Abstract
We present a new numerical abstract domain. This domain automatically detects and proves bounds on the values of program variables. For that purpose, it relates variable values to a clock counter. More precisely, it bounds these values with the i-th iterate of the function [X↦α×X + β] applied on M, where i denotes the clock counter and the floating-point numbers α, β, and M are discovered by the analysis. Such properties are especially useful to analyze loops in which a variable is iteratively assigned with a barycentric mean of the values that were associated with the same variable at some previous iterations. Because of rounding errors, the computation of this barycenter may diverge when the loop is iterated forever. Our domain provides a bound that depends on the execution time of the program.
This work was partially supported by the ASTRÉE RNTL project.
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Blanchet, B., Cousot, P., Cousot, R., Feret, J., Mauborgne, L., Miné, A., Monniaux, D., Rival, X.: Design and implementation of a special-purpose static program analyzer for safety-critical real-time embedded software. In: Mogensen, T.Æ., Schmidt, D.A., Sudborough, I.H. (eds.) The Essence of Computation. LNCS, vol. 2566, pp. 85–108. Springer, Heidelberg (2002)
Blanchet, B., Cousot, P., Cousot, R., Feret, J., Mauborgne, L., Miné, A., Monniaux, D., Rival, X.: A static analyzer for large safety-critical software. In: Proc. PLDI 2003. ACM Press, New York (2003)
Cousot, P.: Méthodes itératives de construction et d’approximation de points fixes d’opérateurs monotones sur un treillis, analyse sémantique des programmes. PhD thesis, Université Scientifique et Médicale de Grenoble (1978)
Cousot, P., Cousot, R.: Abstract interpretation: a unified lattice model for static analysis of programs by construction or approximation of fixpoints. In: Proc. POPL 1977. ACM Press, New York (1977)
Cousot, P., Cousot, R.: Abstract interpretation frameworks. Journal of logic and computation 2(4) (August 1992)
Feret, J.: Static analysis of digital filters. In: Schmidt, D. (ed.) ESOP 2004. LNCS, vol. 2986, pp. 33–48. Springer, Heidelberg (2004)
Leroy, X., Doligez, D., Garrigue, J., Rémy, D., Vouillon, J.: The Objective Caml system, documentation and user’s manual. Technical report, INRIA (2002)
Miné, A.: The octagon abstract domain. In: Proc. WCRE 2001 (AST 2001). IEEE, Los Alamitos (2001)
Miné, A.: Relational abstract domains for the detection of floating-point run-time errors. In: Schmidt, D. (ed.) ESOP 2004. LNCS, vol. 2986, pp. 3–17. Springer, Heidelberg (2004)
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Feret, J. (2005). The Arithmetic-Geometric Progression Abstract Domain. In: Cousot, R. (eds) Verification, Model Checking, and Abstract Interpretation. VMCAI 2005. Lecture Notes in Computer Science, vol 3385. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-30579-8_3
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DOI: https://doi.org/10.1007/978-3-540-30579-8_3
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-24297-0
Online ISBN: 978-3-540-30579-8
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