[go: up one dir, main page]
More Web Proxy on the site http://driver.im/
Skip to main content

Qualitative Probabilistic Modelling in Event-B

  • Conference paper
Integrated Formal Methods (IFM 2007)

Part of the book series: Lecture Notes in Computer Science ((LNPSE,volume 4591))

Included in the following conference series:

Abstract

Event-B is a notation and method for discrete systems modelling by refinement. We introduce a small but very useful construction: qualitative probabilistic choice. It extends the expressiveness of Event-B allowing us to prove properties of systems that could not be formalised in Event-B before. We demonstrate this by means of a small example, part of a larger Event-B development that could not be fully proved before. An important feature of the introduced construction is that it does not complicate the existing Event-B notation or method, and can be explained without referring to the underlying more complicated probabilistic theory. The necessary theory [18] itself is briefly outlined in this article to justify the soundness of the proof obligations given. We also give a short account of alternative constructions that we explored, and rejected.

This research was carried out as part of the EU research project IST 511599 RODIN (Rigorous Open Development Environment for Complex Systems) http://rodin.cs.ncl.ac.uk.

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

Access this chapter

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Similar content being viewed by others

References

  1. Abrial, J.-R. (ed.): The B-Book: Assigning Programs to Meanings. Cambridge University Press, Cambridge (1996)

    Google Scholar 

  2. Abrial, J.-R.: Event driven system construction (1999)

    Google Scholar 

  3. Abrial, J.-R.: Event based sequential program development: Application to constructing a pointer program. In: Araki, K., Gnesi, S., Mandrioli, D. (eds.) FME 2003. LNCS, vol. 2805, pp. 51–74. Springer, Heidelberg (2003)

    Google Scholar 

  4. Abrial, J.-R., Butler, M., Hallerstede, S., Voisin, L.: An open extensible tool environment for Event-B. In: Liu, Z., He, J. (eds.) ICFEM 2006. LNCS, vol. 4260, pp. 588–605. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  5. Abrial, J.-R., Cansell, D., Méry, D.: A mechanically proved and incremental development of IEEE 1394 tree identify protocol. Formal Aspects of Computing 14(3), 215–227 (2003)

    Article  Google Scholar 

  6. Abrial, J.-R., Cansell, D., Méry, D.: Refinement and Reachability in Event B. In: Treharne, H., King, S., Henson, M.C., Schneider, S. (eds.) ZB 2005. LNCS, vol. 3455, pp. 222–241. Springer, Heidelberg (2005)

    Google Scholar 

  7. Abrial, J.-R., Hallerstede, S.: Refinement, Decomposition and Instantiation of Discrete Models: Application to Event-B. Fundamentae Informatica, vol. 77(1-2) (2007)

    Google Scholar 

  8. Back, R.-J.: Refinement Calculus II: Parallel and Reactive Programs. In: de Bakker, J.W., de Roever, W.-P., Rozenberg, G. (eds.) Stepwise Refinement of Distributed Systems. LNCS, vol. 430, pp. 67–93. Springer, Heidelberg (1990)

    Google Scholar 

  9. Back, R.-J., von Wright, J.: Refinement Calculus: A Systematic Introduction. In: Graduate Texts in Computer Science, Springer, Heidelberg (1998)

    Google Scholar 

  10. Dijkstra, E.W.: A Discipline of Programming. Prentice-Hall, Englewood Cliffs, NJ (1976)

    MATH  Google Scholar 

  11. Hallerstede, S.: Parallel hardware design in B. In: Bert, D., Bowen, J.P., King, S., Waldén, M.A. (eds.) ZB 2003. LNCS, vol. 2651, pp. 101–102. Springer, Heidelberg (2003)

    Chapter  Google Scholar 

  12. Hallerstede, S.: Justifications for the Event-B Modelling Notation. In: Julliand, J., Kouchnarenko, O. (eds.) B 2007. LNCS, vol. 4355, pp. 49–63. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  13. Hallerstede, S., Butler, M.J.: Performance analysis of probabilistic action systems. Formal Aspects of Computing 16(4), 313–331 (2004)

    Article  MATH  Google Scholar 

  14. Hoang, T.S.: The Development of a Probabilistic B-Method and a Supporting Toolkit. PhD thesis, School of Computer Science and Engineering — The University of New South Wales (July 2005)

    Google Scholar 

  15. Hoang, T.S., Jin, Z., Robinson, K., McIver, A., Morgan, C.: Probabilistic Invariants for Probabilistic Machines. In: Bert, D., Bowen, J.P., King, S., Waldén, M. (eds.) ZB 2003. LNCS, vol. 2651, pp. 240–259. Springer, Heidelberg (2003)

    Chapter  Google Scholar 

  16. IEEE. IEEE Standard for a High Performance Serial Bus. Std 1394-1995 (1995)

    Google Scholar 

  17. IEEE. IEEE Standard for a High Performance Serial Bus (supplement). Std 1394a-2000 (2000)

    Google Scholar 

  18. McIver, A., Morgan, C., Hoang, T.S.: Probabilistic termination in B. In: Bert, D., Bowen, J.P., King, S., Waldén, M. (eds.) ZB 2003. LNCS, vol. 2651, pp. 216–239. Springer, Heidelberg (2003)

    Chapter  Google Scholar 

  19. Morgan, C.: The Generalised Substitution Language Extended to Probabilistic Programs (Also available at [22]). In: Bert, D. (ed.) B 1998. LNCS, vol. 1393, Springer, Heidelberg (1998)

    Chapter  Google Scholar 

  20. Morgan, C., Hoang, T.S., Abrial, J.-R.: The challenge of probabilistic event B - extended abstract. In: Treharne, H., King, S., Henson, M.C., Schneider, S.A. (eds.) ZB 2005. LNCS, vol. 3455, pp. 162–171. Springer, Heidelberg (2005)

    Google Scholar 

  21. Morgan, C., McIver, A.: Abstraction, Refinement and Proof for Probabilistic Systems. Monographs in Computer Science. Springer, Heidelberg (2005)

    MATH  Google Scholar 

  22. PSG. Probabilistic Systems Group: Collected Reports. at, http://web.comlab.ox.ac.uk/oucl/research/areas/probs/bibliography.html

  23. Puterman, M.L.: Markov Decision Processes: Discrete Stochastic Dynamic Programming. Wiley-Interscience, New York (1994)

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Jim Davies Jeremy Gibbons

Rights and permissions

Reprints and permissions

Copyright information

© 2007 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Hallerstede, S., Hoang, T.S. (2007). Qualitative Probabilistic Modelling in Event-B. In: Davies, J., Gibbons, J. (eds) Integrated Formal Methods. IFM 2007. Lecture Notes in Computer Science, vol 4591. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-73210-5_16

Download citation

  • DOI: https://doi.org/10.1007/978-3-540-73210-5_16

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-73209-9

  • Online ISBN: 978-3-540-73210-5

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics