Discretizing Affine Hybrid Automata with Uncertainty

Over-approximating the set of all reachable states of a given system is an important task for the verification of safety properties. Such an unbounded time verification is in particular challenging for hybrid systems. We recently developed an algorithm that over-approximates the set of all reachable states of a given affine hybrid automata by performing linear template-based abstract interpretation [4]. In this article we extend the previous results by adding uncertainty to the model of affine hybrid automata. Uncertainty can be used for abstracting the behavior of non-linear hybrid systems. We adapt our techniques to this model and show that, w.r.t. given linear templates, the abstract reachability problem is still in coNP by reducing abstract reachability for affine hybrid automata with uncertainty to abstract reachability for affine programs (affine hybrid automata where only discrete transitions are allowed). We thus provide a new connection between a continuous time model and a purely discrete model.