Abstract
In previous work, we have proposed a fully probabilistic version of Event-B where all the non-deterministic choices are replaced by probabilistic ones and, particularly, the events are equipped with weights that allow us to consider their enabling probability. In this work, we focus on the reliability of the system by proposing to constraint the probability of enabling an event (or a set of events) to control its importance with regard to the intended system behaviour. We add a specific upper bound which must limit the enabling probabilities of the chosen events and we consider the necessary proof obligations to check that the considered events respect the bound. At the end, we illustrate our work by presenting a case study specified in probabilistic Event-B and where bounding the enabling of some events is mandatory.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Motwani, R., Raghavan, P.: Randomized Algorithms. Chapman & Hall/CRC, Boca Raton (2010)
Abrial, J.R., Cansell, D., Méry, D.: A mechanically proved and incremental development of IEEE 1394 tree identify protocol. Form. Asp. Comput. 14(3), 215–227 (2003)
Villemeur, A.: Reliability, Availability, Maintainability and Safety Assessment: Assessment, Hardware, Software and Human Factors, vol. 2. Wiley, Hoboken (1992)
Chu, W.W., Sit, C.M.: Estimating task response time with contentions for real-time distributed systems. In: Proceedings of the Real-Time Systems Symposium, pp. 272–281. IEEE (1988)
Trivedi, K.S., Ramani, S., Fricks, R.: Recent advances in modeling response-time distributions in real-time systems. Proc. IEEE 91(7), 1023–1037 (2003)
Stoelinga, M.: An introduction to probabilistic automata. Bull. EATCS 78(176–198), 2 (2002)
Puterman, M.L.: Markov Decision Processes: Discrete Stochastic Dynamic Programming. Wiley, Hoboken (2014)
Katoen, J.-P.: Abstraction of probabilistic systems. In: Raskin, J.-F., Thiagarajan, P.S. (eds.) FORMATS 2007. LNCS, vol. 4763, pp. 1–3. Springer, Heidelberg (2007). https://doi.org/10.1007/978-3-540-75454-1_1
Dehnert, C., Gebler, D., Volpato, M., Jansen, D.N.: On abstraction of probabilistic systems. In: Remke, A., Stoelinga, M. (eds.) Stochastic Model Checking. Rigorous Dependability Analysis Using Model Checking Techniques for Stochastic Systems. LNCS, vol. 8453, pp. 87–116. Springer, Heidelberg (2014). https://doi.org/10.1007/978-3-662-45489-3_4
Jonsson, B., Larsen, K.G.: Specification and refinement of probabilistic processes. In: Logic in Computer Science. LICS 1991, pp. 266–277. IEEE (1991)
Bianco, A., de Alfaro, L.: Model checking of probabilistic and nondeterministic systems. In: Thiagarajan, P.S. (ed.) FSTTCS 1995. LNCS, vol. 1026, pp. 499–513. Springer, Heidelberg (1995). https://doi.org/10.1007/3-540-60692-0_70
Baier, C., Katoen, J.P., et al.: Principles of Model Checking. MIT Press, Cambridge (2008)
Haghighi, H., Afshar, M.: A Z-based formalism to specify Markov chains. Comput. Sci. Eng. 2(3), 24–31 (2012)
Sere, K., Troubitsyna, E.: Probabilities in action systems. In: Proceedings of the 8th Nordic Workshop on Programming Theory, pp. 373–387 (1996)
Hoang, T.S.: The development of a probabilistic B-method and a supporting toolkit. Ph.D. thesis. The University of New South Wales (2005)
Goldreich, O.: Probabilistic proof systems. In: Modern Cryptography, Probabilistic Proofs and Pseudorandomness. AC, vol. 17, pp. 39–72. Springer, Heidelberg (1999). https://doi.org/10.1007/978-3-662-12521-2_2
