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International Conference on Intelligent Computer Mathematics

CICM 2020: Intelligent Computer Mathematics pp 105–122Cite as

A Framework for Formal Dynamic Dependability Analysis Using HOL Theorem Proving

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Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 12236))

Abstract

Dependability analysis is an essential step in the design process of safety-critical systems, where the causes of failure and some other metrics, such as reliability, should be identified at an early design stage. The dynamic failure characteristics of real-world systems are usually captured by various dynamic dependability models, such as continuous time Markov chains (CTMCs), dynamic fault trees (DFTs) and dynamic reliability block diagrams (DRBDs). In order to conduct the formal dependability analysis of systems that exhibit dynamic failure behaviors, these models need to be captured formally. In this paper, we describe recent developments towards this direction along with a roadmap on how to be able to develop a framework for formal reasoning support for DFTs, DRBDs and CTMCs in a higher-order-logic theorem prover.

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References

  1. Avizienis, A., Laprie, J.C., Randell, B., Landwehr, C.: Basic concepts and taxonomy of dependable and secure computing. IEEE Trans. Dependable Secure Comput. 1(1), 11–33 (2004)

    Article  Google Scholar 

  2. Trivedi, K.S.: Probability and Statistics with Reliability, Queuing and Computer Science Applications. Wiley, Hoboken (2002)

    MATH  Google Scholar 

  3. Stamatelatos, M., Vesely, W., Dugan, J., Fragola, J., Minarick, J., Railsback, J.: Fault Tree Handbook with Aerospace Applications. NASA Office of Safety and Mission Assurance (2002)

    Google Scholar 

  4. Distefano, S., Xing, L.: A new approach to modeling the system reliability: dynamic reliability block diagrams. In: Reliability and Maintainability Symposium, pp. 189–195. IEEE (2006)

    Google Scholar 

  5. Baier, C., Katoen, J.: Principles of Model Checking. MIT Press, Cambridge (2008)

    MATH  Google Scholar 

  6. Gordon, M.J., Melham, T.F.: Introduction to HOL: A Theorem Proving Environment for Higher-Order Logic. Cambridge University Press, Cambridge (1993)

    MATH  Google Scholar 

  7. Dehnert, C., Junges, S., Katoen, J.-P., Volk, M.: A storm is coming: a modern probabilistic model checker. In: Majumdar, R., Kunčak, V. (eds.) CAV 2017. LNCS, vol. 10427, pp. 592–600. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-63390-9_31

    Chapter  Google Scholar 

  8. Ghadhab, M., Junges, S., Katoen, J.-P., Kuntz, M., Volk, M.: Model-based safety analysis for vehicle guidance systems. In: Tonetta, S., Schoitsch, E., Bitsch, F. (eds.) SAFECOMP 2017. LNCS, vol. 10488, pp. 3–19. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-66266-4_1

    Chapter  Google Scholar 

  9. Elderhalli, Y., Volk, M., Hasan, O., Katoen, J.-P., Tahar, S.: Formal verification of rewriting rules for dynamic fault trees. In: Ölveczky, P.C., Salaün, G. (eds.) SEFM 2019. LNCS, vol. 11724, pp. 513–531. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-30446-1_27

    Chapter  Google Scholar 

  10. Kwiatkowska, M., Norman, G., Parker, D.: Quantitative analysis with the probabilistic model checker PRISM. Electron. Notes Theor. Comput. Sci. 153(2), 5–31 (2006)

    Article  Google Scholar 

  11. Ahmed, W., Hasan, O.: Formalization of fault trees in higher-order logic: a deep embedding approach. In: Fränzle, M., Kapur, D., Zhan, N. (eds.) SETTA 2016. LNCS, vol. 9984, pp. 264–279. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-47677-3_17

    Chapter  Google Scholar 

  12. Ahmed, W., Hasan, O., Tahar, S.: Formalization of reliability block diagrams in higher-order logic. J. Appl. Logic 18, 19–41 (2016)

    Article  MathSciNet  Google Scholar 

  13. HOL4 (2020). https://hol-theorem-prover.org/

  14. Elderhalli, Y., Ahmad, W., Hasan, O., Tahar, S.: Probabilistic analysis of dynamic fault trees using HOL theorem proving. J. Appl. Logics 6, 467–509 (2019)

    MathSciNet  Google Scholar 

  15. Elderhalli, Y., Hasan, O., Tahar, S.: A formally verified algebraic approach for dynamic reliability block diagrams. In: Ait-Ameur, Y., Qin, S. (eds.) ICFEM 2019. LNCS, vol. 11852, pp. 253–269. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-32409-4_16

    Chapter  Google Scholar 

  16. Hölzl, J.: Markov processes in Isabelle/HOL. In: ACM SIGPLAN Conference on Certified Programs and Proofs, pp. 100–111 (2017)

    Google Scholar 

  17. Isabelle (2020). https://isabelle.in.tum.de/

  18. Ahmed, W., Hasan, O.: Towards formal fault tree analysis using theorem proving. In: Kerber, M., Carette, J., Kaliszyk, C., Rabe, F., Sorge, V. (eds.) CICM 2015. LNCS (LNAI), vol. 9150, pp. 39–54. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20615-8_3

    Chapter  Google Scholar 

  19. Mhamdi, T., Hasan, O., Tahar, S.: On the formalization of the lebesgue integration theory in HOL. In: Kaufmann, M., Paulson, L.C. (eds.) ITP 2010. LNCS, vol. 6172, pp. 387–402. Springer, Heidelberg (2010). https://doi.org/10.1007/978-3-642-14052-5_27

