PSPACE-高难度 2D 超级马里奥游戏：十三道门

arXiv - CS - Computational Complexity Pub Date : 2024-04-16 DOI:arxiv-2404.10380

MIT Hardness Group, Hayashi Ani, Erik D. Demaine, Holden Hall, Matias Korman

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引用次数: 0

摘要

我们证明了《超级马里奥兄弟》2D 平台视频游戏系列中 15 款游戏的 PSPACE-hardness。在此之前，只有最初的《超级马里奥兄弟》被认为是 PSPACE-困难的（FUN 2016），尽管我们研究的几款游戏被认为是 NP-困难的（FUN 2014）。我们的还原用打开、关闭和横向穿越来构建门小工具，在每种情况下都使用了游戏特有的机制。虽然我们的一些门构造与 FUN2016 中的相似，但《超级马里奥兄弟 2》、《超级马里奥乐园 2》、《超级马里奥世界 2》和《新超级马里奥兄弟》系列的门构造却截然不同；值得注意的是，《超级马里奥兄弟 2》的门极其困难。只有两款 2DMario 游戏（《超级马里奥乐园》和《超级马里奥跑酷》）的门仍然难以捉摸；我们证明了这些游戏至少是 NP 难的。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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PSPACE-Hard 2D Super Mario Games: Thirteen Doors

We prove PSPACE-hardness for fifteen games in the Super Mario Bros. 2D platforming video game series. Previously, only the original Super Mario Bros. was known to be PSPACE-hard (FUN 2016), though several of the games we study were known to be NP-hard (FUN 2014). Our reductions build door gadgets with open, close, and traverse traversals, in each case using mechanics unique to the game. While some of our door constructions are similar to those from FUN 2016, those for Super Mario Bros. 2, Super Mario Land 2, Super Mario World 2, and the New Super Mario Bros. series are quite different; notably, the Super Mario Bros. 2 door is extremely difficult. Doors remain elusive for just two 2D Mario games (Super Mario Land and Super Mario Run); we prove that these games are at least NP-hard.

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arXiv - CS - Computational Complexity

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