The Complexity of LTL Rational Synthesis

In rational synthesis, we automatically construct a reactive system that satisfies its specification in all rational environments, namely environments that have objectives and act to fulfill them. We complete the study of the complexity of LTL rational synthesis, when the objectives are given by formulas in Linear Temporal Logic. Our contribution is threefold. First, we tighten the known upper bounds for settings that were left open in earlier work. Second, our complexity analysis is parametric, and we describe tight upper and lower bounds in each of the problem parameters: the game graph, the objectives of the system components, and the objectives of the environment components. Third, we generalize the definition of rational synthesis by adding hostile players to the setting and by combining the cooperative and non-cooperative approaches studied in earlier work.