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

Y. Seladji (1) , O. Bouissou (1)

1 DILS - Département Ingénierie Logiciels et Systèmes

Polyhedra 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.

Keywords: Geometry; Iterative methods; Model checking; Set theory; Static analysis; Tools; Abstract domains; Computation time; Convex analysis; Fixpoint computations; Numerical programs; Program invariants; Support functions; Widening operators; Abstracting

Domains: Computer Science [cs]

Y. Seladji, O. Bouissou. Fixpoint computation in the polyhedra abstract domain using convex and numerical analysis tools. Verification, Model Checking, and Abstract Interpretation. VMCAI 2013. Lecture Notes in Computer Science, Jan 2013, Rome, Italy. pp.149-168, ⟨10.1007/978-3-642-35873-9_11⟩. ⟨cea-01834985⟩