Skip to main content

Reduction and design of well-behaved concurrent systems

  • Selected Presentations
  • Conference paper
  • First Online:

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 458))

Abstract

It is shown that each live and safe free-choice system without frozen token can be reduced either to a live and safe marked T-graph (marked graph) or to a live and safe marked P-graph (state machine). The four proposed reduction rules are purely local and preserve the behavioural properties in both directions. Hence the method can be used for both, effective analysis and correct design.

The class of systems which can be reduced to marked P-graphs (T-graphs, respectively) can be characterized without using the reduction rules by their P- and T-components. The two classes are not disjoint; systems in the intersection of the classes can be reduced to a unique systems with only two elements.

Work supported partly by the Esprit Basic Research Action No. 3148: DEMON.

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

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Andre, C.: Structural Transformations Giving B-equivalent PT-Nets. In: Pagnoni, A, Rozenberg, G. (ed.): Informatik-Fachberichte No. 66: Application and Theory of Petri Nets. pp14–28, Springer-Verlag (1983).

    Google Scholar 

  2. Best, E., Fernandez, C.: Notations and Terminology on Petri Net Theory. Second edition. Arbeitspapiere der GMD No. 195 (1987).

    Google Scholar 

  3. Best, E., Desel, J.: Partial Order Behaviour and Structure of Petri Nets. Arbeitspapiere der GMD No. 373 (1989). Accepted for publication in Formal Aspects of Computing.

    Google Scholar 

  4. Berthelot, G.: Transformations and Decompositions of Nets. LNCS 254: Petri Nets, Central Models and Their Properties, pp. 359–376 (1987).

    Google Scholar 

  5. Datta, A., Ghosh, S.: Synthesis of a Class of Deadlock-Free Petri Nets. Journal of the ACM, Vol. 31, No. 3, pp.486–506 (1984).

    Google Scholar 

  6. Desel, J.: Live and Safe Free-choice Systems without Frozen Token are Well-behaved Bipolar Synchronization Schemes. Forthcoming paper (1990).

    Google Scholar 

  7. Commoner, F., Holt, A.W., Even, S., Pnueli, A.: Marked Directed Graphs. Journal of Computer and System Science 5, pp. 511–523 (1971).

    Google Scholar 

  8. Esparza, J; Silva, M.: Top-Down Synthesis of Live and Bounded Free Choice Nets. 11th International Conference on Application and Theory of Petri Nets, Paris (1990).

    Google Scholar 

  9. Genrich, H.J., Thiagarajan, P.S.: A Theory of Bipolar Synchronization Schemes. TCS Vol. 30, pp.241–318 (1984).

    Google Scholar 

  10. Hack, M.: Analysis of Production Schemata by Petri Nets. TR-94, MIT-MAC (1972).

    Google Scholar 

  11. Suzuki, I.; Murata, T.: A Method for Stepwise Refinement and Abstraction of Petri Nets. Journal of Computer and System Sciences, Vol. 27, pp. 51–76 (1983).

    Google Scholar 

  12. Thiagarajan, P.S.: Elementary Net Systems. In: Brauer, W., Reisig, W., Rozenberg, G. (ed): LNCS 254: Petri Nets, Central Models and Their Properties, pp. 26–59 (1987).

    Google Scholar 

  13. Valette, R.: Analysis of Petri Nets by Stepwise Refinements. Journal of Computer and System Sciences, Vol. 18, pp. 35–46 (1979).

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

J. C. M. Baeten J. W. Klop

Rights and permissions

Reprints and permissions

Copyright information

© 1990 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Desel, J. (1990). Reduction and design of well-behaved concurrent systems. In: Baeten, J.C.M., Klop, J.W. (eds) CONCUR '90 Theories of Concurrency: Unification and Extension. CONCUR 1990. Lecture Notes in Computer Science, vol 458. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0039059

Download citation

  • DOI: https://doi.org/10.1007/BFb0039059

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-53048-0

  • Online ISBN: 978-3-540-46395-5

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics