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.

翻译：利用可见性表示的概念，本文确立了非确定性约束逻辑（NCL）问题实例的一个新性质（该问题是一个PSPACE完全问题，非常适合用于证明涉及推方块的可逆游戏的PSPACE困难性）。直接使用该性质会导致证明PSPACE困难性所需的构件数量激增，但我们展示如何将该数量从32个普遍减少至仅3个，在特定情况下甚至减少至2个！我们将其视为迈向更广泛的、用于研究具有不可逆重力游戏的通用框架的一步，并利用这一联系指导从NCL问题到NP难的Hanano谜题之间的间接多项式时间多一归约，以证明其实际上为PSPACE完全问题。