Barthe, G., Fournet, C., Grégoire, B., Strub, P.Y., Swamy, N., Zanella-Béguelin, S.: Probabilistic relational verification for cryptographic implementations. In: ACM SIGPLAN Notices, vol. 49, pp. 193–205. ACM (2014)
Hurd, J., McIver, A., Morgan, C.: Probabilistic guarded commands mechanized in HOL. Electron. Not. Theoret. Comput. Sci. 112, 95–111 (2005)
Audebaud, P., Paulin-Mohring, C.: Proofs of randomized algorithms in Coq. Sci. Comput. Program. 74(8), 568–589 (2009)
Hurd, J.: Formal verification of probabilistic algorithms. Ph.D. thesis. University of Cambridge, Computer Laboratory (2003)
Abrial, J.R.: Modeling in Event-B: System and Software Engineering. Cambridge University Press, Cambridge (2010)
Abrial, J.R., Butler, M., Hallerstede, S., Hoang, T.S., Mehta, F., Voisin, L.: Rodin: an open toolset for modelling and reasoning in Event-B. Int. J. Softw. Tools Technol. Transf. 12(6), 447–466 (2010)
Morgan, C., Hoang, T.S., Abrial, J.-R.: The challenge of probabilistic Event B—extended abstract—. In: Treharne, H., King, S., Henson, M., Schneider, S. (eds.) ZB 2005. LNCS, vol. 3455, pp. 162–171. Springer, Heidelberg (2005). https://doi.org/10.1007/11415787_10
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). https://doi.org/10.1007/978-3-540-73210-5_16
Yilmaz, E.: Tool support for qualitative reasoning in Event-B. Ph.D. thesis, Master thesis. ETH Zürich (2010)
Tarasyuk, A., Troubitsyna, E., Laibinis, L.: Reliability assessment in Event-B development. In: NODES 2009 (2009)
Tarasyuk, A., Troubitsyna, E., Laibinis, L.: Integrating stochastic reasoning into Event-B development. Form. Asp. Comput. 27(1), 53–77 (2015)
Tarasyuk, A., Troubitsyna, E., Laibinis, L.: Towards probabilistic modelling in Event-B. In: Méry, D., Merz, S. (eds.) IFM 2010. LNCS, vol. 6396, pp. 275–289. Springer, Heidelberg (2010). https://doi.org/10.1007/978-3-642-16265-7_20
Aouadhi, M.A., Delahaye, B., Lanoix, A.: Moving from Event-B to probabilistic Event-B. In: Proceedings of the 32nd Annual ACM Symposium on Applied Computing. ACM (2017)
Aouadhi, M.A., Delahaye, B., Lanoix, A.: Introducing probabilistic reasoning within Event-B. Softw. Syst. Model. (2017)
Gaiero, D., Zola, U.: ICT Vs FCT Test: case studies, June 2014
Electronics notes: PCP Inspection Techniques and Technologies. https://www.electronics-notes.com/articles/test-methods/automatic-automated-test-ate/pcb-inspection.php
Butler, M., Maamria, I.: Practical theory extension in Event-B. In: Liu, Z., Woodcock, J., Zhu, H. (eds.) Theories of Programming and Formal Methods. LNCS, vol. 8051, pp. 67–81. Springer, Heidelberg (2013). https://doi.org/10.1007/978-3-642-39698-4_5
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2018 Springer Nature Switzerland AG
About this paper
Cite this paper
Aouadi, S., Lanoix, A. (2018). Reliability in Fully Probabilistic Event-B: How to Bound the Enabling of Events. In: Abdelwahed, E., et al. New Trends in Model and Data Engineering. MEDI 2018. Communications in Computer and Information Science, vol 929. Springer, Cham. https://doi.org/10.1007/978-3-030-02852-7_17
Download citation
DOI: https://doi.org/10.1007/978-3-030-02852-7_17
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-02851-0
Online ISBN: 978-3-030-02852-7
eBook Packages: Computer ScienceComputer Science (R0)