  This paper presents a property-directed approach to verifying recurrent
neural networks (RNNs). To this end, we learn a deterministic finite automaton
as a surrogate model from a given RNN using active automata learning. This
model may then be analyzed using model checking as verification technique. The
term property-directed reflects the idea that our procedure is guided and
controlled by the given property rather than performing the two steps
separately. We show that this not only allows us to discover small
counterexamples fast, but also to generalize them by pumping towards faulty
flows hinting at the underlying error in the RNN.
