Symbolic Verification and Strategy Synthesis for Turn-based Stochastic Games

TL;DR

This paper presents a symbolic approach using multi-terminal binary decision diagrams for verifying and synthesizing strategies in turn-based stochastic games, improving efficiency and compactness over existing methods.

Contribution

It introduces a symbolic implementation for strategy synthesis in turn-based stochastic games, demonstrating improved performance and strategy compactness.

Findings

Symbolic methods outperform some existing approaches in efficiency.

Strategies synthesized are significantly more compact.

The approach is effective on a diverse set of benchmarks.

Abstract

Stochastic games are a convenient formalism for modelling systems that comprise rational agents competing or collaborating within uncertain environments. Probabilistic model checking techniques for this class of models allow us to formally specify quantitative specifications of either collective or individual behaviour and then automatically synthesise strategies for the agents under which these specifications are guaranteed to be satisfied. Although good progress has been made on algorithms and tool support, efficiency and scalability remain a challenge. In this paper, we investigate a symbolic implementation based on multi-terminal binary decision diagrams. We describe how to build and verify turn-based stochastic games against either zero-sum or Nash equilibrium based temporal logic specifications. We collate a set of benchmarks for this class of games, and evaluate the performance of our approach, showing that it is superior in a number of cases and that strategies synthesised in a symbolic fashion can be considerably more compact.