Game generalized so that it can be played on a board or grid of any size
Sudoku (4×4)
Sudoku (9×9)
Sudoku (25×25)
Generalized Sudoku includes puzzles of different sizes
In computational complexity theory, a generalized game is a game or puzzle that has been generalized so that it can be played on a board or grid of any size. For example, generalized chess is the game of chess played on an board, with pieces on each side. Generalized Sudoku includes Sudokus constructed on an grid.
Complexity theory studies the asymptotic difficulty of problems, so generalizations of games are needed, as games on a fixed size of board are finite problems.
For many generalized games which last for a number of moves polynomial in the size of the board, the problem of determining if there is a win for the first player in a given position is PSPACE-complete. Generalized hex and reversi are PSPACE-complete.[1][2]
For many generalized games which may last for a number of moves exponential in the size of the board, the problem of determining if there is a win for the first player in a given position is EXPTIME-complete. Generalized chess, go (with Japanese ko rules), Quixo,[3] and checkers are EXPTIME-complete.[4][5][6]
^Reisch, Stefan (1981), "Hex ist PSPACE-vollständig", Acta Informatica, 15 (2): 167–191, doi:10.1007/bf00288964, S2CID 9125259
^Iwata, Shigeki; Kasai, Takumi (January 1994), "The Othello game on an board is PSPACE-complete", Theoretical Computer Science, 123 (2): 329–340, doi:10.1016/0304-3975(94)90131-7
^Mishiba, Shohei; Takenaga, Yasuhiko (2020-07-02). "QUIXO is EXPTIME-complete". Information Processing Letters. 162: 105995. doi:10.1016/j.ipl.2020.105995. ISSN 0020-0190.
^Fraenkel, Aviezri S.; Lichtenstein, David (September 1981), "Computing a perfect strategy for chess requires time exponential in ", Journal of Combinatorial Theory, Series A, 31 (2): 199–214, doi:10.1016/0097-3165(81)90016-9
^Robson, J. M. (1983), "The complexity of Go", Proceedings of the IFIP 9th World Computer Congress on Information Processing: 413–417
^Robson, J. M. (May 1984), " by checkers is Exptime complete", SIAM Journal on Computing, 13 (2), Society for Industrial & Applied Mathematics ({SIAM}): 252–267, doi:10.1137/0213018
a generalizedgame is a game or puzzle that has been generalized so that it can be played on a board or grid of any size. For example, generalized chess...
Generalizedgame theory is an extension of game theory incorporating social theory concepts such as norm, value, belief, role, social relationship, and...
Combinatorial game theory measures game complexity in several ways: State-space complexity (the number of legal game positions from the initial position), Game tree...
viewpoint of the generalized other. The attitude of the generalized other is the attitude of the larger community. According to Mead, the generalized other is...
Generalized anxiety disorder (GAD) is a mental and behavioral disorder, specifically an anxiety disorder characterized by excessive, uncontrollable and...
the game is known. This analysis introduced a notion called pagoda function which is a strong tool to show the infeasibility of a given generalized peg...
game cannot be solved, the lack thereof. To perform an interesting complexity analysis one must construct a generalized version of the FreeCell game with...
computational complexity theory, generalized geography is a well-known PSPACE-complete problem. Geography is a children's game, where players take turns naming...
generalized Hex position, which is known to be PSPACE-complete, into an Amazons position. The second way is by reducing a certain kind of generalized...
is a generalized terminology to describe concepts applicable to basic game mechanics and attributes common to nearly all board games. Board game awards...
not be repeated in the same game. The version of the game in which cities are used is called geography, and a generalized version with place names is...
exchange resources with each other, generalized exchange naturally involves more than two parties. Examples of generalized exchange include; matrilateral cross-cousin...
every finite generalized-ordinal-potential game has the FIP. The opposite is also true: every finite game has the FIP has a generalized-ordinal-potential...
In theoretical computer science, the busy beaver game aims at finding a terminating program of a given size that produces the most output possible. Since...
of Methodology Vol. 34(4):379-406. Burns T.R., Roszkowska E. (2005) GeneralizedGame Theory: Assumptions, Principles, and Elaborations Grounded in Social...
of the standard definition of an aggregative game have appeared in the literature. A game is generalized aggregative if there exists an additively separable...
The Turing test, originally called the imitation game by Alan Turing in 1950, is a test of a machine's ability to exhibit intelligent behaviour equivalent...
Match Game is an American television panel game show that premiered on NBC in 1962 and has been revived several times over the course of the last six...