PSPACE-completeness of Pulling Blocks to Reach a Goal
Hayashi Ani, Sualeh Asif, Erik D. Demaine, Jenny Diomidova, Dylan, Hendrickson, Jayson Lynch, Sarah Scheffler, Adam Suhl
TL;DR
This paper establishes the computational complexity of various pulling-block puzzles, proving most are PSPACE-complete and one is NP-hard, depending on different problem parameters such as pulling options and gravity.
Contribution
It systematically analyzes the complexity of a broad class of pulling-block problems, identifying which variants are PSPACE-complete or NP-hard.
Findings
Most pulling-block problems are PSPACE-complete.
One problem variant is NP-hard.
Complexity depends on parameters like pulling strength and gravity.
Abstract
We prove PSPACE-completeness of all but one problem in a large space of pulling-block problems where the goal is for the agent to reach a target destination. The problems are parameterized by whether pulling is optional, the number of blocks which can be pulled simultaneously, whether there are fixed blocks or thin walls, and whether there is gravity. We show NP-hardness for the remaining problem, Pull?-1FG (optional pulling, strength 1, fixed blocks, with gravity).
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