Synthesising Succinct Strategies in Safety Games

TL;DR

This paper introduces a formal framework using alternating simulation to improve the efficiency and succinctness of strategies in safety games, applicable to various synthesis problems.

Contribution

It formalizes properties of state relations via alternating simulation and leverages this to enhance algorithm efficiency and strategy representation in safety games.

Findings

Improved running time of the OTFUR algorithm for safety games

Achieved more succinct representations of winning strategies

Applicable to LTL synthesis, scheduler synthesis, and timed automata determinisation

Abstract

Finite turn-based safety games have been used for very different problems such as the synthesis of linear temporal logic (LTL), the synthesis of schedulers for computer systems running on multiprocessor platforms, and also for the determinisation of timed automata. In these contexts, games are implicitly defined, and their size is at least exponential in the size of the input. Nevertheless, there are natural relations between states of arenas of such games. We first formalise the properties that we expect on the relation between states, thanks to the notion of alternating simulation. Then, we show how such simulations can be exploited to (1) improve the running time of the OTFUR algorithm to compute winning strategies and (2) obtain a succinct representation of a winning strategy. We also show that our general theory applies to the three applications mentioned above.