NP-Completeness Proofs of Puzzles using the T-Metacell Framework

TL;DR

This paper uses the T-metacell framework to prove NP-completeness of four pencil puzzles, revealing their computational difficulty and extending the framework's applicability to diverse puzzle constraints.

Contribution

It introduces NP-completeness proofs for four new pencil puzzles using the T-metacell framework, also establishing three as ASP-complete.

Findings

Four puzzles are NP-complete.

Grand Tour, Entry Exit, Zahlenschlange are ASP-complete.

Framework demonstrates versatility across puzzle types.

Abstract

Pencil puzzles are puzzles that can be solved by writing down solutions on a paper, using only logical reasoning. In this paper, we utilize the "T-metacell" framework developed by Tang and the MIT Hardness Group to prove the NP-completeness of four new pencil puzzles: Grand Tour, Entry Exit, Zahlenschlange, and Yagit. Additionally, the first three are also proven to be ASP-complete. The results demonstrate how versatile the framework is, offering new insights into the computational complexity of problems with various constraints.