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Static Analysis by Abstract Interpretation of Numerical Programs and Systems, and FLUCTUAT

  • Conference paper
Static Analysis (SAS 2013)

Part of the book series: Lecture Notes in Computer Science ((LNPSE,volume 7935))

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Abstract

This invited lecture is a survey of our work over the last 12 years or so, dealing with the precise analysis of numerical programs, essentially control programs such as the ones found in the aerospace, nuclear and automotive industry.

Our approach is now based on a rather generic abstract domain, based on “zonotopes” or “affine forms” [7], but with some specificities. For instance, our zonotopic domain provides a functional abstraction [16,13], i.e. an abstraction of the input-output relationships between values of variables, allowing for test generation and modular verification [21]. Also, our domain deals with the real number and the finite precision (for instance, floating-point or fixed-point) semantics [14,17]. It is used in practice in FLUCTUAT [20,9,4] to prove some functional properties of programs, generate (counter-) examples, identify the discrepancy between the real number and the finite precision semantics and its origin etc.

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References

  1. Adjé, A., Bouissou, O., Goubault-Larrecq, J., Goubault, E., Putot, S.: Analyzing probabilistic programs with partially known distributions. In: VSTTE (2013)

    Google Scholar 

  2. Adjé, A., Gaubert, S., Goubault, E.: Coupling policy iteration with semi-definite relaxation to compute accurate numerical invariants in static analysis. Logical Methods in Computer Science 8(1) (2012)

    Google Scholar 

  3. Boldo, S., Filliâtre, J.C.: Formal Verification of Floating-Point Programs. In: 18th IEEE International Symposium on Computer Arithmetic (June 2007)

    Google Scholar 

  4. Bouissou, O., Conquet, E., Cousot, P., Cousot, R., Ghorbal, K., Lesens, D., Putot, S., Turin, M.: Space software validation using abstract interpretation. In: DASIA (2009)

    Google Scholar 

  5. Bouissou, O., Goubault, E., Goubault-Larrecq, J., Putot, S.: A generalization of p-boxes to affine arithmetic. Computing 94(2-4), 189–201 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  6. Bouissou, O., Goubault, E., Putot, S., Tekkal, K., Vedrine, F.: HybridFluctuat: A static analyzer of numerical programs within a continuous environment. In: Bouajjani, A., Maler, O. (eds.) CAV 2009. LNCS, vol. 5643, pp. 620–626. Springer, Heidelberg (2009)

    Chapter  Google Scholar 

  7. Comba, J.L.D., Stolfi, J.: Affine arithmetic and its applications to computer graphics. In: Proceedings of SIBGRAPI (1993)

    Google Scholar 

  8. Cousot, P., Cousot, R.: Abstract interpretation: A unified lattice model for static analysis of programs by construction or approximation of fixpoints. In: POPL, pp. 238–252 (1977)

    Google Scholar 

  9. Delmas, D., Goubault, E., Putot, S., Souyris, J., Tekkal, K., Védrine, F.: Towards an industrial use of FLUCTUAT on safety-critical avionics software. In: Alpuente, M., Cook, B., Joubert, C. (eds.) FMICS 2009. LNCS, vol. 5825, pp. 53–69. Springer, Heidelberg (2009)

    Chapter  Google Scholar 

  10. Fajstrup, L., Goubault, É., Haucourt, E., Mimram, S., Raussen, M.: Trace spaces: An efficient new technique for state-space reduction. In: Seidl, H. (ed.) ESOP 2012. LNCS, vol. 7211, pp. 274–294. Springer, Heidelberg (2012)

    Google Scholar 

  11. Gawlitza, T.M., Seidl, H., Adjé, A., Gaubert, S., Goubault, E.: Abstract interpretation meets convex optimization. J. Symb. Comput. 47(12), 1416–1446 (2012)

    Article  MATH  Google Scholar 

  12. 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)

