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Computer chess includes both hardware 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.
A* is a graph traversal and pathfinding algorithm, which is used in many fields of computer science due to its completeness, optimality, and optimal efficiency. Given a weighted graph, a source node and a goal node, the algorithm finds the shortest path from source to goal.
The Standard Template Library (STL) is a software library originally designed by Alexander Stepanov for the C++ programming language that influenced many parts of the C++ Standard Library. It provides four components called algorithms, containers, functions, and iterators.
Alpha–beta pruning is a search algorithm that seeks to decrease the number of nodes that are evaluated by the minimax algorithm in its search tree. It is an adversarial search algorithm used commonly for machine playing of two-player combinatorial games. It stops evaluating a move when at least one possibility has been found that proves the move to be worse than a previously examined move. Such moves need not be evaluated further. When applied to a standard minimax tree, it returns the same move as minimax would, but prunes away branches that cannot possibly influence the final decision.
In competitive two-player games, the killer heuristic is a move-ordering method based on the observation that a strong move or small set of such moves in a particular position may be equally strong in similar positions at the same move (ply) in the game tree. Retaining such moves obviates the effort of rediscovering them in sibling nodes.
In computer chess programs, the null-move heuristic is a heuristic technique used to enhance the speed of the alpha–beta pruning algorithm.
In computer science and artificial intelligence, combinatorial search studies search algorithms for solving instances of problems that are believed to be hard in general, by efficiently exploring the usually large solution space of these instances. Combinatorial search algorithms achieve this efficiency by reducing the effective size of the search space or employing heuristics. Some algorithms are guaranteed to find the optimal solution, while others may only return the best solution found in the part of the state space that was explored.
A transposition table is a cache of previously seen positions, and associated evaluations, in a game tree generated by a computer game playing program. If a position recurs via a different sequence of moves, the value of the position is retrieved from the table, avoiding re-searching the game tree below that position. Transposition tables are primarily useful in perfect-information games. The usage of transposition tables is essentially memoization applied to the tree search and is a form of dynamic programming.
Crafty is a chess program written by UAB professor Robert Hyatt, with development and assistance from Michael Byrne, Tracy Riegle, and Peter Skinner. It is derived from Cray Blitz, winner of the 1983 and 1986 World Computer Chess Championships. Tord Romstad, co-author of Stockfish, described Crafty as "arguably the most important and influential chess program ever".
The expectiminimax algorithm is a variation of the minimax algorithm, for use in artificial intelligence systems that play two-player zero-sum games, such as backgammon, in which the outcome depends on a combination of the player's skill and chance elements such as dice rolls. In addition to "min" and "max" nodes of the traditional minimax tree, this variant has "chance" nodes, which take the expected value of a random event occurring. In game theory terms, an expectiminimax tree is the game tree of an extensive-form game of perfect, but incomplete information.
Negamax search is a variant form of minimax search that relies on the zero-sum property of a two-player game.
Principal variation search is a negamax algorithm that can be faster than alpha–beta pruning. Like alpha–beta pruning, NegaScout is a directional search algorithm for computing the minimax value of a node in a tree. It dominates alpha–beta pruning in the sense that it will never examine a node that can be pruned by alpha–beta; however, it relies on accurate node ordering to capitalize on this advantage.
MTD(f) is an alpha-beta game tree search algorithm modified to use ‘zero-window’ initial search bounds, and memory (usually a transposition table) to reuse intermediate search results. MTD(f) is a shortened form of MTD(n,f) which stands for Memory-enhanced Test Driver with node ‘n’ and value ‘f’. The efficacy of this paradigm depends on a good initial guess, and the supposition that the final minimax value lies in a narrow window around the guess (which becomes an upper/lower bound for the search from root). The memory structure is used to save an initial guess determined elsewhere.
Alexander L'vovich Brudno was a Russian computer scientist, best known for fully describing the alpha-beta pruning algorithm. From 1991 until his death he lived in Israel.
SSS* is a search algorithm, introduced by George Stockman in 1979, that conducts a state space search traversing a game tree in a best-first fashion similar to that of the A* search algorithm.
In computer science, B* is a best-first graph search algorithm that finds the least-cost path from a given initial node to any goal node. First published by Hans Berliner in 1979, it is related to the A* search algorithm.
Distributed tree search (DTS) algorithm is a class of algorithms for searching values in an efficient and distributed manner. Their purpose is to iterate through a tree by working along multiple branches in parallel and merging the results of each branch into one common solution, in order to minimize time spent searching for a value in a tree-like data structure.
AlphaZero is a computer program developed by artificial intelligence research company DeepMind to master the games of chess, shogi and go. This algorithm uses an approach similar to AlphaGo Zero.
Leela Chess Zero is a free, open-source, and deep neural network–based chess engine and volunteer computing project. Development has been spearheaded by programmer Gary Linscott, who is also a developer for the Stockfish chess engine. Leela Chess Zero was adapted from the Leela Zero Go engine, which in turn was based on Google's AlphaGo Zero project. One of the purposes of Leela Chess Zero was to verify the methods in the AlphaZero paper as applied to the game of chess.
