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Aspiration Window
An aspiration window is a heuristic used in pair with alpha-beta pruning in order to reduce search time for combinatorial games by supplying a window (or range) around an estimated score guess. Use of an aspiration window allows alpha-beta search to compete in the terms of efficiency against other pruning algorithms. Alpha-beta pruning achieves its performance by using cutoffs from its original range. Aspiration windows take advantage of this by supplying a smaller initial window, which increases the amount of cutoffs and therefore efficiency. However, due to search instability, the score may not always be in the window range. This may lead to a costly re-search that can penalize performance. Despite this, popular engines such as Stockfish still use aspiration windows. The guess that aspiration windows use is usually supplied by the last iteration of iterative deepening In computer science, iterative deepening search or more specifically iterative deepening depth-first sear ... [...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] |
Combinatorial Game Theory
Combinatorial game theory is a branch of mathematics and theoretical computer science that typically studies sequential games with perfect information. Research in this field has primarily focused on two-player games in which a ''position'' evolves through alternating ''moves'', each governed by well-defined rules, with the aim of achieving a specific winning condition. Unlike game theory, economic game theory, combinatorial game theory generally avoids the study of games of chance or games involving imperfect information, preferring instead games in which the current state and the full set of available moves are always known to both players. However, as mathematical techniques develop, the scope of analyzable games expands, and the boundaries of the field continue to evolve. Authors typically define the term "game" at the outset of academic papers, with definitions tailored to the specific game under analysis rather than reflecting the field’s full scope. Combinatorics, Comb ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pruning Algorithms
Pruning is a data compression technique in machine learning and search algorithms that reduces the size of decision trees by removing sections of the tree that are non-critical and redundant to classify instances. Pruning reduces the complexity of the final classifier, and hence improves predictive accuracy by the reduction of overfitting. One of the questions that arises in a decision tree algorithm is the optimal size of the final tree. A tree that is too large risks overfitting the training data and poorly generalizing to new samples. A small tree might not capture important structural information about the sample space. However, it is hard to tell when a tree algorithm should stop because it is impossible to tell if the addition of a single extra node will dramatically decrease error. This problem is known as the horizon effect. A common strategy is to grow the tree until each node contains a small number of instances then use pruning to remove nodes that do not provide addi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Instability
In dynamical systems instability means that some of the outputs or internal states increase with time, without bounds. Not all systems that are not stable are unstable; systems can also be marginally stable or exhibit limit cycle behavior. In structural engineering, a structural beam or column can become unstable when excessive compressive load is applied. Beyond a certain threshold, structural deflections magnify stresses, which in turn increases deflections. This can take the form of buckling or crippling. The general field of study is called structural stability. Atmospheric instability is a major component of all weather systems on Earth. Instability in control systems In the theory of dynamical systems, a state variable in a system is said to be unstable if it evolves without bounds. A system itself is said to be unstable if at least one of its state variables is unstable. In continuous time control theory, a system is unstable if any of the roots of its charac ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Stockfish (chess)
Stockfish is a free and open-source chess engine, available for various desktop and mobile platforms. It can be used in Computer chess, chess software through the Universal Chess Interface. Stockfish has been one of the strongest chess engines in the world for several years; it has won all main events of the Top Chess Engine Championship (TCEC) and the Chess.com Computer Chess Championship (CCC) since 2020 and, , is the strongest CPU chess engine in the world with an estimated Elo rating system, Elo rating of 3644, in a time control of 40/15 (15 minutes to make 40 moves), according to CCRL. The Stockfish engine was developed by Tord Romstad, Marco Costalba, and Joona Kiiski, and was derived from Glaurung, an open-source engine by Tord Romstad released in 2004. It is now being developed and maintained by the Stockfish community. Stockfish historically used only a classical Evaluation function#Handcrafted evaluation functions, hand-crafted function to evaluate board positions, b ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Iterative Deepening
In computer science, iterative deepening search or more specifically iterative deepening depth-first search (IDS or IDDFS) is a state space/graph search strategy in which a depth-limited version of depth-first search is run repeatedly with increasing depth limits until the goal is found. IDDFS is optimal, meaning that it finds the shallowest goal. Since it visits all the nodes in the search tree down to depth d before visiting any nodes at depth d + 1, the cumulative order in which nodes are first visited is effectively the same as in breadth-first search. However, IDDFS uses much less memory. Algorithm for directed graphs The following pseudocode shows IDDFS implemented in terms of a recursive depth-limited DFS (called DLS) for directed graphs. This implementation of IDDFS does not account for already-visited nodes. function IDDFS(root) is for depth from 0 to ∞ do found, remaining ← DLS(root, depth) if found ≠ null then return found ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Principal Variation Search
Principal variation search (sometimes equated with the practically identical NegaScout) 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. NegaScout works best when there is a good move ordering. In practice, the move ordering is often determined by previous shallower searches. It produces more cutoffs than alpha–beta by assuming that the first explored node is the best. In other words, it supposes the first node is in the principal variation. Then, it can check whether that is true by searching the remaining nodes with a null window (also known as a scout window; when alpha and beta are equal), which is faster than searching with the regular al ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
