  Identifying safe areas is a key point to guarantee trust for systems that are
based on Deep Neural Networks (DNNs). To this end, we introduce the
AllDNN-Verification problem: given a safety property and a DNN, enumerate the
set of all the regions of the property input domain which are safe, i.e., where
the property does hold. Due to the #P-hardness of the problem, we propose an
efficient approximation method called epsilon-ProVe. Our approach exploits a
controllable underestimation of the output reachable sets obtained via
statistical prediction of tolerance limits, and can provide a tight (with
provable probabilistic guarantees) lower estimate of the safe areas. Our
empirical evaluation on different standard benchmarks shows the scalability and
effectiveness of our method, offering valuable insights for this new type of
verification of DNNs.
