Formal Verification of Rewriting Rules for Dynamic Fault Trees
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.
KeywordsDynamic Fault Trees Rewriting rules Theorem proving HOL4
The authors would like to thank Sebastian Junges, from RWTH Aachen University, for the discussions and comments on the rewrite rules.
- 1.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)Google Scholar
- 3.Dugan, J.B., Bavuso, S.J., Boyd, M.A.: Fault trees and sequence dependencies. In: Proceedings of RAMS, pp. 286–293 (1990)Google Scholar
- 5.Elderhalli, Y.: DFT rewriting rules: HOL4 script, Concordia University, Montreal, QC, Canada (2019). http://hvg.ece.concordia.ca/code/hol/DFT-rewrite/index.php
- 6.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)Google Scholar
- 7.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_10CrossRefGoogle Scholar
- 9.HOL4 (2019). https://hol-theorem-prover.org/
- 11.Junges, S.: Simplifying dynamic fault trees by graph rewriting. Master thesis, RWTH Aachen University (2015)Google Scholar
- 12.Merle, G.: Algebraic modelling of dynamic fault trees, contribution to qualitative and quantitative analysis. Ph.D. thesis, ENS Cachan, France (2010)Google Scholar
- 16.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