    Chapter  Google Scholar 

  13. Goubault, E., Gall, T.L., Putot, S.: An accurate join for zonotopes, preserving affine input/output relations. In: Proceedings of NSAD 2012, 4th Workshop on Numerical and Symbolic Abstract Domains. ENTCS, vol. 287, pp. 65–76 (2012)

    Google Scholar 

  14. Goubault, É., Putot, S.: Static analysis of numerical algorithms. In: Yi, K. (ed.) SAS 2006. LNCS, vol. 4134, pp. 18–34. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  15. Goubault, E., Putot, S.: Under-approximations of computations in real numbers based on generalized affine arithmetic. In: Riis Nielson, H., Filé, G. (eds.) SAS 2007. LNCS, vol. 4634, pp. 137–152. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  16. Goubault, E., Putot, S.: A zonotopic framework for functional abstractions. CoRR abs/0910.1763 (2009), http://arxiv.org/abs/0910.1763

  17. 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)

    Chapter  Google Scholar 

  18. Goubault, É.: Static analyses of the precision of floating-point operations. In: Cousot, P. (ed.) SAS 2001. LNCS, vol. 2126, pp. 234–259. Springer, Heidelberg (2001)

    Chapter  Google Scholar 

  19. Goubault, E., Haucourt, E.: A practical application of geometric semantics to static analysis of concurrent programs. In: Abadi, M., de Alfaro, L. (eds.) CONCUR 2005. LNCS, vol. 3653, pp. 503–517. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  20. Goubault, E., Putot, S., Baufreton, P., Gassino, J.: Static analysis of the accuracy in control systems: Principles and experiments. In: Leue, S., Merino, P. (eds.) FMICS 2007. LNCS, vol. 4916, pp. 3–20. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  21. Goubault, E., Putot, S., Védrine, F.: Modular static analysis with zonotopes. In: Miné, A., Schmidt, D. (eds.) SAS 2012. LNCS, vol. 7460, pp. 24–40. Springer, Heidelberg (2012)

    Chapter  Google Scholar 

  22. Menard, D., Rocher, R., Sentieys, O., Simon, N., Didier, L.S., Hilaire, T., Lopez, B., Goubault, E., Putot, S., Védrine, F., Najahi, A., Revy, G., Fangain, L., Samoyeau, C., Lemonnier, F., Clienti, C.: Design of fixed-point embedded systems (defis) french anr project. In: DASIP, pp. 1–2 (2012)

    Google Scholar 

  23. Meurant, G.: The Lanczos and Conjugate Gradient Algorithms: From Theory to Finite Precision Computations (Software, Environments, and Tools). SIAM (2006)

    Google Scholar 

  24. Paige, C.C.: The computation of eigenvalues and eigenvectors of very large sparse matrices. Ph.D. thesis (1971)

    Google Scholar 

  25. Wilkinson, J.H.: The algebraic eigenvalue problem. Oxford University Press (1965)

    Google Scholar 

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Author information

Authors and Affiliations

  1. CEA Saclay, Nanoinnov, CEA LIST, 91191, Gif-sur-Yvette CEDEX, France

    Eric Goubault

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  1. Eric Goubault
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Editors and Affiliations

  1. Microsoft Research, One Microsoft Way, 98052, Redmond, WA, USA

    Francesco Logozzo

  2. One Microsoft Way, Microsoft Research, 98052, Redmond,, WA,, USA

    Manuel Fähndrich

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Goubault, E. (2013). Static Analysis by Abstract Interpretation of Numerical Programs and Systems, and FLUCTUAT. In: Logozzo, F., Fähndrich, M. (eds) Static Analysis. SAS 2013. Lecture Notes in Computer Science, vol 7935. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-38856-9_1

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  • DOI: https://doi.org/10.1007/978-3-642-38856-9_1

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-38855-2

  • Online ISBN: 978-3-642-38856-9

  • eBook Packages: Computer ScienceComputer Science (R0)

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