ASP-Completeness Proofs of Puzzles Using the T-Metacell Framework

2025-08-15

AI Summary

This paper investigates the computational complexity of four classic pencil-and-paper logic puzzles—Grand Tour, Entry Exit, Yagit, and Zahlenschlange. Addressing their heterogeneous constraint structures, we introduce, for the first time, the T-cell framework to establish Answer Set Programming (ASP) completeness. Through a unified logical encoding and polynomial-time reductions, we rigorously characterize the structural properties of their solution spaces. Our main result proves that all four puzzle classes are ASP-complete—a new complexity-theoretic benchmark for logic puzzles. This work extends the applicability of the T-cell framework beyond prior domains and reveals how diverse local constraints jointly induce high computational hardness. By bridging constraint-based puzzle design with formal complexity theory, our analysis advances the understanding of the intrinsic computational nature of pencil-and-paper logic puzzles.

Technology Category

• Knowledge Representation and Reasoning: Computational Complexity of Reasoning
• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories
• Reasoning under Uncertainty: Other Foundations of Reasoning under Uncertainty

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Web Mining and Content Analysis: Models for Web evolution

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 ASP-completeness of four new pencil puzzles: Grand Tour, Entry Exit, Yagit, and Zahlenschlange. The results demonstrate how versatile the framework is, offering new insights into the computational complexity of problems with various constraints.

Problem

• Proving ASP-completeness of four new pencil puzzles
• Using T-metacell framework for computational complexity analysis
• Exploring versatility of framework in constraint-based problems

Innovation

• Uses T-metacell framework for ASP-completeness proofs
• Applies framework to four new pencil puzzles
• Demonstrates versatility in computational complexity analysis