Abstract
A desirable property of control systems is robustness to inputs, when small perturbations of the inputs of a system will cause only small perturbations on outputs. This property should be maintained at the implementation level, where close inputs can lead to different execution paths. The problem becomes crucial for finite precision implementations, where any elementary computation is affected by an error. In this context, almost every test is potentially unstable, that is, for a given input, the finite precision and real numbers paths may differ. Still, state-of-the-art error analyses rely on the stable test hypothesis, yielding unsound error bounds when the conditional block is not robust to uncertainties. We propose a new abstract-interpretation based error analysis of finite precision implementations, which is sound in presence of unstable tests, by bounding the discontinuity error for path divergences. This gives a tractable analysis implemented in the FLUCTUAT analyzer.
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References
Boldo, S., Filliâtre, J.-C.: Formal Verification of Floating-Point Programs. In: 18th IEEE International Symposium on Computer Arithmetic (June 2007)
Chaudhuri, S., Gulwani, S., Lublinerman, R.: Continuity analysis of programs. In: POPL, pp. 57–70 (2010)
Chaudhuri, S., Gulwani, S., Lublinerman, R.: Continuity and robustness of programs. Commun. ACM 55(8), 107–115 (2012)
Chesneaux, J.-M., Lamotte, J.-L., Limare, N., Lebars, Y.: On the new cadna library. In: SCAN (2006)
Ghorbal, K., Goubault, E., Putot, S.: The zonotope abstract domain taylor1+. In: Bouajjani, A., Maler, O. (eds.) CAV 2009. LNCS, vol. 5643, pp. 627–633. Springer, Heidelberg (2009)
Ghorbal, K., Goubault, E., Putot, S.: A logical product approach to zonotope intersection. In: Touili, T., Cook, B., Jackson, P. (eds.) CAV 2010. LNCS, vol. 6174, pp. 212–226. Springer, Heidelberg (2010)
Goubault, E., Le Gall, T., Putot, S.: An accurate join for zonotopes, preserving affine input/output relations. In: Proceedings of NSAD 2012. ENTCS, pp. 65–76 (2012)
Goubault, E., Putot, S.: Static analysis of numerical algorithms. In: Yi, K. (ed.) SAS 2006. LNCS, vol. 4134, pp. 18–34. Springer, Heidelberg (2006)
Goubault, E., Putot, S.: Perturbed affine arithmetic for invariant computation in numerical program analysis. CoRR, abs/0807.2961 (2008)
Goubault, E., Putot, S.: A zonotopic framework for functional abstractions. CoRR, abs/0910.1763 (2009)
Goubault, E., Putot, S.: Static analysis of finite precision computations. In: Jhala, R., Schmidt, D. (eds.) VMCAI 2011. LNCS, vol. 6538, pp. 232–247. Springer, Heidelberg (2011)
Goubault, E., Putot, S.: Robustness analysis of finite precision implementationss. CoRR, abs/1309.3910 (2013)
Hamlet, D.: Continuity in software systems. In: ISSTA, pp. 196–200 (2002)
Majumdar, R., Saha, I.: Symbolic robustness analysis. In: RTSS (2009)
Ponsini, O., Michel, C., Rueher, M.: Refining abstract interpretation based value analysis with constraint programming techniques. In: Milano, M. (ed.) CP 2012. LNCS, vol. 7514, pp. 593–607. Springer, Heidelberg (2012)
Tabuada, P., Balkan, A., Caliskan, S.Y., Shoukry, Y., Majumdar, R.: Input-output robustness for discrete systems. In: EMSOFT, pp. 217–226 (2012)
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Goubault, E., Putot, S. (2013). Robustness Analysis of Finite Precision Implementations. In: Shan, Cc. (eds) Programming Languages and Systems. APLAS 2013. Lecture Notes in Computer Science, vol 8301. Springer, Cham. https://doi.org/10.1007/978-3-319-03542-0_4
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DOI: https://doi.org/10.1007/978-3-319-03542-0_4
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