Toward a Sound Analysis of Guarded LTI Loops with Inputs by Abstract Acceleration (extended version)

International audienceIn a POPL 2014 paper, Jeannet et al. showed that abstract acceleration is a relevant approach for general linear loops thanks to the Jordan decomposition of the linear transformer. Bounding the number of loop iterations involves interval-linear constraints. After identifying sources of over-approximation, we present some improvements over their method. First, we improve precision by using interval hulls in the Jordan parameters space instead of the state space, avoiding further interval arithmetic. Then, we show how to use conic hulls instead of interval hulls to further improve precision. Furthermore, we extend their work to handle linear loops with bounded nondeterministic input. This was already attempted by Cattaruzza et al. in a SAS 2015 paper, unfortunately their method is unsound. After explaining why, we propose a sound approach to guarded LTI loops with bounded nondeterministic inputs by reduction to the autonomous case