Fixpoint computation in the polyhedra abstract domain using convex and numerical analysis tools

Conference of 14th International Conference on Verification, Model Checking, and Abstract Interpretation, VMCAI 2013 ; Conference Date: 20 January 2013 Through 22 January 2013; Conference Code:102475International audiencePolyhedra abstract domain is one of the most expressive and used abstract domains for the static analysis of programs. Together with Kleene algorithm, it computes precise yet costly program invariants. Widening operators speed up this computation and guarantee its termination, but they often induce a loss of precision, especially for numerical programs. In this article, we present a process to accelerate Kleene iteration with a good trade-off between precision and computation time. For that, we use two tools: convex analysis to express the convergence of convex sets using support functions, and numerical analysis to accelerate this convergence applying sequence transformations. We demonstrate the efficiency of our method on benchmarks