An Automaton Learning Approach to Solving Safety Games over Infinite Graphs
This work addresses the challenge of controller synthesis in infinite-state systems for applications like robotic motion planning, representing an incremental improvement over existing methods by adapting automata learning to handle large or infinite state spaces.
The paper tackles the problem of synthesizing finite-state reactive controllers for safety games over infinite graphs, which are impractical for conventional synthesis techniques, by proposing an automata learning approach that constructs controllers using a symbolic representation and iterative refinement with counterexamples, achieving performance evaluated on robotic motion planning examples.
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.