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Reachability Switching Games

by   John Fearnley, et al.
University of Liverpool
University of Bonn

In this paper, we study the problem of deciding the winner of reachability switching games. These games provide deterministic analogues of Markovian systems. We study zero-, one-, and two-player variants of these 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. In the one- and two-player cases, the problem of determining the winner of a switching game turns out to be much harder than the problem of determining the winner of a Markovian game. We also study the structure of winning strategies in these games, and in particular we show that both players in a two-player reachability switching game require exponential memory.


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