Abstract
Probabilistic B (pB) [2,8] extends classical B [7] to incorporate probabilistic updates together with the specification of quantitative safety properties. As for classical B, probabilistic B formulates safety as inductive invariants which can be checked mechanically relative to the program code. In the case that the invariants cannot be shown to be inductive, classical B uses model checking to allow experimental investigation, returning a counterexample execution trace in the case that the safety condition is violated. In this paper we introduce YAGA which provides similar support for probabilistic B and quantitative safety specifications. YAGA automatically interprets quantitative safety and the pB machine as a model checking problem to investigate the presence of counterexamples. Since inductive invariants characterise a strong form of safety, we are able to identify the specific point at which failure occurs as individual counterexample traces, which can then be ranked for importance, for example according to the probability of occurrence.
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References
Han, T., Katoen, J.-P., Damman, B.: Counterexample Generation in Probabilistic Model Checking. IEEE Trans. Software Eng. 35(2), 241–257 (2009)
Hoang, T.S., Jin, Z., Robinson, K., McIver, A.K., Morgan, C.C.: Probabilistic Invariants for Probabilistic Machines. In: Bert, D., Bowen, J.P., King, S. (eds.) ZB 2003. LNCS, vol. 2651, pp. 240–259. Springer, Heidelberg (2003)
Leuschel, M., Butler, M.: ProB: A Model Checker for B. In: Araki, K., Gnesi, S., Mandrioli, D. (eds.) FME 2003. LNCS, vol. 2805, pp. 855–874. Springer, Heidelberg (2003)
Kwiatkowska, M., Norman, G., Parker, D.: Stochastic Model Checking. In: Bernardo, M., Hillston, J. (eds.) SFM 2007. LNCS, vol. 4486, pp. 220–270. Springer, Heidelberg (2007)
Ndukwu, U.: Quantitative Safety: Linking Proof-based Verification with Model Checking for Probabilistic Systems. In: Proceedings of First International Workshop on Quantitative Formal Methods (QFM 2009), Eindhoven, Netherlands (2009)
Motwani, R., Raghavan, P.: Randomized Algorithms. Cambridge University Press, Cambridge (1995)
Abrial, J.-R.: The B-Book: Assigning Programs to Meaning. Cambridge University Press, Cambridge (1996)
Hoang, T.S.: Developing a Probabilistic B-Method and a Supporting Toolkit. PhD Thesis, University of New South Wales, Australia (2005)
Ndukwu, U.: Generating Counterexamples for Quantitative Safety Specifications in Probabilistic B. Submitted to the Journal of Logic and Algebraic Programming, JLAP (May 2010), http://web.science.mq.edu.au/~ukndukwu/counterexamples.pdf
PRISM: Probabilistic Symbolic Model Checker, http://www.prismmodelchecker.org/
Deploy: http://www.deploy-project.eu/
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Ndukwu, U., McIver, A.K. (2010). YAGA: Automated Analysis of Quantitative Safety Specifications in Probabilistic B. In: Bouajjani, A., Chin, WN. (eds) Automated Technology for Verification and Analysis. ATVA 2010. Lecture Notes in Computer Science, vol 6252. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-15643-4_31
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DOI: https://doi.org/10.1007/978-3-642-15643-4_31
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