1 x 1 Rush Hour with Fixed Blocks是PSPACE完整的
1 x 1 Rush Hour with Fixed Blocks is PSPACE-complete
摘要：
考虑$n^2-1$单元--$n \times n$正方形板中的正方形块，其中每个块被标记为水平可移动（仅）、垂直可移动（仅）或不可移动--这是尖峰时刻的一种变体，只有$1 \times 1$汽车和固定块。我们证明了它是PSPACE-完全的，以决定是否一个给定的块可以达到板的左边缘，通过减少从非确定性约束逻辑通过2-颜色定向地铁洗牌。相比之下，多项式时间算法是已知的，用于决定给定块是否可以移动一个空间，或者每个块何时是不可移动的或者可以水平和垂直移动。我们的结果回答了Tromp和Cilibrasi提出的一个15年前的开放问题，并加强了以前的PSPACE完整性结果与垂直$1 \times 2$和水平$2 \times 1$可移动块和4色地铁洗牌。
英文摘要：
Consider $n^2-1$ unit-square blocks in an $n \times n$ square board, where each block is labeled as movable horizontally (only), movable vertically (only), or immovable -- a variation of Rush Hour with only $1 \times 1$ cars and fixed blocks. We prove that it is PSPACE-complete to decide whether a given block can reach the left edge of the board, by reduction from Nondeterministic Constraint Logic via 2-color oriented Subway Shuffle. By contrast, polynomial-time algorithms are known for deciding whether a given block can be moved by one space, or when each block either is immovable or can move both horizontally and vertically. Our result answers a 15-year-old open problem by Tromp and Cilibrasi, and strengthens previous PSPACE-completeness results for Rush Hour with vertical $1 \times 2$ and horizontal $2 \times 1$ movable blocks and 4-color Subway Shuffle.
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。