    Chapter  Google Scholar 

  20. Mhamdi, T., Hasan, O., Tahar, S.: Formalization of entropy measures in HOL. In: van Eekelen, M., Geuvers, H., Schmaltz, J., Wiedijk, F. (eds.) ITP 2011. LNCS, vol. 6898, pp. 233–248. Springer, Heidelberg (2011). https://doi.org/10.1007/978-3-642-22863-6_18

    Chapter  Google Scholar 

  21. Ruijters, E., Stoelinga, M.: Fault tree analysis: a survey of the state-of-the-art in modeling. Anal. Tools Comput. Sci. Rev. 15–16, 29–62 (2015)

    Article  MathSciNet  Google Scholar 

  22. Merle, G.: Algebraic modelling of dynamic fault trees, contribution to qualitative and quantitative analysis. Ph.D. thesis, ENS, France (2010)

    Google Scholar 

  23. Sullivan, K.J., Dugan, J.B., Coppit, D.: The galileo fault tree analysis tool. In: IEEE Symposium on Fault-Tolerant Computing, pp. 232–235 (1999)

    Google Scholar 

  24. Elderhalli, Y., Hasan, O., Ahmad, W., Tahar, S.: Formal dynamic fault trees analysis using an integration of theorem proving and model checking. In: Dutle, A., Muñoz, C., Narkawicz, A. (eds.) NFM 2018. LNCS, vol. 10811, pp. 139–156. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-77935-5_10

    Chapter  Google Scholar 

  25. Elderhalli, Y., Hasan, O., Tahar, S.: A methodology for the formal verification of dynamic fault trees using HOL theorem proving. IEEE Access 7, 136176–136192 (2019)

    Article  Google Scholar 

  26. Boudali, H., Crouzen, P., Stoelinga, M.: A rigorous, compositional, and extensible framework for dynamic fault tree analysis. IEEE Trans. Dependable Secure Comput. 7, 128–143 (2010)

    Article  Google Scholar 

  27. Altby, A., Majdandzic, D.: Design and implementation of a fault-tolerant drive-by-wire system. Master’s thesis, Chalmers University of Technology, Sweden (2014)

    Google Scholar 

  28. Distefano, S., Puliafito, A.: Dynamic reliability block diagrams vs dynamic fault trees. In: Reliability and Maintainability Symposium, pp. 71–76. IEEE (2007)

    Google Scholar 

  29. BlockSim (2020). https://www.reliasoft.com/products/reliability-analysis/blocksim

  30. Distefano, S.: System dependability and performances: techniques, methodologies and tools. Ph.D. thesis, University of Messina, Italy (2005)

    Google Scholar 

  31. Xu, H., Xing, L.: Formal semantics and verification of dynamic reliability block diagrams for system reliability modeling. In: International Conference on Software Engineering and Applications, pp. 155–162 (2007)

    Google Scholar 

  32. Smith, G.: The Object-Z Specification Language, vol. 1. Springer, Boston (2012). https://doi.org/10.1007/978-1-4615-5265-9

    Book  MATH  Google Scholar 

  33. Xu, H., Xing, L., Robidoux, R.: Drbd: dynamic reliability block diagrams for system reliability modelling. Int. J. Comput. Appl. 31(2), 132–141 (2009)

    Google Scholar 

  34. Hasan, O., Ahmed, W., Tahar, S., Hamdi, M.S.: Reliability block diagrams based analysis: a survey. In: International Conference of Numerical Analysis and Applied Mathematics, vol. 1648, p. 850129.1-4. AIP (2015)

    Google Scholar 

  35. Liu, L., Hasan, O., Tahar, S.: Formal reasoning about finite-state discrete-time Markov chains in HOL. J. Comput. Sci. Technol. 28(2), 217–231 (2013)

    Article  MathSciNet  Google Scholar 

  36. Grimmett, G., Stirzaker, D., et al.: Probability and Random Processes. Oxford University Press, Oxford (2001)

    MATH  Google Scholar 

  37. Elderhalli, Y., Hasan, O., Tahar, S.: Using machine learning to minimize user intervention in theorem proving based dynamic fault tree analysis. In: Conference on Artificial Intelligence and Theorem Proving, pp. 36–37 (2019)

    Google Scholar 

  38. Li, Y., Lee, P.P.C., Lui, J.C.S.: Stochastic analysis on RAID reliability for solid-state drives. In: IEEE International Symposium on Reliable Distributed Systems, pp. 71–80 (2013)

    Google Scholar 

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Authors and Affiliations

  1. Electrical and Computer Engineering, Concordia University, Montréal, Canada

    Yassmeen Elderhalli, Osman Hasan & Sofiène Tahar

Authors
  1. Yassmeen Elderhalli
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  2. Osman Hasan
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  3. Sofiène Tahar
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Corresponding author

Correspondence to Yassmeen Elderhalli .

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Editors and Affiliations

  1. Department of Mathematics and Computer Science, Freie Universität Berlin, Berlin, Germany

    Christoph Benzmüller

  2. National Institute of Standards and Technology, Gaithersburg, MD, USA

    Bruce Miller

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Elderhalli, Y., Hasan, O., Tahar, S. (2020). A Framework for Formal Dynamic Dependability Analysis Using HOL Theorem Proving. In: Benzmüller, C., Miller, B. (eds) Intelligent Computer Mathematics. CICM 2020. Lecture Notes in Computer Science(), vol 12236. Springer, Cham. https://doi.org/10.1007/978-3-030-53518-6_7

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  • DOI: https://doi.org/10.1007/978-3-030-53518-6_7

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  • Online ISBN: 978-3-030-53518-6

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