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Game Tree
In the context of combinatorial game theory, a game tree is a graph representing all possible game states within a sequential game that has perfect information. Such games include chess, checkers, Go, and tic-tac-toe. A game tree can be used to measure the complexity of a game, as it represents all the possible ways that the game can pan out. Due to the large game trees of complex games such as chess, algorithms that are designed to play this class of games will use partial game trees, which makes computation feasible on modern computers. Various methods exist to solve game trees. If a complete game tree can be generated, a deterministic algorithm, such as backward induction or retrograde analysis can be used. Randomized algorithms and minmax algorithms such as MCTS can be used in cases where a complete game tree is not feasible. Understanding the game tree To better understand the game tree, it can be thought of as a technique for analyzing adversarial games, whi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Artificial Intelligence
Artificial intelligence (AI) is the capability of computer, computational systems to perform tasks typically associated with human intelligence, such as learning, reasoning, problem-solving, perception, and decision-making. It is a field of research in computer science that develops and studies methods and software that enable machines to machine perception, perceive their environment and use machine learning, learning and intelligence to take actions that maximize their chances of achieving defined goals. High-profile applications of AI include advanced web search engines (e.g., Google Search); recommendation systems (used by YouTube, Amazon (company), Amazon, and Netflix); virtual assistants (e.g., Google Assistant, Siri, and Amazon Alexa, Alexa); autonomous vehicles (e.g., Waymo); Generative artificial intelligence, generative and Computational creativity, creative tools (e.g., ChatGPT and AI art); and Superintelligence, superhuman play and analysis in strategy games (e.g., ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Judea Pearl
Judea Pearl (; born September 4, 1936) is an Israeli-American computer scientist and philosopher, best known for championing the probabilistic approach to artificial intelligence and the development of Bayesian networks (see the article on belief propagation). He is also credited for developing a theory of causal and counterfactual inference based on structural models (see article on causality). In 2011, the Association for Computing Machinery (ACM) awarded Pearl with the Turing Award, the highest distinction in computer science, "for fundamental contributions to artificial intelligence through the development of a calculus for probabilistic and causal reasoning". He is the author of several books, including the technical '' Causality: Models, Reasoning and Inference'', and '' The Book of Why'', a book on causality aimed at the general public. Judea Pearl is the father of journalist Daniel Pearl, who was kidnapped and murdered by terrorists in Pakistan connected with Al-Qaeda a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Extensive Form Game
In game theory, an extensive-form game is a specification of a game allowing for the explicit representation of a number of key aspects, like the sequencing of players' possible moves, their choices at every decision point, the (possibly imperfect) information each player has about the other player's moves when they make a decision, and their payoffs for all possible game outcomes. Extensive-form games also allow for the representation of incomplete information in the form of chance events modeled as " moves by nature". Extensive-form representations differ from normal-form in that they provide a more complete description of the game in question, whereas normal-form simply boils down the game into a payoff matrix. Finite extensive-form games Some authors, particularly in introductory textbooks, initially define the extensive-form game as being just a game tree with payoffs (no imperfect or incomplete information), and add the other elements in subsequent chapters as refinements ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Alpha-beta Pruning
Alphabeta or Alpha Beta may also refer to: * Alphabeta, an Israeli musical group * Alpha Beta, a former chain of Californian supermarkets * The Greek alphabet, from ''Alpha'' (Αα) and ''Beta'' (Ββ), the first two letters * Alpha and beta anomers (chemistry) * Alpha–beta pruning, a type of search algorithm * Alpha–beta transformation, a mathematical transformation in electrical engineering * α,β-Unsaturated carbonyl compound, a class of organic compounds * Alpha beta filter, a predictive filter * Alpha (finance) and Beta (finance) In finance, the beta ( or market beta or beta coefficient) is a statistic that measures the expected increase or decrease of an individual stock price in proportion to movements of the stock market as a whole. Beta can be used to indicate the c ..., two measures characterizing the return of an investment portfolio * The Alpha Betas, a fraternity in the '' Revenge of the Nerds'' film series * ''Alpha Betas,'' an animated webseries created by ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Short-circuit Evaluation
Short-circuit evaluation, minimal evaluation, or McCarthy evaluation (after John McCarthy) is the semantics of some Boolean operators in some programming languages in which the second argument is executed or evaluated only if the first argument does not suffice to determine the value of the expression: when the first argument of the AND function evaluates to false, the overall value must be false; and when the first argument of the OR function evaluates to true, the overall value must be true. In programming languages with lazy evaluation (Lisp, Perl, Haskell), the usual Boolean operators short-circuit. In others ( Ada, Java, Delphi), both short-circuit and standard Boolean operators are available. For some Boolean operations, like ''exclusive or'' (XOR), it is impossible to short-circuit, because both operands are always needed to determine a result. Short-circuit operators are, in effect, control structures rather than simple arithmetic operators, as they are not strict. I ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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] |
Alpha-beta Pruning
Alphabeta or Alpha Beta may also refer to: * Alphabeta, an Israeli musical group * Alpha Beta, a former chain of Californian supermarkets * The Greek alphabet, from ''Alpha'' (Αα) and ''Beta'' (Ββ), the first two letters * Alpha and beta anomers (chemistry) * Alpha–beta pruning, a type of search algorithm * Alpha–beta transformation, a mathematical transformation in electrical engineering * α,β-Unsaturated carbonyl compound, a class of organic compounds * Alpha beta filter, a predictive filter * Alpha (finance) and Beta (finance) In finance, the beta ( or market beta or beta coefficient) is a statistic that measures the expected increase or decrease of an individual stock price in proportion to movements of the stock market as a whole. Beta can be used to indicate the c ..., two measures characterizing the return of an investment portfolio * The Alpha Betas, a fraternity in the '' Revenge of the Nerds'' film series * ''Alpha Betas,'' an animated webseries created by ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Chess-playing Program
Computer chess includes both hardware (dedicated computers) and software capable of playing chess. Computer chess provides opportunities for players to practice even in the absence of human opponents, and also provides opportunities for analysis, entertainment and training. Computer chess applications that play at the level of a chess grandmaster or higher are available on hardware from supercomputers to smart phones. Standalone chess-playing machines are also available. Stockfish, Leela Chess Zero, GNU Chess, Fruit, and other free open source applications are available for various platforms. Computer chess applications, whether implemented in hardware or software, use different strategies than humans to choose their moves: they use heuristic methods to build, search and evaluate trees representing sequences of moves from the current position and attempt to execute the best such sequence during play. Such trees are typically quite large, thousands to millions of nodes. The com ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
