Pushing Blocks via Checkable Gadgets: PSPACE-completeness of Push-1F and Block/Box Dude

Hayashi Ani; Lily Chung; Erik D. Demaine; Jenny Diomidova; Della Hendrickson; Jayson Lynch

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arXiv · 2412.20079

Pushing Blocks via Checkable Gadgets: PSPACE-completeness of Push-1F and Block/Box Dude

Hayashi Ani·Lily Chung·Erik D. Demaine·Jenny Diomidova·Della Hendrickson·Jayson Lynch

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Abstract

We prove PSPACE-completeness of the well-studied pushing-block puzzle Push-1F, a theoretical abstraction of many video games (introduced in 1999). The proof also extends to Push-$k$ for any $k \ge 2$. We also prove PSPACE-completeness of two versions of the recently studied block-moving puzzle game with gravity, Block Dude - a video game dating back to 1994 - featuring either liftable blocks or pushable blocks. Two of our reductions are built on a new framework for "checkable" gadgets, extending the motion-planning-through-gadgets framework to support gadgets that can be misused, provided those misuses can be detected later.

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Hayashi Ani, Lily Chung, Erik D. Demaine, Jenny Diomidova, Della Hendrickson, Jayson Lynch. 2024-12-28. Pushing Blocks via Checkable Gadgets: PSPACE-completeness of Push-1F and Block/Box Dude. https://arxiv.org/abs/2412.20079

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