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Go And Mathematics
The game of Go is one of the most popular games in the world. As a result of its elegant and simple rules, the game has long been an inspiration for mathematical research. Shen Kuo, an 11th century Chinese scholar, estimated in his '' Dream Pool Essays'' that the number of possible board positions is around 10172. In more recent years, research of the game by John H. Conway led to the development of the surreal numbers and contributed to development of combinatorial game theory (with Go Infinitesimals being a specific example of its use in Go). Computational complexity Generalized Go is played on ''n'' × ''n'' boards, and the computational complexity of determining the winner in a given position of generalized Go depends crucially on the ko rules. Go is “almost” in PSPACE, since in normal play, moves are not reversible, and it is only through capture that there is the possibility of the repeating patterns necessary for a harder complexity. Without ko Without ko, Go is ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Go (board Game)
# Go is an abstract strategy game, abstract strategy board game for two players in which the aim is to fence off more territory than the opponent. The game was invented in China more than 2,500 years ago and is believed to be the oldest board game continuously played to the present day. A 2016 survey by the International Go Federation's 75 member nations found that there are over 46 million people worldwide who know how to play Go, and over 20 million current players, the majority of whom live in East Asia. The Game piece (board game), playing pieces are called ''Go equipment#Stones, stones''. One player uses the white stones and the other black stones. The players take turns placing their stones on the vacant intersections (''points'') on the #Boards, board. Once placed, stones may not be moved, but ''captured stones'' are immediately removed from the board. A single stone (or connected group of stones) is ''captured'' when surrounded by the opponent's stones on all Orthogona ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Chess
Chess is a board game for two players. It is an abstract strategy game that involves Perfect information, no hidden information and no elements of game of chance, chance. It is played on a square chessboard, board consisting of 64 squares arranged in an 8×8 grid. The players, referred to as White and Black in chess, "White" and "Black", each control sixteen Chess piece, pieces: one king (chess), king, one queen (chess), queen, two rook (chess), rooks, two bishop (chess), bishops, two knight (chess), knights, and eight pawn (chess), pawns, with each type of piece having a different pattern of movement. An enemy piece may be captured (removed from the board) by moving one's own piece onto the square it occupies. The object of the game is to "checkmate" (threaten with inescapable capture) the enemy king. There are also several ways a game can end in a draw (chess), draw. The recorded history of chess goes back to at least the emergence of chaturanga—also thought to be an ancesto ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Christos Papadimitriou
Christos Charilaos Papadimitriou (; born August 16, 1949) is a Greek-American theoretical computer scientist and the Donovan Family Professor of Computer Science at Columbia University. Education Papadimitriou studied at the National Technical University of Athens, where in 1972 he received his Bachelor of Arts degree in electrical engineering. He then pursued graduate studies at Princeton University, where he received his Ph.D. in electrical engineering and computer science in 1976 after completing a doctoral dissertation titled "The complexity of combinatorial optimization problems." Career Papadimitriou has taught at Harvard, MIT, the National Technical University of Athens, Stanford, UCSD, University of California, Berkeley and is currently the Donovan Family Professor of Computer Science at Columbia University. Papadimitriou co-authored a paper on pancake sorting with Bill Gates, then a Harvard undergraduate. Papadimitriou recalled "Two years later, I called to tell him ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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New York Times
''The New York Times'' (''NYT'') is an American daily newspaper based in New York City. ''The New York Times'' covers domestic, national, and international news, and publishes opinion pieces, investigative reports, and reviews. As one of the longest-running newspapers in the United States, the ''Times'' serves as one of the country's Newspaper of record, newspapers of record. , ''The New York Times'' had 9.13 million total and 8.83 million online subscribers, both by significant margins the List of newspapers in the United States, highest numbers for any newspaper in the United States; the total also included 296,330 print subscribers, making the ''Times'' the second-largest newspaper by print circulation in the United States, following ''The Wall Street Journal'', also based in New York City. ''The New York Times'' is published by the New York Times Company; since 1896, the company has been chaired by the Ochs-Sulzberger family, whose current chairman and the paper's publ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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God's Algorithm
God's algorithm is a notion originating in discussions of ways to solve the Rubik's Cube puzzle, but which can also be applied to other combinatorial puzzles and mathematical games. It refers to any algorithm which produces a solution having the fewest possible moves (i.e., the solver should not require any ''more'' than this number). The allusion to the deity is based on the notion that an omniscient being would know an optimal step from any given configuration. Scope Definition The notion applies to puzzles that can assume a wiktionary:Finite, finite number of "configurations", with a relatively small, well-defined arsenal of "moves" that may be applicable to configurations and then lead to a new configuration. Solving the puzzle means to reach a designated "final configuration", a singular configuration, or one of a collection of configurations. To solve the puzzle a sequence of moves is applied, starting from some arbitrary initial configuration. Solution An algorithm can ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Game Complexity
