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Games, Puzzles, and Computation

By Robert A. Hearn, Erik D. Demaine

A K Peters/CRC Press – 2009 – 250 pages

Purchasing Options:

  • Add to CartHardback: $51.95
    978-1-56881-322-6
    June 30th 2009

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.

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

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 Bio

Robert A. Hearn, Dartmouth College, Hanover, New Hampshire, USA

Erik Demaine, Massachusetts Institute of Technology, Cambridge, USA

Related Subjects

  1. Game Theory

Name: Games, Puzzles, and Computation (Hardback)A K Peters/CRC Press 
Description: By Robert A. Hearn, Erik D. Demaine. 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...
Categories: Game Theory