Computational Complexity of Game Boy Games

TL;DR

This paper investigates the computational complexity of several classic Game Boy games, proving they are NP-hard through reductions from well-known NP-complete problems, thus highlighting their computational difficulty.

Contribution

It provides the first rigorous proofs that certain popular Game Boy games are NP-hard, using novel reductions from classic NP-complete problems.

Findings

Donkey Kong, Wario Land, Harvest Moon GB, and Mole Mania are NP-hard.

Reductions are from Sat, 3-Cnf-Sat, Hamiltonian Cycle, and Knapsack.

Additional NP-hardness proofs for Lock 'n' Chase and The Lion King.

Abstract

We analyze the computational complexity of several popular video games released for the Nintendo Game Boy video game console. We analyze the complexity of generalized versions of four popular Game Boy games: Donkey Kong, Wario Land, Harvest Moon GB, and Mole Mania. We provide original proofs showing that these games are \textbf{NP}-hard. Our proofs rely on Karp reductions from four of Karp's original 21 \textbf{NP}-complete problems: \textsc{Sat}, \textsc{3-Cnf-Sat}, \textsc{Hamiltonian Cycle}, and \textsc{Knapsack}. We also discuss proofs easily derived from known results demonstrating the \textbf{NP}-hardness of Lock `n' Chase and The Lion King.