Computational Complexity of Two-Dimensional Platform Games

Abstract. We analyze the computational complexity of various twodimensional platform games. We identify common properties of these games that allow us to state several meta-theorems: general constructions that allow us to identify a class of these games for which the set of solvable levels is NP-hard, and another class for which the set is even PSPACE-hard. Notably CommanderKeen is shown to be NP-hard, and PrinceOfPersia is shown to be PSPACE-complete. We then analyze the related game Lemmings, where we show that an assumption made by Cormode in [3] is false. We construct a set of instances which only have exponentially long solutions. Thereby we invalidate Cormode’s proof that the general version of the Lemmings decision problem is in NP. We then augment our construction to only include one entrance, which makes our instances perfectly natural within the context of the original game. 1 Overview The area of two-player combinatorial games, and one-player games and puzzles has already ...

• Type: Conference
• Year: 2010
• Where: FUN
• Authors: Michal Forisek
• Keywords: Algorithms, Computational Complexity, FUN 2010, Two-player Combinatorial Games, Twodimensional Platform Games