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 0-, 1-, and 2-player settings, in particular extending past motion-planningthrough-gadgets work [DGLR18, DHL20] to 0-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 Factorio, [the Sequence], and a restricted version of Trainyard, improving the result of [ALP18a]. This work strengthens prior results on switching graphs [DGK + 17] and reachability switching games [FGMS18].

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Consider an agent traversing a graph of “gadgets”, where each gadget has local state that changes with each traversal by the agent according to specified rules. Prior work has studied the computational complexity of deciding whether the agent can reach a specified location, a problem we call reachability. This paper introduces new goals for the agent, aiming to characterize when the computational complexity of these problems is the same or differs from that of reachability. First we characterize the complexity of universal traversal—where the goal is to traverse every gadget at least once—for DAG gadgets (partially), one-state gadgets, and reversible deterministic gadgets. Then we study the complexity of reconfiguration—where the goal is to bring the system of gadgets to a specified state. We prove many cases PSPACE-complete, and show in some cases that reconfiguration is strictly harder than reachability, while in other cases, reachability is strictly harder than reconfiguration.

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