A Stepwise Development Process for Reasoning About the Reliability of Real-Time Systems

  • Larissa Meinicke
  • Graeme Smith
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4591)


This paper investigates the use of the probabilistic and continuous extensions of action systems in the development and calculation of reliability of continuous, real-time systems. Rather than develop a new semantics to formally combine the existing extensions, it investigates a methodology for using them together, and the conditions under which this methodology is sound. A key feature of the methodology is that it simplifies the development process by separating the probabilistic calculations of system reliability from the details of the system’s real-time, continuous behaviour.


action systems refinement probability real-time reliability 


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  1. 1.
    Abrial, J.-R., Börger, E., Langmaack, H.: Formal Methods for Industrial Applications: Specifying and Programming the Steam Boiler Control. LNCS, vol. 1165. Springer, Heidelberg (1996)Google Scholar
  2. 2.
    Back, R.J.R., Kurki-Suonio, R.: Decentralization of process nets with centralized control. In: 2nd ACM SIGACT-SIGOPS Symp. on Principles of Distributed Computing, pp. 131–142. ACM Press, New York (1983)Google Scholar
  3. 3.
    Back, R.J.R., Kurki-Suonio, R.: Distributed cooperation with action systems. ACM Trans. Program. Lang. Syst. 10(4), 513–554 (1988)MATHCrossRefGoogle Scholar
  4. 4.
    Back, R.J.R., Petre, L., Porres, I.: Generalizing action systems to hybrid systems. In: Joseph, M. (ed.) FTRTFT 2000. LNCS, vol. 1926, pp. 202–213. Springer, Heidelberg (2000)CrossRefGoogle Scholar
  5. 5.
    Back, R.J.R., von Wright, J.: Trace refinement of action systems. In: Jonsson, B., Parrow, J. (eds.) CONCUR 1994. LNCS, vol. 836, pp. 367–384. Springer, Heidelberg (1994)CrossRefGoogle Scholar
  6. 6.
    Back, R.J.R., von Wright, J.: Refinement Calculus: A Systematic Introduction. Springer, Heidelberg (1998)MATHGoogle Scholar
  7. 7.
    Broy, M.: Refinement of time. In: Rus, T., Bertran, M. (eds.) AMAST-ARTS 1997, ARTS 1997, and AMAST-WS 1997. LNCS, vol. 1231, Springer, Heidelberg (1997)Google Scholar
  8. 8.
    Fidge, C.J., Hayes, I.J., Mahony, B.P.: Defining differentiation and integration in Z. In: Staples, J., Hinchey, M.G., Liu, S. (eds.) International Conference on Formal Engineering Methods (ICFEM 1998), pp. 64–73. IEEE Computer Society Press, Los Alamitos (1998)Google Scholar
  9. 9.
    Hurd, J.: Formal Verification of Probabilistic Algorithms. PhD thesis, University of Cambridge (2002)Google Scholar
  10. 10.
    Kozen, D.: Semantics of probabilistic programs. Journal of Computer and System Sciences 22, 328–350 (1981)MATHCrossRefMathSciNetGoogle Scholar
  11. 11.
    Mahony, B.P., Hayes, I.J.: A case-study in timed refinement: A mine pump. IEEE Transactions on Software Engineering 18(9), 817–826 (1992)CrossRefGoogle Scholar
  12. 12.
    McIver, A., Morgan, C., Troubitsyna, E.: The probabilistic steam boiler: a case study in probabilistic data refinement. In: Grundy, J., Schwenke, M., Vickers, T. (eds.) International Refinement Workshop/Formal Methods Pacific 1998. Series in Discrete Mathematics and Theoretical Computer Science, pp. 250–265. Springer, Heidelberg (1998)Google Scholar
  13. 13.
    Meinicke, L.: Probabilistic action system trace semantics. Technical report, School of Information Technology and Electrical Engineering, The University of Queensland, Australia (2007)Google Scholar
  14. 14.
    Meinicke, L., Hayes, I.J.: Continuous action system refinement. In: Uustalu, T. (ed.) MPC 2006. LNCS, vol. 4014, pp. 316–337. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  15. 15.
    Scholefield, D., Zedan, H., Jifeng, H.: A specification-oriented semantics for the refinement of real-time systems. Theoretical Computer Science 131, 219–241 (1994)MATHCrossRefMathSciNetGoogle Scholar
  16. 16.
    Sere, K., Troubitsyna, E.: Probabilities in action systems. In: 8th Nordic Workshop on Programming Theory (1996)Google Scholar
  17. 17.
    Storey, N.: Safety-Critical Computer Systems. Addison-Wesley, Reading (1996)Google Scholar
  18. 18.
    Troubitsyna, E.: Reliability assessment through probabilistic refinement. Nordic Journal of Computing 6(3), 320–342 (1999)MATHMathSciNetGoogle Scholar
  19. 19.
    Chaochen, Z., Hoare, C.A.R., Ravn, A.P.: A calculus of durations. Information Processing Letters 40, 269–271 (1991)MATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  • Larissa Meinicke
    • 1
  • Graeme Smith
    • 2
  1. 1.Department of Computer Science, Åbo AkademiFinland
  2. 2.School of Information Technology and Electrical Engineering, The University of QueenslandAustralia

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