Defying Gravity: The Complexity of the Hanano Puzzle

05/06/2022

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by   Michael C. Chavrimootoo, et al.

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Liu and Yang [LY19] recently proved the Hanano Puzzle to be NP-≤_m^p-hard. We prove it is in fact PSPACE-≤_m^p-complete. Our paper introduces the notion of a planar grid and establishes a relationship between planar grids and instances of the Nondeterministic Constraint Logic (NCL) problem (a known PSPACE-≤_m^p-complete problem [HD09]) by using graph theoretic methods, and uses this connection to guide an indirect many-one reduction from the NCL problem to the Hanano Puzzle. The technique introduced is versatile and can be reapplied to other games with gravity.