Hybridfluctuat: a static analyzer of numerical programs within a continuous environment

Abstract. A new static analyzer is described, based on the analyzer Fluctuat. Its goal is to synthetize invariants for hybrid systems, encompassing a continuous environment described by a system of possibly switched ODEs, and an ANSI C program, in interaction with it. The evolution of the continuous environment is over-approximated using a guaranteed integrator that we developped, and special assertions are added to the program that simulate the action of sensors and actuators, making the continuous environment and the program communicate. We demonstrate our approach on an industrial case study 3, a part of the flight control software of ASTRIUM’s Automated Transfer Vehicle (ATV).

S.: Static analysis of finite precision computations

Abstract. We define several abstract semantics for the static analysis of finite precision computations, that bound not only the ranges of values taken by numerical variables of a program, but also the difference with the result of the same sequence of operations in an idealized real number semantics. These domains point out with more or less detail (control point, block, function for instance) sources of numerical errors in the program and the way they were propagated by further computations, thus allowing to evaluate not only the rounding error, but also sensitivity to inputs or parameters of the program. We describe two classes of abstractions, a non relational one based on intervals, and a weakly relational one based on parametrized zonotopic abstract domains called affine sets, especially well suited for sensitivity analysis and test generation. These abstract domains are implemented in the Fluctuat static analyzer, and we finally present some experiments.

Proving the correctness of the implementation of a control-command algorithm

Abstract. In this article, we study the interactions between a controlcommand program and its physical environment via sensors and actuators. We are interested in finding invariants on the continuous trajectories of the physical values that the program is supposed to control. The invariants we are looking for are periodic sequences of intervals that are abstractions of the values read by the program. To compute them, we first build octrees that abstract the impact of the program on its environment. Then, we compute a period of the abstract periodic sequence and we finally define the values of this sequence as the fixpoint of a monotone map. We present a prototype analyzer that computes such invariants for C programs using a simple specification language for describing the continuous environment. It shows good results on classical benchmarks for hybrid systems verification. 1 Introduction. The behavior of an embedded, control-command program depends on both