defy gravity：Hanano Puzzle的复杂性
Defying Gravity: The Complexity of the Hanano Puzzle
AI总结：
本文利用NCL实例的可见性表示性质，将PSPACE困难性证明所需小装置从32个减至一般3个、特定情形2个，并据此通过多项式时间多一归约证明Hanano Puzzle是PSPACE完全的。
摘要：
利用可见性表示的概念，本文建立了非确定性约束逻辑（Nondeterministic Constraint Logic，NCL）问题实例的一项新性质；该问题是一个PSPACE完全问题，非常便于证明带推方块的可逆游戏的PSPACE困难性。直接使用这一性质会导致证明PSPACE困难性所需的小装置数量激增，但我们展示了如何将该数量从32个一般地减少到仅3个，并在一种特定情形下减少到2个！我们提议将其作为迈向研究具有不可逆重力的游戏的更广泛、更通用框架的一步，并利用这一联系引导从NCL问题到Hanano Puzzle的间接多项式时间多一归约——Hanano Puzzle已知是NP困难的——以证明它实际上是PSPACE完全的。
英文摘要：
Using the notion of visibility representations, our paper establishes a new property of instances of the Nondeterministic Constraint Logic (NCL) problem (a PSPACE-complete problem that is very convenient to prove the PSPACE-hardness of reversible games with pushing blocks). Direct use of this property introduces an explosion in the number of gadgets needed to show PSPACE-hardness, but we show how to bring that number from 32 down to only three in general, and down to two in a specific case! We propose it as a step towards a broader and more general framework for studying games with irreversible gravity, and use this connection to guide an indirect polynomial-time many-one reduction from the NCL problem to the Hanano Puzzle -- which is NP-hard -- to prove it is in fact PSPACE-complete.
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。
