Delta-Complete Analysis for Bounded Reachability of Hybrid Systems

We present the framework of δ-complete analysis for bounded reachability problems of general hybrid systems. We perform bounded reachability checking through solving δ-decision problems over the reals. The techniques take into account of robustness properties of the systems under numerical perturbations. We prove that the verification problems become much more mathematically tractable in this new framework. Our implementation of the techniques, an open-source tool dReach, scales well on several highly nonlinear hybrid system models that arise in biomedical and robotics applications.