Acceleration in Data-Flow Analysis

Acceleration in symbolic verification consists in computing the exact effect of some control-flow loops in order to speed up the iterative fix-point computation of reachable states. Even if no termination guarantee is provided in theory, successful results were obtained in practice by different tools implementing this framework. In this presentation, the acceleration framework is extended to data-flow analysis. Compared to a classical widening/narrowing-based abstract interpretation, the loss of precision is controlled here by the choice of the abstract domain and does not depend on the way the abstract value is computed. Our approach is geared towards precision, but we don't loose efficiency on the way. Indeed, we provide a cubic-time acceleration-based algorithm for solving interval constraints with full multiplication. We extends investigation to acceleration in convex data-flow analysis of systems with real-valued variables where guards are convex polyhedra and assignments are translations. In particular, we present a simple and algorithmically efficient characterization of MFP-acceleration for cycles with a unique initial location. We also show that the MFP-solution is a computable algebraic polyhedron for systems with two variables.

This is joint work with Grégoire Sutre (LaBRI, Bordeaux, France).