systems with certain number of abstraction/ refinement layers. Petri net morphisms have been proven to be useful in this process as long as certain desired structural and behavioral properties of such systems are preserved. We use example of a renting agency to illustrate applicability of morphisms in systematic development of distributed systems. Preservation of structural and behavioral properties of Petri net morphisms is also discussed.

Keywords

Behavioral Property Concurrent System Liveness Property Sign Contract Customer Perspective 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    Bednarczyk, M.A., Borzyszkowski, A.M.: General Morphisms of Petri nets. In: Wiedermann, J., Van Emde Boas, P., Nielsen, M. (eds.) ICALP 1999. LNCS, vol. 1644, p. 190. Springer, Heidelberg (1999)CrossRefGoogle Scholar
  2. 2.
    Desel, J., Merceron, A.: Vicinity Rrespecting Net Morphisms. In: Rozenberg, G. (ed.) APN 1990. LNCS, vol. 483, pp. 165–185. Springer, Heidelberg (1991)Google Scholar
  3. 3.
    Desel, J., Merceron, A.: Vicinity Rrespecting Homomorphisms for Abstracting System Requirements, Bericht 337., Karlsruhe (1996)Google Scholar
  4. 4.
    Devillers, R., Klaudel, H., Riemann, R.C.: General Refinement for High Level Petri Nets. In: Ramesh, S., Sivakumar, G. (eds.) FST TCS 1997. LNCS, vol. 1346, pp. 297–311. Springer, Heidelberg (1997)CrossRefGoogle Scholar
  5. 5.
    Fehling, R.: A Concept of Hierarchical Petri nets with Building Blocks. In: The 12th International Conference on Application and Theory of Petri Nets, Gjern, Denmark, June 1991, pp. 370–389 (1991)Google Scholar
  6. 6.
    Girault, C., Valk, R.: Petri Nets for Systems Engineering: a Guide to Modeling, Verification, and Applications. Springer, Heidelberg (2003)Google Scholar
  7. 7.
    Lakos, C.: Composing Abstraction of Colored Petri nets. In: Nielsen, M., Simpson, D. (eds.) ICATPN 2000. LNCS, vol. 1825, pp. 323–345. Springer, Heidelberg (2000)CrossRefGoogle Scholar
  8. 8.
    Mikolajczak, B.: A Parallel Algorithm for Computing all Homomorphisms of Deterministic Finite Automata. In: Parallel Processing of Discrete Optimization Problems. DIMACS Series in Discrete Mathematics and Theoretical Computer Science, vol. 22, American Mathematical Society, Providence (1994)Google Scholar
  9. 9.
  10. 10.
    Petri, C.A.: Introduction to General Net Theory Net and Applications. In: Brauer, W. (ed.). LNCS, pp. 1–19. Springer, Heidelberg (1980)Google Scholar
  11. 11.
    Padberg, J., Gajewsky, M., Ermel, C.: Rule-based Refinement of High-level Nets Preserving Safety Properties. In: Astesiano, E. (ed.) ETAPS 1998 and FASE 1998. LNCS, vol. 1382, pp. 221–238. Springer, Heidelberg (1998)CrossRefGoogle Scholar
  12. 12.
  13. 13.
    Reisig, W.: Petri Nets, An Iintroduction. Springer, Heidelberg (1985)Google Scholar
  14. 14.
    Reisig, W.: Elements of Distributed Algorithms: Modeling and Analysis with Petri Nets. Springer, Heidelberg (1998)zbMATHGoogle Scholar
  15. 15.
    Wang, Z.: Morphisms of Petri Nets and their Role in Formal Modeling of Concurrent Systems, Master Project, UMASS Dartmouth (May 2002)Google Scholar
  16. 16.
    Winskel, G.: Petri Nets, Algebras, Morphisms and Compositionality. Information and Computation 72, 197–238 (1987)zbMATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Boleslaw Mikolajczak
    • 1
    • 2
  • Zuyan Wang
    • 1
  1. 1.University of Massachusetts DartmouthDartmouthUSA
  2. 2.Polish-Japanese School of Information TechnologyWarsawPoland

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