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The game tree size is the total number of possible games that can be played. This is the number of leaf nodes in the game tree rooted at the game's initial position.. The game tree is typically vastly larger than the state-space because the same positions can occur in many games by making moves in a different order (for example, in a tic-tac-toe game with two X and one O on the board, this ...
If the size of the state space is finite, calculating the size of the state space is a combinatorial problem. [4] For example, in the Eight queens puzzle, the state space can be calculated by counting all possible ways to place 8 pieces on an 8x8 chessboard. This is the same as choosing 8 positions without replacement from a set of 64, or
State-space models are applied in fields such as economics, [3] statistics, [4] computer science, electrical engineering, [5] and neuroscience. [6] In econometrics , for example, state-space models can be used to decompose a time series into trend and cycle, compose individual indicators into a composite index, [ 7 ] identify turning points of ...
The complete game tree for a game is the game tree starting at the initial position and containing all possible moves from each position; the complete tree is the same tree as that obtained from the extensive-form game representation. To be more specific, the complete game is a norm for the game in game theory.
If the state space is the real line, then the stochastic process is referred to as a real-valued stochastic process or a process with continuous state space. If the state space is n {\displaystyle n} -dimensional Euclidean space, then the stochastic process is called a n {\displaystyle n} - dimensional vector process or n {\displaystyle n ...
In computer science, state space enumeration are methods that consider each reachable program state to determine whether a program satisfies a given property. [1] As programs increase in size and complexity, the state space grows exponentially. The state space used by these methods can be reduced by maintaining only the parts of the state space ...
In artificial intelligence and computer programming, state space planning is a process used in designing programs to search for data or solutions to problems. In a computer algorithm that searches a data structure for a piece of data, for example a program that looks up a word in a computer dictionary, the state space is a collective term for all the data to be searched.
In control theory, a state observer, state estimator, or Luenberger observer is a system that provides an estimate of the internal state of a given real system, from measurements of the input and output of the real system. It is typically computer-implemented, and provides the basis of many practical applications.