International Conference on Fundamentals of Software Engineering

Fundamentals of Software Engineering pp 292-307 | Cite as

An Interval-Based Approach to Modelling Time in Event-B

  • Gintautas Sulskus
  • Michael Poppleton
  • Abdolbaghi Rezazadeh
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9392)

Abstract

Our work was inspired by our modelling and verification of a cardiac pacemaker, which includes concurrent aspects and a set of interdependent and cyclic timing constraints. To model timing constraints in such systems, we present an approach based on the concept of timing interval. We provide a template-based timing constraint modelling scheme that could potentially be applicable to a wide range of modelling scenarios. We give a notation and Event-B semantics for the interval. The Event-B coding of the interval is decoupled from the application logic of the model, therefore a generative design of the approach is possible. We demonstrate our interval approach and its refinement through a small example. The example is verified, model-checked and animated (manually validated) with the ProB animator.

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References

  1. 1.
    Pacemaker Challenge (2007). http://sqrl.mcmaster.ca/pacemaker.htm
  2. 2.
    Interactive Prover Reference Manual 3.7 (2013). http://www.atelierb.eu/ressources/DOC/english/prover-reference-manual.pdf
  3. 3.
  4. 4.
    Abrial, J.-R.: The B-Book: Assigning Programs to Meanings. Cambridge University Press, New York (1996)Google Scholar
  5. 5.
    Abrial, J.-R.: Modeling in Event-B: System and Software Engineering, 1st edn. Cambridge University Press, New York (2010)CrossRefMATHGoogle Scholar
  6. 6.
    Abrial, J.-R., Butler, M., Hallerstede, S., Hoang, T.S., Mehta, F., Voisin, L.: Rodin: an Open Toolset for Modelling and Reasoning in Event-B. International Journal on Software Tools for Technology Transfer 12(6), 447–466 (2010)CrossRefGoogle Scholar
  7. 7.
    Back, R.-J., Kurki-Suonio, R.: Decentralization of Process Nets with Centralized Control. In: Symposium on Principles of Distributed Computing, pp. 131–142. ACM, Montreal (1983)Google Scholar
  8. 8.
    Barold, S.S., Stroobandt, R., Sinnaeve, A.F.: Cardiac Pacemakers and Resynchronization Step-by-Step: an Illustrated Guide. Wiley-Blackwell (2010)Google Scholar
  9. 9.
  10. 10.
    Bryans, J., Fitzgerald, J., Romanovsky, A., Roth, A.: Patterns for Modelling Time and Consistency in Business Information Systems, pp. 105–114. IEEE Computer Society, Oxford (2010)Google Scholar
  11. 11.
    Butler, M., Falampin, J.: An Approach to Modelling and Refining Timing Properties in B. In: Proceedings of Workshop on Refinement of Critical Systems (RCS) (January 2002)Google Scholar
  12. 12.
    Cansell, D., Méry, D., Rehm, J.: Time Constraint Patterns for Event B Development. In: Julliand, J., Kouchnarenko, O. (eds.) B 2007. LNCS, vol. 4355, pp. 140–154. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  13. 13.
    Déharbe, D., Fontaine, P., Guyot, Y., Voisin, L.: SMT Solvers for Rodin. In: Derrick, J., Fitzgerald, J., Gnesi, S., Khurshid, S., Leuschel, M., Reeves, S., Riccobene, E. (eds.) ABZ 2012. LNCS, vol. 7316, pp. 194–207. Springer, Heidelberg (2012)CrossRefGoogle Scholar
  14. 14.
    Gomes, A.O., Oliveira, M.: Formal Development of a Cardiac Pacemaker: From Specification to Code. In: Davies, J. (ed.) SBMF 2010. LNCS, vol. 6527, pp. 210–225. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  15. 15.
    Jee, E., Wang, S., Kim, J.K., Lee, J., Sokolsky, O., Lee, I.: A Safety-Assured Development Approach for Real-Time Software. In: The Proceedings of the 16th IEEE International Conference on Embedded and Real-Time Computing Systems and Applications, pp. 133–142 (August 2010)Google Scholar
  16. 16.
    Jiang, Z., Pajic, M., Moarref, S., Alur, R., Mangharam, R.: Modeling and Verification of a Dual Chamber Implantable Pacemaker. In: Flanagan, C., König, B. (eds.) TACAS 2012. LNCS, vol. 7214, pp. 188–203. Springer, Heidelberg (2012)CrossRefGoogle Scholar
  17. 17.
    Leuschel, M., Butler, M.: ProB: A Model Checker for B. In: Araki, K., Gnesi, S., Mandrioli, D. (eds.) FME 2003. LNCS, vol. 2805, pp. 855–874. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  18. 18.
    Macedo, H., Larsen, P., Fitzgerald, J.: Incremental Development of a Distributed Real-Time Model of a Cardiac Pacing System Using VDM. In: Cuellar, J., Sere, K. (eds.) FM 2008. LNCS, vol. 5014, pp. 181–197. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  19. 19.
    Méry, D., Singh, N.K.: Pacemaker’s Functional Behaviors in Event-B. Research Report inria-00419973 (2009)Google Scholar
  20. 20.
    Rehm, J.: From Absolute-Timer to Relative-Countdown: Patterns for Model-Checking (May 2008) (Unpublished)Google Scholar
  21. 21.
    Sarshogh, M.R.: Extending Event-B with Discrete Timing Properties. PhD thesis, University of Southampton (2013)Google Scholar
  22. 22.
    Savicks, V., Butler, M., Colley, J.: Co-simulating Event-B and Continuous Models via FMI. In: 2014 Summer Computer Simulation Conference, Society for Modeling & Simulation International (SCS) (July 2014)Google Scholar
  23. 23.
    Sulskus, G., Poppleton, M., Rezazadeh, A.: Example Event-B project (2014). http://users.ecs.soton.ac.uk/gs6g10/SimplifiedPMExample.zip
  24. 24.
    Sulskus, G., Poppleton, M., Rezazadeh, A.: An Investigation into Event-B Methodologies and Timing Constraint Modelling. Mini-Thesis, University of Southampton (2014)Google Scholar
  25. 25.
    Wang, J.: Handbook of Finite State Based Models and Applications. Discrete Mathematics and Its Applications. Chapman and Hall/CRC (2012)Google Scholar
  26. 26.
    Yang, F., Jacquot, J.-P.: Scaling Up with Event-B: A Case Study. In: Bobaru, M., Havelund, K., Holzmann, G.J., Joshi, R. (eds.) NFM 2011. LNCS, vol. 6617, pp. 438–452. Springer, Heidelberg (2011)CrossRefGoogle Scholar

Copyright information

© IFIP International Federation for Information Processing 2015

Authors and Affiliations

  • Gintautas Sulskus
    • 1
  • Michael Poppleton
    • 1
  • Abdolbaghi Rezazadeh
    • 1
  1. 1.University of SouthamptonSouthamptonUK

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