推拉块拼图很难
Push-Pull Block Puzzles are Hard
摘要：
本文证明了3D推拉积木问题是PSPACE-完全可解的，而2D薄壁推拉积木问题是NP-难解的，解决了Zubaran和Ritt的一个公开问题。推拉方块拼图是一种娱乐性的运动规划问题，类似于推箱子，涉及在有$1 \times 1$障碍物的正方形网格上移动“机器人”。机器人无法穿越障碍物，但有些障碍物可以被机器人推到相邻的方格中。薄墙阻止两个相邻的方块之间的移动。这项工作遵循了一长串的算法和复杂性的工作类似的问题。2D推拉方块拼图出现在视频游戏Pukoban以及塞尔达传说：过去的链接中，为后者提供了另一个硬度证明。这种推块谜题的变体特别有趣，因为它与可逆性有关，因为任何动作（例如，推或拉）可以被另一有效动作（例如，拉或推）。
英文摘要：
This paper proves that push-pull block puzzles in 3D are PSPACE-complete to solve, and push-pull block puzzles in 2D with thin walls are NP-hard to solve, settling an open question by Zubaran and Ritt. Push-pull block puzzles are a type of recreational motion planning problem, similar to Sokoban, that involve moving a `robot' on a square grid with $1 \times 1$ obstacles. The obstacles cannot be traversed by the robot, but some can be pushed and pulled by the robot into adjacent squares. Thin walls prevent movement between two adjacent squares. This work follows in a long line of algorithms and complexity work on similar problems. The 2D push-pull block puzzle shows up in the video games Pukoban as well as The Legend of Zelda: A Link to the Past, giving another proof of hardness for the latter. This variant of block-pushing puzzles is of particular interest because of its connections to reversibility, since any action (e.g., push or pull) can be inverted by another valid action (e.g., pull or push).
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