This Game Is Not Going To Analyze Itself

TL;DR

This paper rigorously analyzes the computational complexity of the puzzle game 'This Game Is Not Going To Load Itself', establishing its classification within various complexity classes and characterizing optimal arrow tile placements for certain game configurations.

Contribution

It provides a detailed complexity classification of the game across different scenarios and characterizes conditions for perfect arrow tile placements, advancing understanding of the game's computational aspects.

Findings

Game is in Sigma_2^P complexity class.

NP-complete for three colors and six sources.

Simulating the game is NP- and coNP-hard for certain configurations.

Abstract

We analyze the puzzle video game This Game Is Not Going To Load Itself, where the player routes data packets of three different colors from given sources to given sinks of the correct color. Given the sources, sinks, and some previously placed arrow tiles, we prove that the game is in Sigma_2^P; in NP for sources of equal period; NP-complete for three colors and six equal-period sources with player input; and even without player input, simulating the game is both NP- and coNP-hard for two colors and many sources with different periods. On the other hand, we characterize which locations for three data sinks admit a perfect placement of arrow tiles that guarantee correct routing no matter the placement of the data sources, effectively solving most instances of the game as it is normally played.