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 computationquite different from the usual models of automata and circuitsoffering 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.
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1 | (12) |
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3 | (3) |
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Computational Complexity Classes |
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6 | (3) |
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9 | (2) |
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11 | (2) |
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13 | (92) |
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The Constraint-Logic Formalism |
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15 | (10) |
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16 | (3) |
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19 | (1) |
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Constraint-Graph Conversion Techniques |
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20 | (5) |
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25 | (14) |
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Zero-Player Games (Simulations) |
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26 | (3) |
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One-Player Games (Puzzles) |
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29 | (2) |
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31 | (3) |
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34 | (5) |
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Zero-Player Games (Simulations) |
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39 | (16) |
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40 | (3) |
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43 | (12) |
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One-Player Games (Puzzles) |
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55 | (16) |
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56 | (5) |
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61 | (10) |
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71 | (14) |
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72 | (4) |
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76 | (5) |
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81 | (4) |
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85 | (16) |
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86 | (3) |
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89 | (12) |
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101 | (4) |
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Hierarchies of Complete Problems |
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101 | (1) |
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Games, Physics, and Computation |
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102 | (3) |
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105 | (56) |
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One-Player Games (Puzzles) |
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107 | (34) |
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107 | (5) |
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112 | (3) |
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115 | (5) |
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The Warehouseman's Problem |
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120 | (1) |
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120 | (2) |
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122 | (4) |
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126 | (3) |
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129 | (4) |
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133 | (3) |
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136 | (1) |
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Hinged Polygon Dissections |
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137 | (4) |
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141 | (14) |
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141 | (5) |
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146 | (3) |
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149 | (6) |
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155 | (2) |
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157 | (4) |
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157 | (1) |
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158 | (3) |
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161 | (56) |
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A Survey of Games and Their Complexities |
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163 | (30) |
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164 | (1) |
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A.2 Games of Block Manipulation |
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165 | (5) |
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A.3 Games of Tokens on Graphs |
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170 | (4) |
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174 | (1) |
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174 | (1) |
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175 | (1) |
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175 | (5) |
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180 | (2) |
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182 | (4) |
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186 | (1) |
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186 | (7) |
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B Computational-Complexity Reference |
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193 | (10) |
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193 | (3) |
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B.2 Generalizations of Turing Machines |
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196 | (3) |
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B.3 Relationship of Complexity Classes |
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199 | (1) |
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B.4 List of Complexity Classes Used in this Book |
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199 | (1) |
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200 | (3) |
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C Deterministic Constraint Logic Activation Sequences |
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203 | (12) |
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D Constraint-Logic Quick Reference |
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215 | (2) |
Bibliography |
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217 | (13) |
Index |
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230 | |
Robert A. Hearn, Dartmouth College, Hanover, New Hampshire, USA
Erik Demaine, Massachusetts Institute of Technology, Cambridge, USA