Combinatorial game theory measures game complexity in several ways: #State-space complexity (the number of legal game positions from the initial position) #Game tree size (total number of possible games) #Decision complexity (number of leaf nodes in the smallest decision tree for initial position) #Game-tree complexity (number of leaf nodes in the smallest full-width decision tree for initial position) #Computational complexity (asymptotic difficulty of a game as it grows arbitrarily large) These measures involve understanding the game positions, possible outcomes, and Computational complexity theory, computational complexity of various game scenarios. Measures of game complexity State-space complexity The ''state-space complexity'' of a game is the number of legal game positions reachable from the initial position of the game. When this is too hard to calculate, an upper bound can often be computed by also counting (some) illegal positions (positions that can never arise i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Googolplex
A googolplex is the large number 10, or equivalently, 10 or . Written out in ordinary decimal notation, it is 1 followed by 10100 zeroes; that is, a 1 followed by a googol of zeroes. Its prime factorization is 2 ×5. History In 1920, Edward Kasner's nine-year-old nephew, Milton Sirotta, coined the term ''googol'', which is 10, and then proposed the further term ''googolplex'' to be "one, followed by writing zeroes until you get tired". Kasner decided to adopt a more formal definition because "different people get tired at different times and it would never do to have Carnera ea better mathematician than Dr. Einstein, simply because he had more endurance and could write for longer". It thus became standardized to 10(10100) = 1010100, due to the right-associativity of exponentiation. Size A typical book can be printed with 10 zeros (around 400 pages with 50 lines per page and 50 zeros per line). Therefore, it requires 10 such books to print all the zeros of a googolp ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Game-tree Complexity
Combinatorial game theory measures game complexity in several ways: #State-space complexity (the number of legal game positions from the initial position) #Game tree size (total number of possible games) #Decision complexity (number of leaf nodes in the smallest decision tree for initial position) #Game-tree complexity (number of leaf nodes in the smallest full-width decision tree for initial position) #Computational complexity (asymptotic difficulty of a game as it grows arbitrarily large) These measures involve understanding the game positions, possible outcomes, and computational complexity of various game scenarios. Measures of game complexity State-space complexity The ''state-space complexity'' of a game is the number of legal game positions reachable from the initial position of the game. When this is too hard to calculate, an upper bound can often be computed by also counting (some) illegal positions (positions that can never arise in the course of a game). Game t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Victor Allis
Louis Victor Allis (born 19 May 1965) is a Dutch computer scientist and co-founder of the election information technology firm Activote. In his graduate work, he revealed AI solutions for Connect Four, Qubic, and Gomoku. His dissertation introduced two new game search techniques: proof-number search and dependency-based search. Proof-number search has seen further successful application in computer Go tactical search and many other games. Career Allis holds a Ph.D. in Artificial Intelligence from Maastricht University, The Netherlands, and graduated ''cum laude'' with a M. Sc. in Computer Science from the Vrije Universiteit, The Netherlands. He has more than 30 publications to his name; the majority of his published work reports on research in search technologies. He started his career in 1987 as a freelance teacher, course developer and mentor of various AMBI courses for NOVI. Allis has lectured at the Vrije Universiteit in Amsterdam as an assistant professor in artificia ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Computer Scientist
A computer scientist is a scientist who specializes in the academic study of computer science. Computer scientists typically work on the theoretical side of computation. Although computer scientists can also focus their work and research on specific areas (such as algorithm and data structure development and design, software engineering, information theory, database theory, theoretical computer science, numerical analysis, programming language theory, compiler, computer graphics, computer vision, robotics, computer architecture, operating system), their foundation is the theoretical study of computing from which these other fields derive. A primary goal of computer scientists is to develop or validate models, often mathematical, to describe the properties of computational systems (Processor (computing), processors, programs, computers interacting with people, computers interacting with other computers, etc.) with an overall objective of discovering designs that yield useful ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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John Tromp
John Tromp is a Dutch computer scientist. He formerly worked for Dutch Centre for Mathematics and Computer Science. Tromp discovered the number of legal states of the board game Go, and co-authored with Bill Taylor the Tromp-Taylor Rules, which they call "the logical rules of Go". He is also known for Binary combinatory logic (Binary lambda calculus) and lambda diagrams that supply a graphical way of representing lambda calculus expressions. References External linksJohn Tromp's homepageat GitHub GitHub () is a Proprietary software, proprietary developer platform that allows developers to create, store, manage, and share their code. It uses Git to provide distributed version control and GitHub itself provides access control, bug trackin ...John Tromp's entry on the Chess Programming Wiki* * Living people Dutch computer scientists Year of birth missing (living people) {{compu-scientist-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |