Advertisement

On abstractions of nets

  • Jörg Desel
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 524)

Abstract

The central idea of General Net Theory is to emphasize morphisms between nets instead of studying single nets. The paper contributes to this theory and proposes a formalism for net transformations which is based on a subclass of surjective net morphisms, called abstractions.

Up to isomorphism, each abstraction of a net can be characterized by an equivalence relation on its elements. Feasible equivalence relations, which define abstractions, are characterized. They define quotient nets, analogously to quotients of sets. Some closure properties of feasible relations are studied.

Finally, it is shown that each abstraction can be decomposed into a folding (foldings are a known subclass of abstractions) and a simple contraction (which is a local transformation defined in the paper).

Keywords

Net morphisms transformations coarsening and composition of nets 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [BF 87]
    Best, E.; Fernandez C., C.: Notations and Terminology on Petri Net Theory. Arbeitspapiere der GMD Nr.195 (1987)Google Scholar
  2. [DM 91]
    Desel, J; Merceron, A.: Vicinity Respecting Net Morphisms. Advances in Petri Nets 1990, LNCS Vol.483, 165–185 (1991)Google Scholar
  3. [GLT 80]
    Genrich, H.J.; Lautenbach, K; Thiagarajan, P.S.: Elements of General Net Theory. Net Theory and Applications, LNCS Vol.84, 21–163 (1980)Google Scholar
  4. [GG 90]
    Goltz, U., van Glabbeek, R.: Refinement of Actions in Causality Based Models. REX Workshop on Stepwise Refinement of Distributed Systems, LNCS Vol.430, 267–300 (1990)Google Scholar
  5. [Pe 73]
    Petri, C.A.: Concepts of Net Theory. MFCS, Proceedings of Symposium and Summer School, High Tatras. Math. Inst. of the Slovak Acad. of Science, 137–146 (1973)Google Scholar
  6. [SR 87]
    Smith, E.; Reisig, W.: The Semantics of a Net is a Net — An Exercise in General Net Theory. In: Concurrency and Nets / Voss, K.; Genrich, H.J., Rozenberg, G. (eds.), Advances in Petri Nets. Springer-Verlag, 461–480 (1987)Google Scholar
  7. [Sm 89]
    Smith, E.: Zur Bedeutung der Concurrency-Theorie für den Aufbau hochverteilter Systeme. GMD-Bericht Nr.180, R. Oldenbourg Verlag (1989)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1991

Authors and Affiliations

  • Jörg Desel
    • 1
  1. 1.Institut für InformatikTechnische Universität MünchenMünchen 2

Personalised recommendations