Abstract
Using the notion of visibility representations, our paper establishes a new property of instances of the Nondeterministic Constraint Logic (NCL) problem (a $$\textrm{PSPACE}$$ -complete problem that is very convenient to prove the $$\textrm{PSPACE}$$ -hardness of reversible games with pushing blocks). Direct use of this property introduces an explosion in the number of gadgets needed to show $$\textrm{PSPACE}$$ -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 $$\textrm{NP}$$ -hard—to prove it is in fact $$\textrm{PSPACE}$$ -complete.
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