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Games, Puzzles, and Computation

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Table of Contents

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

About the Author

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


Games, Puzzles, and Computation will serve well in roles similar to that of Garey and Johnson's book. In particular, the text would work exceedingly well as a reference for what's known in the subfield of game/puzzle complexity or for self-study by someone familiar with basic computational complexity principles who is interested in learning more about the complexity of games and puzzles. It would also serve well as supplementary material to an upper-level undergraduate or entry-level graduate special topics course in game/puzzle complexity. It could also be used as the primary text for such a course (in principle) given extra preparation by the instructor ! . --Daniel Apon, SIGACT News, September 2011 The authors show that there are underlying mathematical reasons that games and puzzles are challenging (which perhaps explains why they are so much fun). Complementarily, 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. --L'Enseignement Mathematique, December 2009 ! intriguing book ! Hearn and Demaine present an elegant family of benchmarks they have developed, allowing them to settle open questions on the complexity of various games. ! and the authors certainly provide plenty to mull over. The publisher A K Peters has done a quite nice job of production, as well. All in all, this is a book well worth looking into. --Leon Harkleroad, MAA Reviews, December 2009 This book will be of interest to advanced readers working in this area. --Brian Borchers, CHOICE, February 2010

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