Games, Puzzles, and Computation
Preview
Book Description
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.
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
Author(s)
Biography
Robert A. Hearn, Dartmouth College, Hanover, New Hampshire, USA
Erik Demaine, Massachusetts Institute of Technology, Cambridge, USA
Reviews
"… the games also provide an extremely well-suited platform for the introduction of a unified method for determining complexity using constraint logic … considers not only mathematically oriented games, but also games that may well be suitable for non-mathematicians … The book also contains a comprehensive overview of known results on the complexity of games and therefore with its 177 references is also an excellent reference book on the topic … warmly recommended for anyone who likes games and wants to know more about their (mathematical) complexity."
—Internaionale Mathematische Nachrichten, December 2012"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