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Vicinity Respecting Homomorphisms for Abstracting System Requirements

  • Jörg Desel
  • Agathe Merceron
Chapter
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6550)

Abstract

This paper is concerned with structuring system requirements on an abstract conceptual level. Channel/Agency Petri nets are taken as a formal model. They allow to represent functional aspects as well as data aspects of the requirements in a graphical way. Vicinity respecting homomorphisms are presented as a means to refine and abstract these nets. They preserve paths, i.e., dependencies between computational elements and they preserve important structural properties of nets, such as S- and T-components, siphons and traps and the free choice property. These properties have important interpretations for marked Petri nets and can therefore be used for the analysis of system models at more concrete levels.

Keywords

Channel/Agency Nets Homomorphisms Abstraction 

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References

  1. 1.
    Bruno, G.: Model-Based Software Engineering. Chapman and Hall, Boca Raton (1995)Google Scholar
  2. 2.
    Deiters, W., Gruhn, V.: The FUNSOFT net approach to software process management. International Journal on Software Engineering and Knowledge Engineering 4(2) (1994)Google Scholar
  3. 3.
    Desel, J., Esparza, J.: Free Choice Petri Nets. Cambridge Tracts in Theoretical Computer Science, vol. 40. Cambridge University Press, Cambridge (1995)CrossRefzbMATHGoogle Scholar
  4. 4.
    Desel, J., Merceron, A.: Vicinity respecting net morphisms. In: Rozenberg, G. (ed.) APN 1990. LNCS, vol. 483, pp. 165–185. Springer, Heidelberg (1991)CrossRefGoogle Scholar
  5. 5.
    Desel, J.: On abstractions of nets. In: Rozenberg, G. (ed.) APN 1991. LNCS, vol. 524, pp. 78–92. Springer, Heidelberg (1991)CrossRefGoogle Scholar
  6. 6.
    Desel, J., Merceron, A.: Vicinity respecting homomorphisms for abstracting system requirements. Bericht No. 337 of Institut AIFB, Universität Karlsruhe (1996)Google Scholar
  7. 7.
    Desel, J., Petrucci, L.: Aggregating views for Petri net model construction. In: Petri Nets and Distributed Systems (PNDS 2008), Workshop at the 29th International Conference on Application and Theory of Petri Nets and Other Models of Councurrency, Xi’an, China (2008)Google Scholar
  8. 8.
    Ehrig, H., Hoffmann, K., Padberg, J.: Transformations of Petri nets. Electr. Notes Theor. Comput. Sci. 148(1), 151–172 (2006)CrossRefGoogle Scholar
  9. 9.
    Fernández, C.: Net Topology I. Interner Bericht der GMD ISF-75-9 GMD St. Augustin, Germany (1975); Net Topology II. Interner Bericht der GMD ISF-76-2, GMD St. Augustin, Germany (1976)Google Scholar
  10. 10.
    Genrich, H.J., Lautenbach, K., Thiagarajan, P.S.: Elements of general net theory. In: Brauer, W. (ed.) Net Theory and Applications. LNCS, vol. 84, pp. 21–163. Springer, Heidelberg (1980)CrossRefGoogle Scholar
  11. 11.
    Genrich, H.J., Stankiewicz-Wiechno, E.: A dictionary of some basic notions of net theory. In: Brauer, W. (ed.) Net Theory and Applications. LNCS, vol. 84, pp. 519–535. Springer, Heidelberg (1980)CrossRefGoogle Scholar
  12. 12.
    van Glabbeek, R., Goltz, U.: Refinements of actions in causality based models. In: de Bakker, J.W., de Roever, W.-P., Rozenberg, G. (eds.) REX 1989. LNCS, vol. 430, pp. 267–300. Springer, Heidelberg (1990)Google Scholar
  13. 13.
    van Hee, K.M.: Information Systems Engineering - a Formal Approach. Cambridge University Press, Cambridge (1994)zbMATHGoogle Scholar
  14. 14.
    Lakos, C.: Composing abstractions of coloured Petri nets. In: Nielsen, M., Simpson, D. (eds.) ICATPN 2000. LNCS, vol. 1825, pp. 323–345. Springer, Heidelberg (2000)CrossRefGoogle Scholar
  15. 15.
    Luckham, D.C., Kenney, J.J., et al.: Specification and analysis of system architecture using Rapide. IEEE Transactions on Software Engineering, Special Issue on Software Architecture 21(4) (April 1995)Google Scholar
  16. 16.
    Merceron, A.: Morphisms to preserve structural properties of Petri nets. Computer Science – Research and Applications, pp. 439–454. Plenum Press, New York (1994)Google Scholar
  17. 17.
    Meseguer, J., Montanari, U.: Petri nets are monoids. In: Information and Computation, vol. 88, pp. 105–155 (1990)Google Scholar
  18. 18.
    Mikolajczak, B., Wang, Z.: Conceptual Modeling of Concurrent Systems through Stepwise Abstraction and Refinement Using Petri Net Morphisms. In: Song, I.-Y., Liddle, S.W., Ling, T.-W., Scheuermann, P. (eds.) ER 2003. LNCS, vol. 2813, pp. 433–445. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  19. 19.
    Mikolajczak, B.: Conceptual modeling of concurrent information systems with general morphisms of Petri nets. In: Intelligent Information Systems, Advances in Soft Computing, pp. 535–539. Springer, Heidelberg (2003)Google Scholar
  20. 20.
    Ore, O.: Theory of Graphs, vol. XXXVIII. American Mathematical Society, Colloquium Publications (1962)Google Scholar
  21. 21.
    Petri, C.A.: Concepts of net theory. In: Proceedings of Symposium and Summer School on Mathematical Foundations of Computer Science, High Tatras, September 3-8, 1973Google Scholar
  22. 22.
    Petri, C.A.: Introduction to General Net Theory. In: Brauer, W. (ed.) Net Theory and Applications. LNCS, vol. 84, pp. 1–20. Springer, Heidelberg (1980)CrossRefGoogle Scholar
  23. 23.
    Reisig, W.: Petri nets in software engineering. In: Brauer, W., Reisig, W., Rozenberg, G. (eds.) APN 1986. LNCS, vol. 255, pp. 63–96. Springer, Heidelberg (1987)Google Scholar
  24. 24.
    Reisig, W.: A Primer in Petri Net Design. Springer, Heidelberg (1992)CrossRefzbMATHGoogle Scholar
  25. 25.
    Reisig, W.: Simple composition of nets. In: Franceschinis, G., Wolf, K. (eds.) PETRI NETS 2009. LNCS, vol. 5606, pp. 23–42. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  26. 26.
    Winskel, G.: Petri nets, algebras, morphisms and compositionality. In: Information and Computation, vol. 72, pp. 197–238 (1987)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Jörg Desel
    • 1
  • Agathe Merceron
    • 2
  1. 1.FernUniversität in HagenGermany
  2. 2.Beuth Hochschule für Technik BerlinGermany

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