1 The Computational Complexity of Portal and 2 Other 3D Video Games 3 Erik D. Demaine 4 MIT CSAIL, 32 Vassar Street, Cambridge, MA 02139, USA 5
[email protected] 1 6 Joshua Lockhart 7 Department of Computer Science, University College London, London, WC1E 6BT, UK 8
[email protected] 9 Jayson Lynch 10 MIT CSAIL, 32 Vassar Street, Cambridge, MA 02139, USA 11
[email protected] 12 Abstract 13 We classify the computational complexity of the popular video games Portal and Portal 2. We 14 isolate individual mechanics of the game and prove NP-hardness, PSPACE-completeness, or 15 pseudo-polynomiality depending on the specific game mechanics allowed. One of our proofs 16 generalizes to prove NP-hardness of many other video games such as Half-Life 2, Halo, Doom, 17 Elder Scrolls, Fallout, Grand Theft Auto, Left 4 Dead, Mass Effect, Deus Ex, Metal Gear Solid, 18 and Resident Evil. These results build on the established literature on the complexity of video 19 games [1, 3, 7, 18]. 20 2012 ACM Subject Classification Dummy classification 21 Keywords and phrases video games, hardness, motion planning, NP, PSPACE 22 Digital Object Identifier 10.4230/LIPIcs.FUN.2018.19 23 Related Version arXiv:1611.10319 24 1 Introduction 25 In Valve’s critically acclaimed Portal franchise, the player guides Chell (the game’s silent 26 protagonist) through a “test facility” constructed by the mysterious fictional organization 27 Aperture Science. Its unique game mechanic is the Portal Gun, which enables the player 28 to place a pair of portals on certain surfaces within each test chamber.