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Games on graphs provide a natural model for reactive non-terminating systems.In such games, the interaction of two players on an arena results in aninfinite path that describes a run of the system. Different settings are usedto model various open systems in computer science, as for instance turn-basedor concurrent moves, and deterministic or stochastic transitions. In thispaper, we are interested in turn-based games, and specifically in deterministicparity games and stochastic reachability games (also known as simple stochasticgames). We present a simple, direct and efficient reduction from deterministicparity games to simple stochastic games: it yields an arena whose size islinear up to a logarithmic factor in size of the original arena.

A reduction from parity games to simple stochastic games