Abstract Interpretation with Higher-Dimensional Ellipsoids and Conic Extrapolation

Mendes Oulamara (1) , Arnaud J. Venet (2, 3)

1 ENS-PSL - École normale supérieure - Paris
2 ARC - NASA Ames Research Center
3 CMU - Carnegie Mellon University [Pittsburgh]

The inference and the verification of numerical relationships among variables of a program is one of the main goals of static analysis. In this paper, we propose an Abstract Interpretation framework based on higher-dimensional ellipsoids to automatically discover symbolic quadratic invariants within loops, using loop counters as implicit parameters. In order to obtain non-trivial invariants, the diameter of the set of values taken by the numerical variables of the program has to evolve (sub-)linearly during loop iterations. These invariants are called ellipsoidal cones and can be seen as an extension of constructs used in the static analysis of digital filters. Semidefinite programming is used to both compute the numerical results of the domain operations and provide proofs (witnesses) of their correctness.

Mots clés: static analysis; semidefinite programming; ellipsoids; conic extrapolation

Domaines: Systèmes et contrôle [cs.SY]; Automatique

Mendes Oulamara, Arnaud J. Venet. Abstract Interpretation with Higher-Dimensional Ellipsoids and Conic Extrapolation. Computer Aided Verification, Daniel Kroening; Corina S. Păsăreanu, Jul 2015, San Francisco, United States. ⟨10.1007/978-3-319-21690-4_24⟩. ⟨hal-01202346⟩