We prove PSPACE-completeness of Push-1: given a rectangular grid of 1 x 1 cells, each possibly occupied by a movable block, can a robot move from one specified location to another, given the ability to push up to one block at a time? In particular, we remove the need for fixed (immovable) walls from a 2022 result. This fundamental model of block pushing, introduced in 1999, abstracts the mechanics of many video games. It was shown NP-hard in 2000, but its final complexity remained open for 25 years. Our result uses a new framework for checkable gadgets/gizmos, extending a prior framework for checkable gadgets to handle reconfiguration problems, at the cost of requiring a stronger auxiliary gadget. We also introduce a new connection between the motion-planning-through-gadgets framework (with an agent) and the Graph Orientation Reconfiguration Problem (with no agent), including Nondeterministic Constraint Logic.

翻译：我们证明了推-1问题的PSPACE完全性：给定一个由1×1单元格组成的矩形网格，每个单元格可能被可移动方块占据，在每次最多能推动一个方块的能力下，机器人能否从指定起始位置移动到另一指定位置？特别地，我们移除了2022年结果中对固定（不可移动）墙壁的需求。这一于1999年提出的基础推箱子模型，抽象了许多电子游戏的机制。它于2000年被证明是NP难的，但其最终复杂度在长达25年间悬而未决。我们的结果采用了一种新的可检查机关/小机件框架，将先前的可检查机关框架扩展至可处理重构问题，代价是需要更强的辅助小机件。我们还建立了（含智能体的）机关路径规划框架与（无智能体的）图定向重构问题之间的新联系，包括非确定性约束逻辑。