Abstract
Dynamic Fault Trees (DFTs) model the failure behavior of systems dynamics. Several rewriting rules have been recently developed, which allow the simplification of DFTs prior to a formal analysis with tools such as the Storm model checker. To ascertain the soundness of the analysis, we propose to formally verify these rewriting rules using higher-order-logic (HOL) theorem proving. We first present the formalization in HOL of commonly used DFT gates, i.e., AND, OR and PAND, with an arbitrary number of inputs. Then we describe our formal specification of the rewriting rules and the verification of their intended behavior using the HOL4 theorem prover.
This work is partially supported by the DFG RTG 2236 UnRAVeL.
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Boudali, H., Crouzen, P., Stoelinga, M.: Dynamic fault tree analysis using input/output interactive Markov chains. In: Proceedings of DSN, pp. 708–717. IEEE (2007)
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
Dugan, J.B., Bavuso, S.J., Boyd, M.A.: Fault trees and sequence dependencies. In: Proceedings of RAMS, pp. 286–293 (1990)
Ehrig, H., Ehrig, K., Prange, U., Taentzer, G.: Fundamentals of Algebraic Graph Transformation. Monographs in Theoretical Computer Science. An EATCS Series. Springer, Heidelberg (2006). https://doi.org/10.1007/3-540-31188-2
Elderhalli, Y.: DFT rewriting rules: HOL4 script, Concordia University, Montreal, QC, Canada (2019). http://hvg.ece.concordia.ca/code/hol/DFT-rewrite/index.php
Elderhalli, Y., Ahmad, W., Hasan, O., Tahar, S.: Probabilistic analysis of dynamic fault trees using HOL theorem proving. J. Appl. Log. 6, 467–509 (2019)
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
Ghadhab, M., Junges, S., Katoen, J., Kuntz, M., Volk, M.: Safety analysis for vehicle guidance systems with dynamic fault trees. Reliab. Eng. Syst. Saf. 186, 37–50 (2019)
HOL4 (2019). https://hol-theorem-prover.org/
Junges, S., Guck, D., Katoen, J., Rensink, A., Stoelinga, M.: Fault trees on a diet: automated reduction by graph rewriting. Form. Asp. Comput. 29(4), 651–703 (2017)
Junges, S.: Simplifying dynamic fault trees by graph rewriting. Master thesis, RWTH Aachen University (2015)
Merle, G.: Algebraic modelling of dynamic fault trees, contribution to qualitative and quantitative analysis. Ph.D. thesis, ENS Cachan, France (2010)
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
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
Ruijters, E., Stoelinga, M.: Fault tree analysis: a survey of the state-of-the-art in modeling, analysis and tools. Comput. Sci. Rev. 15–16, 29–62 (2015)
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)
Volk, M., Junges, S., Katoen, J.P.: Fast dynamic fault tree analysis by model checking techniques. IEEE Trans. Ind. Inform. 14(1), 370–379 (2018)
Acknowledgments
The authors would like to thank Sebastian Junges, from RWTH Aachen University, for the discussions and comments on the rewrite rules.
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Elderhalli, Y., Volk, M., Hasan, O., Katoen, JP., Tahar, S. (2019). Formal Verification of Rewriting Rules for Dynamic Fault Trees. In: Ölveczky, P., Salaün, G. (eds) Software Engineering and Formal Methods. SEFM 2019. Lecture Notes in Computer Science(), vol 11724. Springer, Cham. https://doi.org/10.1007/978-3-030-30446-1_27
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DOI: https://doi.org/10.1007/978-3-030-30446-1_27
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