A Framework for Loop and Path Puzzle Satisfiability NP-Hardness Results
Hadyn Tang
TL;DR
This paper introduces a general framework using a 'T-metacell' gadget to prove NP-hardness for various loop and path puzzles, advancing understanding of their computational complexity.
Contribution
The paper presents a novel, versatile framework for establishing NP-hardness of multiple puzzle genres through a unified gadget-based approach.
Findings
Proves NP-completeness for several loop and path puzzles
Introduces the 'T-metacell' gadget as a key tool
Discusses limitations of the gadget in complexity proofs
Abstract
Building on the results published in arxiv:2004.12849 we present a general framework for demonstrating the NP-hardness of satisfying many genres of loop and path puzzles using a 'T-metacell' gadget. We then use this to prove the NP-completeness of a variety of such genres, and discuss some of the limitations of this gadget.
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