Constraint Logic: A Uniform Framework for Modeling Computation as Games

We introduce a simple game family, called Constraint Logic, where players reverse edges in a directed graph while satisfying vertex in-flow constraints. This game family can be interpreted in many different game-theoretic settings, ranging from zero-player automata to a more economic setting of team multiplayer games with hidden information. Each setting gives rise to a model of computation that we show corresponds to a classic complexity class. In this way we obtain a uniform framework for modeling various complexities of computation as games. Most surprising among our results is that a game with three players and a bounded amount of state can simulate any (infinite) Turing computation, making the game undecidable. Our framework also provides a more graphical, less formulaic viewpoint of computation. This graph model has been shown to be particularly appropriate for reducing to many existing combinatorial games and puzzles--such as Sokoban, Rush Hour, River Crossing, TipOver, the War...

• Type: Conference
• Year: 2008
• Where: COCO
• Authors: Erik D. Demaine, Robert A. Hearn
• Keywords: Algorithms, COCO 2008, Game Family, Players Reverse Edges, Vertex In-flow Constraints