Trains, Games, and Complexity: 0/1/2-Player Motion Planning through Input/Output Gadgets

Hayashi Ani; Erik D. Demaine; Dylan H. Hendrickson; Jayson Lynch

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arXiv · 2005.03192

Trains, Games, and Complexity: 0/1/2-Player Motion Planning through Input/Output Gadgets

Hayashi Ani·Erik D. Demaine·Dylan H. Hendrickson·Jayson Lynch

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Abstract

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].

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Hayashi Ani, Erik D. Demaine, Dylan H. Hendrickson, Jayson Lynch. 2020-05-07. Trains, Games, and Complexity: 0/1/2-Player Motion Planning through Input/Output Gadgets. https://arxiv.org/abs/2005.03192

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