Assume-Guarantee Strategy Synthesis for Stochastic Games

This thesis presents a framework for the automatic strategy synthesis fromquantitative specifications, in order to control autonomous systems. Wemodel systems as turn-based two-player zero-sum stochastic games, whichare able to express both stochastic and nondeterministic environmentaluncertainty. Given a system model and a specification, we define thestrategy synthesis problem as that of finding a strategy for the systemthat is winning against every environment. Since large, complex systemsare typically built from multiple components, we consider synthesis ofstrategies for the individual components separately, which can then becomposed to a winning strategy for the full system. Modelling interactionbetween components is facilitated using assume-guarantee rules, whichcan express contracts such as “maintain the room temperature of at least20 C, as long as the windows are closed at least 30% of the time.” For thesynthesis of strategies for the individual components, we develop synthesisalgorithms for Boolean combinations of long-run objectives, specifically,maintaining above a threshold (i) a mean-payoff, almost surely; (ii) anexpected mean-payoff; (iii) a ratio of rewards, almost surely; or (iv) aratio of expected rewards. We implement our algorithms in the PRISM-games 2.0 tool and demonstrate their viability on four case studies.