Stochastic Games with Disjunctions of Multiple Objectives

Electronic Proceedings in Theoretical Computer Science, vol. 346, pp. 83–100

Abstract

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. Multi-objective stochastic games are natural in situations where several - possibly conflicting - performance criteria like time and energy consumption are relevant. Such conjunctive combinations are the most studied multi-objective setting in the literature. In this paper, we consider the dual disjunctive problem. More concretely, we study turn-based stochastic two-player games on graphs where the winning condition is to guarantee at least one reachability or safety objective from a given set of alternatives. We present a fine-grained overview of strategy and computational complexity of such disjunctive queries (DQs) and provide new lower and upper bounds for several variants of the problem, significantly extending previous works. We also propose a novel value iteration-style algorithm for approximating the set of Pareto optimal thresholds for a given DQ.

Authors 2

1. Tobias Winkler Aachen

   RWTH Aachen University

   Affiliation as printed

   RWTH Aachen University, Aachen, Germany

2. Maximilian Weininger

   Technical University of Munich

   Affiliation as printed

   Technical University of Munich, Germany