We study the problem of deciding the winner of reachability switching games for zero-, one-, and two-player variants. Switching games provide a deterministic analogue of stochastic games. We show that the zero-player case is NL-hard, the one-player case is NP-complete, and that the two-player case is PSPACE-hard and in EXPTIME. For the zero-player case, we also show P-hardness for a succinctly-represented model that maintains the upper bound of NP $\cap$ coNP. For the one- and two-player cases, our results hold in both the natural, explicit model and succinctly-represented model. Our results show that the switching variant of a game is harder in complexity-theoretic terms than the corresponding stochastic version.

• 03E75 - Applications of set theory
• 18A99 - General theory of categories and functors