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].

翻译：我们分析了通过具有独立入口和出口的局部“输入/输出”小工具进行运动规划的计算复杂性，这些小工具允许从入口到出口的受限遍历子集，每次遍历会改变小工具的状态，从而改变允许的遍历方式。我们在零玩家、一玩家和两玩家设定下研究此类小工具，特别地，首次将以往通过小工具进行运动规划的工作 [DGLR18, DHL20] 扩展到零玩家游戏，通过考虑小工具之间的“无分支”连接，将每个小工具的出口路由到唯一一个小工具的入口。我们的复杂性结果包括属于 L、NL、P、NP 和 PSPACE 复杂度类，以及针对 NL、P、NP 和 PSPACE 的困难性。我们将这些结果应用于证明视频游戏《异星工厂》、《[序列]》及《Trainyard》受限版本中某些机制的 PSPACE 完全性，改进了 [ALP18a] 的结果。本研究强化了此前关于切换图、ARRIVAL [DGK+17] 及可达性切换游戏 [FGMS21] 的结果。