  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 [DGLR18, DHL20] 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 [ALP18a]. This work strengthens prior
results on switching graphs, ARRIVAL [DGK+17], and reachability switching games
[FGMS21].
