Abstract
We present a framework to formally describe system behavior and symbolically reason about possible failures. We regard systems which are composed of different units: sensors, computational parts and actuators. Considering worst-case failure behavior of system components, our framework is used to derive reliability guarantees for composed systems. The behavior of system components is modeled using monad like constructs that serve as an abstract representation for system behavior. We introduce rules to reason about these representations and derive results like, e.g., guaranteed upper bounds for system failure. Our approach is characterized by the fact that we do not just map a certain component to a failure probability, but regard distributions of error behavior. These serve as basis for deriving failure probabilities.
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References
Audebaud, P., Paulin-Mohring, C.: Proofs of randomized algorithms in Coq. Science of Computer Programming (2008)
Ayache, S., Conquet, E., Humbert, P., Rodriguez, C., Sifakis, J., Gerlich, R.: Formal methods for the validation of fault tolerance in autonomous spacecraft. In: International Symposium on Fault-Tolerant Computing, FTCS 1996 (1996)
Blech, J.O.: Proving the Security of ElGamal Encryption Via Indistinguishability Logic. In: ACM Symposium On Applied Computing (2011)
Blech, J.O., Hattendorf, A., Huang, J.: An Invariant Preserving Transformation for PLC Models. In: IEEE International Workshop on Model-Based Engineering for Real-Time Embedded Systems Design (2011)
Blech, J.O., Périn, M.: Generating Invariant-based Certificates for Embedded Systems. ACM Transactions on Embedded Computing Systems (TECS) (to appear)
The Coq development team: The Coq Proof Assistant Reference Manual v8.3 (2010), http://coq.inria.fr
Hallerstede, S., Hoang, T.S.: Qualitative Probabilistic Modelling in Event-B*. In: Davies, J., Gibbons, J. (eds.) IFM 2007. LNCS, vol. 4591, pp. 293–312. Springer, Heidelberg (2007)
Hanmer, R.: Patterns for Fault Tolerant Software. Wiley (October 2007) ISBN: 978-0-470-31979-6
Jeffords, R., Heitmeyer, C., Archer, M., Leonard, E.: A Formal Method for Developing Provably Correct Fault-Tolerant Systems Using Partial Refinement and Composition. In: Cavalcanti, A., Dams, D.R. (eds.) FM 2009. LNCS, vol. 5850, pp. 173–189. Springer, Heidelberg (2009)
Kljaich, J., Smith, B.T., Wojcik, A.S.: Formal Verification of Fault Tolerance Using Theorem-Proving Techniques. IEEE Transactions on Computers 38(3) (March 1989)
Kwiatkowska, M., Norman, G., Parker, D.: PRISM: Probabilistic Symbolic Model Checker. In: Field, T., Harrison, P.G., Bradley, J., Harder, U. (eds.) TOOLS 2002. LNCS, vol. 2324, pp. 200–204. Springer, Heidelberg (2002)
McIver, A., Morgan, C.: Abstraction, Refinement and Proof for Probabilistic Systems. Springer, Heidelberg (2005)
Owre, S., Rushby, J., Shankar, N., von Henke, F.: Formal verification for fault-tolerant architectures: prolegomena to the design of PVS. IEEE Transactions on Software Engineering (February 1995)
Steiner, W., Rushby, J., Sorea, M., Pfeifer, H.: Model Checking a Fault-Tolerant Startup Algorithm: From Design Exploration To Exhaustive Fault Simulation. In: The International Conference on Dependable Systems and Networks. IEEE Computer Society (2004)
Programmable controllers - Part 3: Programming languages, IEC 61131-3: 1993, International Electrotechnical Commission (1993)
Wadler, P.: The essence of functional programming. In: 19’th Symposium on Principles of Programming Languages. ACM Press (January 1992)
Pike, L., Maddalon, J., Miner, P., Geser, A.: Abstractions for Fault-Tolerant Distributed System Verification. In: Slind, K., Bunker, A., Gopalakrishnan, G.C. (eds.) TPHOLs 2004. LNCS, vol. 3223, pp. 257–270. Springer, Heidelberg (2004)
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Blech, J.O. (2011). Probabilistic Compositional Reasoning for Guaranteeing Fault Tolerance Properties. In: Fernà ndez Anta, A., Lipari, G., Roy, M. (eds) Principles of Distributed Systems. OPODIS 2011. Lecture Notes in Computer Science, vol 7109. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-25873-2_16
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DOI: https://doi.org/10.1007/978-3-642-25873-2_16
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