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Title:  Computational Complexity of Puzzles and Games (Invited Talk) 
Authors:  Uehara, Ryuhei 
Keywords:  computational complexity reconfiguration problem constraint logic 
Issue Date:  201506 
Publisher:  Springer 
Magazine name:  Lecture Notes in Computer Science 
Volume:  9135 
Start page:  XXVI 
DOI:  10.1007/9783662476666 
Abstract:  A computation consists of algorithm of basic operations. When you consider an algorithm, you assume, say, the standard RAM model, that has “usual” arithmetic operations. On the other hand, when you consider an algorithm on a DNA computer, your basic operations are duplication and inversion on a string. Then you need to consider completely different algorithms, and their computational complexity also changes. That is, when we discuss computational complexity of a problem, it strongly depends on the set of basic operations you use. When you enjoy a puzzle, you have to find an algorithm by combining reasonable basic operations to its goal. (Some puzzles require to find the basic operations themselves, but we do not consider such puzzles in this talk.) From the viewpoint of theoretical computer science, puzzles give us some insight to computation and computational complexity classes in various way. Some puzzles and games give reasonable characterizations to computational complexity classes. For example, “pebble game” is a classic model that gives some complexity classes in a natural way, and “constraint logic” is recent model that succeeds to solve a long standing open problem due to Martin Gardner that asks the computational complexity of sliding block puzzles. Such puzzles gives us “typical” and characterization and “intuitive” understanding for some computational complexity classes. On the other hand, there are some puzzles and games that give nontrivial interesting aspects of computational complexity classes. For example, consider "1415 puzzle" which is classic well known sliding puzzle. By parity, we can determine if one arrangement can be slid to the other in linear time. Moreover, we can always find a way for sliding between them in quadratic time. However, interestingly, finding the optimal solution is NPcomplete in general. I also introduce a relatively new notion of the reconfiguration problem. This series of new problems will give some new notion of computational complexity classes. 
Rights:  This is the authorcreated version of Springer, Ryuhei Uehara, Lecture Notes in Computer Science, 9135, 2015, XXVI. The original publication is available at www.springerlink.com, http://dx.doi.org/10.1007/9783662476666 
URI:  http://hdl.handle.net/10119/15306 
Material Type:  author 
Appears in Collections:  b101. 雑誌掲載論文 (Journal Articles)

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