Synthesising succinct strategies in safety games with an application to real-time scheduling

We introduce general techniques to compute, efficiently, succinct representations of winning strategies in safety and reachability games. Our techniques adapt the antichain framework to the setting of games, and rely on the notion of turn-based alternating simulation, which is used to formalise natural relations that exist between the states of those games in many applications. Then, we demonstrate the applicability of our approach by considering an important problem borrowed from the real-time scheduling community, i.e. the problem of finding a correct schedule(r) for a set of sporadic tasks upon a multiprocessor platform. We formalise this problem by means of a game whose number of states is exponential in the description of the task set, thereby making it a perfect candidate for our approach. We have implemented our algorithm and show experimentally that it scales better than classical solutions. To the best of our knowledge, this is the first attempt at implementing an exact feasibility test for this particular problem.