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Application of Symbolic Approach to the Bernstein Expansion for Program Analysis and Optimization

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Abstract

Mathematical packages for static analysis of programs have recently been developed. Although these packages are widely used, they have a number of limitations. In particular, they do not support multivariate polynomials with integer coefficients, which are often met in programs and used for the analysis of systems. Some methods to overcome this difficulty have already been suggested, but, unfortunately, they can be applied to only a subclass of such expressions. In this paper, we suggest a more general approach based on the Bernstein expansion, which facilitates the analysis of integer multivariate polynomials.

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REFERENCES

  1. Bernstein, S.N., Sobranie sochinenii (Collected Works), Akad. Nauk SSSR, 1952, vol. 1.

  2. Bernstein, S.N, Sobranie sochinenii (Collected Works), Akad. Nauk SSSR, 1954, vol. 2.

  3. Berchtold, J. and Bowyer, A., Robust Arithmetic for Multivariate Bernstein-form Polynomials, Computer-aided Design, 2000, vol. 32, pp. 681–689.

    Google Scholar 

  4. Galrloff, J., Application of Bernstein Expansion to the Solution of Control Problems, Proc. of MISC'99 (Workshop on Applications of Interval Analysis to Systems and Control), Vehi, J. and Sainz, M.A., Eds., University of Girona, Girona, Spain, pp. 421–430.

  5. Galrloff, J. and Graf, B., The Use of Symbolic Methods in Control System Analysis and Design. Solving Strict Polynomial Inequalities by Bernstein Expansion, London: Inst. Electrical Engineers (IEE), 1999, pp. 339–352.

    Google Scholar 

  6. Maslov, V. and Pugh, W., Simplifying Polynomial Constraints over Integers to Make Dependence Analysis More Precise, Proc. of CONPAR 94—VAPP VI Int. Conf. on Parallel and Vector Processing, 1994.

  7. Blume, W. and Eigenmann, R., Non-Linear and Symbolic Data Dependence Testing, IEEE Trans. Parallel Distributed Systems, 1998, vol. 9,no. 12, pp. 1180–1194.

    Google Scholar 

  8. Chatfield, C., Time-Series Forecasting, Chapman & Hall, 2000.

  9. Feautrier, P., The Data Parallel Programming Model. Automatic Parallelization in the Polytype Model, Lecture Notes in Computer Science, Berlin: Springer, 1996, vol. 1132, pp. 79–100.

    Google Scholar 

  10. Ernst, M.D., Cockrell, J., Griswold, W.G., and Notkin, D., Dynamically Discovering Likely Program Invariants to Support Program Evolution, Proc. of Int. Conf. on Software Eng., 1999, pp. 213–224.

  11. Chilimbi, T.M., Hill, M.D., and Larus, J.R., Cache-Conscious Structure Layout, Proc. of SIGPLAN Conf. on Programming Language Design and Implementation, 1999, pp. 1–12.

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Authors and Affiliations

  1. ICPS/LSIIT, Université Louis Pasteur, Strasbourg Pôle API, Bd Sébastien Brant, 67400, Illkirch—, France

    F. Clauss

  2. A3 Project, INRIA Rocquencourt, 78153, Le Chesnay Cedex—, France

    F. Clauss

  3. Department of Mechanics and Mathematics, Moscow State University, Vorob'evy gory, Moscow, 119992, Russia

    I. Yu. Chupaeva

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  1. F. Clauss
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  2. I. Yu. Chupaeva
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Clauss, F., Chupaeva, I.Y. Application of Symbolic Approach to the Bernstein Expansion for Program Analysis and Optimization. Programming and Computer Software 30, 164–172 (2004). https://doi.org/10.1023/B:PACS.0000029581.97227.42

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  • DOI: https://doi.org/10.1023/B:PACS.0000029581.97227.42

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