Games, Puzzles, and Computation

The authors show that there are underlying mathematical reasons for why games and puzzles are challenging (and perhaps why they are so much fun). They also show that games and puzzles can serve as powerful models of computation—quite different from the usual models of automata and circuits—offering a new way of thinking about computation. The appendices provide a substantial survey of all known results in the field of game complexity, serving as a reference guide for readers interested in the computational complexity of particular games, or interested in open problems about such complexities.

Introduction What is a Game? Computational Complexity Classes Constraint Logic What’s Next? I Games in General The Constraint-Logic Formalism Constraint Graphs Planar Constraint Graphs Constraint-Graph Conversion Techniques Constraint-Logic Games Zero-Player Games (Simulations) One-Player Games (Puzzles) Two-Player Games Team Games Zero-Player Games (Simulations) Bounded Games Unbounded Games One-Player Games (Puzzles) Bounded Games Unbounded Games Two-Player Games Bounded Games Unbounded Games No-Repeat Games Team Games Bounded Games Unbounded Games Perspectives on Part I Hierarchies of Complete Problems Games, Physics, and Computation II Games in Particular One-Player Games (Puzzles) Tip Over Hitori Sliding-Block Puzzles The Warehouseman’s Problem Sliding-Coin Puzzles Plank Puzzles Sokoban Push-2-F Rush Hour Triangular Rush Hour Hinged Polygon Dissections Two-Player Games Amazons Konane Cross Purposes Perspectives on Part II Conclusions Contributions Future Work Appendices Survey of Games and Their Complexities Cellular Automata Games of Block Manipulation Games of Tokens on Graphs Peg-Jumping Games Connection Games Other Board Games Pencil Puzzles Formula Games Other Games Constraint Logic Open Problems Computational-Complexity Reference Basic Definitions Generalizations of Turing Machines Relationship of Complexity Classes List of Complexity Classes Used in this Book Formula Games Deterministic Constraint Logic Activation Sequences Constraint-Logic Quick Reference

Robert A. Hearn, Dartmouth College, Hanover, New Hampshire, USA Erik Demaine, Massachusetts Institute of Technology, Cambridge, USA