通过门是困难的，即使没有楼梯：平面门装置的普遍性和PSPACE难性
Walking through Doors is Hard, even without Staircases: Universality and PSPACE-hardness of Planar Door Gadgets
AI总结：
研究证明在平面系统中通过门装置的可达性问题PSPACE难，且门装置可模拟其他运动规划装置，简化了以往游戏的复杂性证明。
摘要：
一个开合门装置有两状态和三个通道：开启和关闭通道分别设置装置为开启或关闭状态，而通行通道仅在门处于开启状态时可被通过。我们证明判断代理能否通过任意此类门装置系统从一位置移动到另一位置是PSPACE完全的，从而移除了传统需要交叉装置的需要，简化了Lemmings和超级马里奥等游戏的PSPACE难性证明。更进一步，我们证明任何运动规划通过装置框架中的装置均可被平面门装置系统模拟：开合门装置是一个通用装置。我们证明这些结果适用于多种门装置。特别是，开启、关闭和通行通道的位置可以有任意循环顺序围绕门；每个通道可以是定向或非定向；且开启通道可以是可选按钮（具有相同入口和出口位置）。此外，我们还展示了两种更简单的门装置类型（自闭合门装置和对称自闭合门装置）的相同难度和通用性结果。再次证明任何自闭合门装置平面模拟任何装置，因此可达性运动规划问题是PSPACE完全的。然后我们应用此框架证明了八个不同3D马里奥视频游戏和Sokobond的新的PSPACE难性结果。
英文摘要：
An open-close door gadget has two states and three tunnels that can be traversed by an agent (player, robot, etc.): the "opening" and "closing" tunnels set the gadget's state to open and closed, respectively, while the "traverse" tunnel can be traversed if and only if the door is in the open state. We prove that it is PSPACE-complete to decide whether an agent can move from one location to another through a planar system of any such door gadget, removing the traditional need for crossover gadgets and thereby simplifying past PSPACE-hardness proofs of Lemmings and Nintendo games Super Mario Bros., Legend of Zelda, and Donkey Kong Country. Even stronger, we show that any gadget in the motion-planning-through-gadgets framework can be simulated by a planar system of door gadgets: the open-close door gadget is a universal gadget. We prove that these results hold for a variety of door gadgets. In particular, the opening, closing, and traverse tunnel locations can have an arbitrary cyclic order around the door; each tunnel can be directed or undirected; and the opening tunnel can instead be an optional button (with identical entrance and exit locations). Furthermore, we show the same hardness and universality results for two simpler types of door gadgets: self-closing door gadgets and symmetric self-closing door gadgets. Again we show that any self-closing door gadget planarly simulates any gadget, and thus the reachability motion planning problem is PSPACE-complete. Then we apply this framework to prove new PSPACE-hardness results for eight different 3D Mario video games and Sokobond.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
