Stochastic Games with Disjunctions of Multiple Objectives (Technical Report)

Stochastic games combine controllable and adversarial non-determinism with stochastic behavior and are a common tool in control, verification and synthesis of reactive systems facing uncertainty. In this paper, we study turn-based stochastic two-player games on graphs where the winning condition is to satisfy at least one reachability or safety objective from a given set of alternatives with at least some desired probability. These objectives are also known as disjunctive queries (DQs). We present a fine-grained overview of strategy and computational complexity and provide new lower and upper bounds for several variants of the problem. These results extend the previous literature on DQs significantly. We also propose a novel value iteration-style algorithm for approximating the set of Pareto optimal thresholds for a given DQ.