The Computational Complexity of Fire Emblem Series and similar Tactical Role-Playing Games

TL;DR

This paper analyzes the computational complexity of simplified Fire Emblem and similar tactical RPGs, proving they are PSPACE-complete and NP-complete under certain conditions, highlighting their inherent computational difficulty.

Contribution

It establishes the PSPACE-completeness of simplified Fire Emblem and NP-completeness of Poly-round FE, extending these results to other similar tactical RPGs.

Findings

Simplified FE is PSPACE-complete.

Poly-round FE is NP-complete under specific conditions.

Hardness results apply to other tactical RPG series.

Abstract

Fire Emblem (FE) is a popular turn-based tactical role-playing game (TRPG) series on the Nintendo gaming consoles. This paper studies the computational complexity of a simplified version of FE (only floor tiles and wall tiles, the HP and other attributes of characters are constants at most 8, the movement distance per character each turn is fixed to 6 tiles), and proves that: 1. Simplified FE is PSPACE-complete (Thus actual FE is at least as hard). 2. Poly-round FE is NP-complete, even when the map is cycle-free, without healing units, and the weapon durability is a small constant. Poly-round FE is to decide whether the player can win the game in a certain number of rounds that is polynomial to the map size. A map is called cycle-free if its corresponding planar graph is cycle-free. These hardness results also hold for other similar TRPG series, such as Final Fantasy Tactics, Tactics Ogre and Disgaea.