An Automaton Learning Approach to Solving Safety Games over Infinite Graphs

Abstract

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.