Trains, games, and complexity: 0/1/2-player motion planning through input/output gadgets.

We analyze the computational complexity of motion planning through local "input/output" gadgets with separate entrances and exits, and a subset of allowed traversals from entrances to exits, each of which changes the state of the gadget and thereby the allowed traversals. We study such gadgets in the zero-, one-, and two-player settings, in particular extending past motion-planning-through-gadgets work [7,8] to zero-player games for the first time, by considering "branchless" connections between gadgets that route every gadget's exit to a unique gadget's entrance. Our complexity results include containment in L, NL, P, NP, and PSPACE; as well as hardness for NL, P, NP, and PSPACE. We apply these results to show PSPACE-completeness for certain mechanics in the video games Factorio, [the Sequence], and a restricted version of Trainyard, improving the result of [3]. This work strengthens prior results on switching graphs, ARRIVAL [6] , and reachability switching games [10]. [ABSTRACT FROM AUTHOR]