  We propose a method to construct finite-state reactive controllers for
systems whose interactions with their adversarial environment are modeled by
infinite-duration two-player games over (possibly) infinite graphs. The
proposed method targets safety games with infinitely many states or with such a
large number of states that it would be impractical---if not impossible---for
conventional synthesis techniques that work on the entire state space. We
resort to constructing finite-state controllers for such systems through an
automata learning approach, utilizing a symbolic representation of the
underlying game that is based on finite automata. Throughout the learning
process, the learner maintains an approximation of the winning region
(represented as a finite automaton) and refines it using different types of
counterexamples provided by the teacher until a satisfactory controller can be
derived (if one exists). We present a symbolic representation of safety games
(inspired by regular model checking), propose implementations of the learner
and teacher, and evaluate their performance on examples motivated by robotic
motion planning in dynamic environments.
