A Framework for Formal Dynamic Dependability Analysis Using HOL Theorem Proving

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.

[1]  Makis Stamatelatos,et al.  Fault tree handbook with aerospace applications , 2002 .

[2]  Osman Hasan,et al.  A Formally Verified Algebraic Approach for Dynamic Reliability Block Diagrams , 2019, ICFEM.

[3]  Carl E. Landwehr,et al.  Basic concepts and taxonomy of dependable and secure computing , 2004, IEEE Transactions on Dependable and Secure Computing.

[4]  Sofiène Tahar,et al.  Formal Dynamic Fault Trees Analysis Using an Integration of Theorem Proving and Model Checking , 2018, NFM.

[5]  Mariëlle Stoelinga,et al.  Fault tree analysis: A survey of the state-of-the-art in modeling, analysis and tools , 2014, Comput. Sci. Rev..

[6]  Osman Hasan,et al.  Formalization of Fault Trees in Higher-Order Logic: A Deep Embedding Approach , 2016, SETTA.

[7]  A. Puliafito,et al.  Dynamic Reliability Block Diagrams VS Dynamic Fault Trees , 2007, 2007 Annual Reliability and Maintainability Symposium.

[8]  Johannes Hölzl,et al.  Markov processes in Isabelle/HOL , 2017, CPP.

[9]  Alexander Altby,et al.  Design and implementation of a fault-tolerant drive-by-wire system , 2014 .

[10]  Mariëlle Stoelinga,et al.  A Rigorous, Compositional, and Extensible Framework for Dynamic Fault Tree Analysis , 2010, IEEE Transactions on Dependable and Secure Computing.

[11]  Sofiène Tahar,et al.  Using Machine Learning to Minimize User Intervention in Theorem Proving based Dynamic Fault Tree Analysis , 2018 .

[12]  Christel Baier,et al.  Principles of model checking , 2008 .

[13]  Guillaume Merle,et al.  Algebraic modelling of Dynamic Fault Trees, contribution to qualitative and quantitative analysis , 2010 .

[14]  Sofiène Tahar,et al.  Formal Verification of Rewriting Rules for Dynamic Fault Trees , 2019, SEFM.

[15]  Ali Esmaili,et al.  Probability and Random Processes , 2005, Technometrics.

[16]  Osman Hasan,et al.  Towards Formal Fault Tree Analysis Using Theorem Proving , 2015, CICM.

[17]  G. Grimmett,et al.  Probability and random processes , 2002 .

[18]  Sofiène Tahar,et al.  Formal Reasoning About Finite-State Discrete-Time Markov Chains in HOL , 2013, Journal of Computer Science and Technology.

[19]  Liudong Xing,et al.  Drbd: Dynamic Reliability Block Diagrams for System Reliability Modelling , 2009 .

[20]  John C. S. Lui,et al.  Stochastic Analysis on RAID Reliability for Solid-State Drives , 2013, 2013 IEEE 32nd International Symposium on Reliable Distributed Systems.

[21]  M. Gordon,et al.  Introduction to HOL: a theorem proving environment for higher order logic , 1993 .

[22]  Sofiène Tahar,et al.  Formalization of Entropy Measures in HOL , 2011, ITP.

[23]  Sofiène Tahar,et al.  Formalization of Reliability Block Diagrams in Higher-order Logic , 2016, J. Appl. Log..

[24]  RuijtersEnno,et al.  Fault tree analysis , 2015 .

[25]  Matthias Kuntz,et al.  Model-Based Safety Analysis for Vehicle Guidance Systems , 2017, SAFECOMP.

[26]  S. Distefano,et al.  A new approach to modeling the system reliability: dynamic reliability block diagrams , 2006, RAMS '06. Annual Reliability and Maintainability Symposium, 2006..

[27]  Sofiène Tahar,et al.  Probabilistic Analysis of Dynamic Fault Trees using HOL Theorem Proving , 2019, FLAP.

[28]  Sofiène Tahar,et al.  A Methodology for the Formal Verification of Dynamic Fault Trees Using HOL Theorem Proving , 2019, IEEE Access.

[29]  Sofiène Tahar,et al.  On the Formalization of the Lebesgue Integration Theory in HOL , 2010, ITP.

[30]  Liudong Xing,et al.  Formal semantics and verification of dynamic reliability block diagrams for system reliability modeling , 2007, ICSE 2007.

[31]  Marta Z. Kwiatkowska,et al.  Quantitative Analysis With the Probabilistic Model Checker PRISM , 2006, QAPL.

[32]  David Coppit,et al.  The Galileo fault tree analysis tool , 1999, Digest of Papers. Twenty-Ninth Annual International Symposium on Fault-Tolerant Computing (Cat. No.99CB36352).

[33]  Graeme Smith,et al.  The Object-Z Specification Language , 1999, Advances in Formal Methods.

[34]  Sebastian Junges,et al.  A Storm is Coming: A Modern Probabilistic Model Checker , 2017, CAV.

[35]  Sofiène Tahar,et al.  Reliability block diagrams based analysis: A survey , 2015 .

[36]  Kishor S. Trivedi.  Probability and Statistics with Reliability, Queuing, and Computer Science Applications , 1984 .