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Concurrency Based Transition Refinement for the Verification of Distributed Algorithms

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Petri Net Technology for Communication-Based Systems

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2472))

Abstract

We suggest a new notion of behaviour preserving transition refinement based on partial order semantics. This notion is called transition refinement. We introduced transition refinement for elementary (low-level) Petri Nets earlier [Peu01a]. For modelling and verifying complex distributed algorithms, high-level (Algebraic) Petri nets are usually used.

In this paper, we define transition refinement for Algebraic Petri Nets. This notion is more powerful than transition refinement for elementary Petri nets because it corresponds to the simultaneous refinement of several transitions in an elementary Petri net.

Transition refinement is particularly suitable for refinement steps that increase the degree of distribution of an algorithm, e.g. when synchronous communication is replaced by asynchronous message passing. We study how to prove that a replacement of a transition is a transition refinement.

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References

  1. Alpern, B., Schneider, F.B.: Defining liveness. Information Processing Letters 21, 181–185 (1985)

    Article  MATH  MathSciNet  Google Scholar 

  2. Gallager, R.G., Humblet, P.A., Spira, P.M.: A distributed algorithm for minimum-weight spanning trees. ACM Transactions on Programming Languages and Systems 5(1), 66–77 (1983)

    Article  MATH  Google Scholar 

  3. Jensen, K.: Coloured Petri Nets. EATCS Monographs on Theoretical Computer Science, vol. 1. Springer, Heidelberg (1992)

    MATH  Google Scholar 

  4. Kindler, E., Peuker, S.: Integrating distributed algorithms into distributed systems. Fundamenta Informaticae 37, 291–309 (1999)

    MATH  MathSciNet  Google Scholar 

  5. Kindler, E., Reisig, W.: Algebraic system nets for modelling distributed algorithms. Petri Net Newsletter 51, 16–31 (1996)

    Google Scholar 

  6. Kindler, E., Völzer, H.: Algebraic nets with flexible arcs. Theoretical Computer Science 262(1-2), 285–310 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  7. Peuker, S.: Property preserving transition refinement with concurrent runs: An example. In: International Conference on Application of Concurrency to System Design, pp. 77–86. IEEE Computer Society, Los Alamitos (2001)

    Chapter  Google Scholar 

  8. Peuker, S.: Halbordnungsbasierte Verfeinerung zur Verifikation verteilter Algorithmen. PhD thesis, Humboldt-Universität zu Berlin (2001), available via, http://dochost.rz.hu-berlin.de/abstract.php3/dissertationen/peuker-sibylle-2001-07-03

  9. Peuker, S.: Deriving a distributed minimum weight spanning tree algorithm with transition refinement for Algebraic Petri nets. In: Proceedings of Petri Nets 2002. LNCS. Springer, Heidelberg (2002) (to appear)

    Google Scholar 

  10. Padberg, J., Hoffman, K., Gajewski, M.: Introduction and preservation of safety properties in algebraic high-level net systems. In: Maibaum, T. (ed.) FASE 2000. LNCS, vol. 1783, pp. 249–265. Springer, Heidelberg (2000)

    Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

  12. Reisig, W.: Elements of Distributed Algorithms: Modeling and Analysis with Petri Nets. Springer, Heidelberg (1998)

    MATH  Google Scholar 

  13. Valette, R.: Analysis of Petri Nets by stepwise refinement. Journal of Computer and System Sciences 18, 35–46 (1979)

    Article  MATH  MathSciNet  Google Scholar 

  14. van Glabbeek, R.J., Goltz, U.: Refinement 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 

  15. Vogler, W.: Behaviour preserving refinements of Petri nets. In: Tinhofer, G., Schmidt, G. (eds.) WG 1986. LNCS, vol. 246, pp. 82–93. Springer, Heidelberg (1987)

    Google Scholar 

  16. Wirth, N.: Program development by stepwise refinement. Communications of the ACM 14(4), 221–227 (1971)

    Article  MATH  Google Scholar 

  17. Weber, M., Walter, R., Völzer, H., Vesper, T., Reisig, W., Peuker, S., Kindler, E., Freiheit, J., Desel, J.: DAWN: Petrinetzmodelle zur Verifikation Verteilter Algorithmen. Informatik-Bericht 88, Humboldt- Universität zu Berlin (December 1997)

    Google Scholar 

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Author information

Authors and Affiliations

  1. Software Verification Research Centre, The University of Queensland, Brisbane, Australia

    Sibylle Peuker

Authors
  1. Sibylle Peuker
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Editor information

Editors and Affiliations

  1. Technische Universität Berlin, Germany

    Hartmut Ehrig

  2. Institut für Informatik, Humboldt-Universität zu Berlin, Unter den Linden 6, 10099, Berlin, Germany

    Wolfgang Reisig

  3. Leiden Center of Advanced Computer Science (LIACS), Leiden University, Niels Bohrweg 1, 2333, Leiden, CA, The Netherlands

    Grzegorz Rozenberg

  4. Computergestützte InformationsSysteme (CIS), Technische Universität Berlin, Germany

    Herbert Weber

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© 2003 Springer-Verlag Berlin Heidelberg

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Peuker, S. (2003). Concurrency Based Transition Refinement for the Verification of Distributed Algorithms. In: Ehrig, H., Reisig, W., Rozenberg, G., Weber, H. (eds) Petri Net Technology for Communication-Based Systems. Lecture Notes in Computer Science, vol 2472. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-40022-6_21

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  • DOI: https://doi.org/10.1007/978-3-540-40022-6_21

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-20538-8

  • Online ISBN: 978-3-540-40022-6

  • eBook Packages: Springer Book Archive

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