Conference Paper

The Zonotope Abstract Domain Taylor1+.

DOI: 10.1007/978-3-642-02658-4_47 Conference: Computer Aided Verification, 21st International Conference, CAV 2009, Grenoble, France, June 26 - July 2, 2009. Proceedings
Source: DBLP

ABSTRACT Static analysis by abstract interpretation [1] aims at automatically inferring properties on the behaviour of programs. We
focus here on a specific kind of numerical invariants: the set of values taken by numerical variables, with a real numbers
semantics, at each control point of a program.

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    ABSTRACT: Embedded system control often relies on linear systems, which admit quadratic invariants. The parts of the code that host linear system implementations need dedicated analysis tools, since intervals or linear abstract domains will give imprecise results, if any at all, on these systems. Previous work by FERET proposes a specific abstraction for digital filters that addresses this issue on a specific class of controllers. This paper aims at generalizing the idea. It works directly on system representation, relying on existing methods from control theory to automatically generate quadratic invariants for linear time invariant systems, whose stability is provable. This class encompasses n-th order digital filters and, in general, controllers embedded in critical systems. While control theorists only focus on the existence of such invariants, this paper proposes a method to effectively compute tight ones. The method has been implemented and applied to some benchmark systems, giving good results. It also considers floating points issues and validates the soundness of the computed invariants.
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    ABSTRACT: Being able to analyze programs function by function, or module by module is a key ingredient to scalable static analyses. The main difficulty for modular static analysis is to be able to do so while not losing too much precision. In this paper, we present a new summary-based approach that builds on previous work of the authors, a zonotopic functional abstraction, that is economical both in space and time complexity. This approach has been implemented, and experiments on numerical programs, reported here, show that this approach is very efficient, and that we still obtain precise analyses in realistic cases.
    Proceedings of the 19th international conference on Static Analysis; 09/2012
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    ABSTRACT: Zonotopes are a convenient abstract domain for the precise analysis of programs with numerical variables. Compared to the domain of convex polyhedra, it is less expensive and may easily handle non-linear assignments. However, the classical join operator of this abstract domain does not always preserve linear invariants, unlike the convex hull. We present a global join operator that preserves some affine relations. We end up by showing some experiments conducted on the constrained Taylor1+ domain of Apron.
    Electronic Notes in Theoretical Computer Science 11/2012; 287:65–76.

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