Abstract acceleration in Linear relation analysis

Abstract : {Linear Relation Analysis~\cite{cousot78,halbwach79} is now a classical abstract interpretation based on an approximation of reachable numerical states of a program by convex polyhedra. Since it works with a lattice of infinite depth, it makes use of a widening operator to enforce the convergence of fixpoint computations. This paper takes place in the many attempts to improve the precision of the results reached using such a widening. It will first present an extended survey of the existing approaches in that direction. Then it will investigate the cases where the exact (abstract) effect of a loop can be computed. This technique is fully compatible with the use of widening, and whenever it applies, it generally improves both the precision and the performances of the analysis.
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Laure Gonnord, Nicolas Halbwachs. Abstract acceleration in Linear relation analysis. 2010. 〈hal-00785116〉

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