Abstract
We build a new, implicitly relational abstract domain which gives accurate under-approximations of the set of real values that program variables can take. This statement is demonstrated both on a theoretical basis and on non-trivial numerical examples. It is, we believe, the first non-trivial under-approximating numerical domain in the static analysis literature.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Chapoutot, A., Martel, M.: Différentiation automatique et formes de Taylor en analyse statique de programmes numériques (in French). In: AFADL 2007 (2007)
Costan, A., Gaubert, S., Goubault, E., Martel, M., Putot, S.: A policy iteration algorithm for computing fixed points in static analysis of programs. In: Etessami, K., Rajamani, S.K. (eds.) CAV 2005. LNCS, vol. 3576, Springer, Heidelberg (2005)
Cousot, P., Cousot, R.: Abstract interpretation: A unified lattice model for static analysis of programs by construction of approximations of fixed points. Principles of Programming Languages 4, 238–252 (1977)
Cousot, P., Cousot, R.: Abstract interpretation frameworks. Journal of Logic and Computation 2(4), 511–547 (1992)
Cousot, P., Halbwachs, N.: Automatic discovery of linear restraints among variables of a program. In: POPL 1978, pp. 84–97 (1978)
Dams, D., Gerth, R., Grumberg, O.: Abstract interpretation of reactive systems. ACM Trans. Prog. Lang. Systems 19, 253–291 (1997)
Goldsztejn, A.: Modal intervals revisited. Reliable Computing (submitted)
Goldsztejn, A., Daney, D., Rueher, M., Taillibert, P.: Modal intervals revisited: a mean-value extension to generalized intervals. In: QCP 2005 (2005)
Goubault, E., Putot, S.: Static analysis of numerical algorithms. In: Yi, K. (ed.) SAS 2006. LNCS, vol. 4134, pp. 18–34. Springer, Heidelberg (2006)
Grumberg, O., Lerda, F., Strichman, O., Theobald, M.: Proof-guided underapproximation-widening for multi-process systems. In: POPL (2005)
Kaucher, E.W.: Interval analysis in the extended interval space IR. Computing (Supplementum) 2, 33–49 (1980)
Kaucher, E.W.: Uber metrische und algebraische eigenshaften einiger beim numerischen rechnen auftretender raume, PhD thesis, Karlsruhe (1973)
Miné, A.: A new numerical abstract domain based on difference-bound matrices. In: Danvy, O., Filinski, A. (eds.) PADO 2001. LNCS, vol. 2053, pp. 155–172. Springer, Heidelberg (2001)
Pasareanu, C.S., Pelánek, R., Visser, W.: Concrete model checking with abstract matching and refinement. In: Etessami, K., Rajamani, S.K. (eds.) CAV 2005. LNCS, vol. 3576, pp. 52–66. Springer, Heidelberg (2005)
Schmidt, D.A.: A calculus of logical relations for over- and underapproximating static analyses. Sci. Comput. Program 64(1), 29–53 (2007)
Schmidt, D.A.: Underapproximating predicate transformers. In: Yi, K. (ed.) SAS 2006. LNCS, vol. 4134, pp. 127–143. Springer, Heidelberg (2006)
Stolfi, J., de Figueiredo, L.H.: An introduction to affine arithmetic, TEMA (2003)
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
� 2007 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Goubault, E., Putot, S. (2007). Under-Approximations of Computations in Real Numbers Based on Generalized Affine Arithmetic. In: Nielson, H.R., Fil�, G. (eds) Static Analysis. SAS 2007. Lecture Notes in Computer Science, vol 4634. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-74061-2_9
Download citation
DOI: https://doi.org/10.1007/978-3-540-74061-2_9
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-74060-5
Online ISBN: 978-3-540-74061-2
eBook Packages: Computer ScienceComputer Science (R0)