Trains, Games, and Complexity: 0/1/2-Player Motion Planning through Input/Output Gadgets
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].
Keywords
Cite
@article{arxiv.2005.03192,
title = {Trains, Games, and Complexity: 0/1/2-Player Motion Planning through Input/Output Gadgets},
author = {Hayashi Ani and Erik D. Demaine and Dylan H. Hendrickson and Jayson Lynch},
journal= {arXiv preprint arXiv:2005.03192},
year = {2023}
}
Comments
37 pages, 42 figures. Presented at WALCOM 2022. Expanded version accepted to Theoretical Computer Science