The computational complexity of portal and other 3D video games

Abstract

© Erik D. Demaine, Joshua Lockhart, and Jayson Lynch; licensed under Creative Commons License CC-BY 9th International Conference on Fun with Algorithms (FUN 2018). We classify the computational complexity of the popular video games Portal and Portal 2. We isolate individual mechanics of the game and prove NP-hardness, PSPACE-completeness, or pseudo-polynomiality depending on the specific game mechanics allowed. One of our proofs generalizes to prove NP-hardness of many other video games such as Half-Life 2, Halo, Doom, Elder Scrolls, Fallout, Grand Theft Auto, Left 4 Dead, Mass Effect, Deus Ex, Metal Gear Solid, and Resident Evil. These results build on the established literature on the complexity of video games [1, 3, 7, 18].