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The Game of Life, also known as Conway's Game of Life or simply Life, is a cellular automaton devised by the British mathematician John Horton Conway in 1970. [1] It is a zero-player game , [ 2 ] [ 3 ] meaning that its evolution is determined by its initial state, requiring no further input.
Among the 88 possible unique elementary cellular automata, Rule 110 is the only one for which Turing completeness has been directly proven, although proofs for several similar rules follow as simple corollaries (e.g. Rule 124, which is the horizontal reflection of Rule 110). Rule 110 is arguably the simplest known Turing complete system. [2] [5]
In computability theory, a system of data-manipulation rules (such as a model of computation, a computer's instruction set, a programming language, or a cellular automaton) is said to be Turing-complete or computationally universal if it can be used to simulate any Turing machine [1] [2] (devised by English mathematician and computer scientist Alan Turing).
Named after Alan Turing, the game could, in the abstract, duplicate the processes of any computer whatsoever if the game field itself were sufficiently large. This follows because the game is P-complete by the circuit value problem and PSPACE-complete if an exponential number of marbles is allowed. [1] [2] The device has implications for ...
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The game was in full production for a further year. [2] Creative producer Howard Philpott cited Croteam's 2014 puzzle game, The Talos Principle, as a reference point for the progression of introducing gameplay mechanics in The Turing Test. [2] The game was published by Square Enix as part of their indie initiative, Square Enix Collective.
Counter machines with two counters are Turing complete: they can simulate any appropriately-encoded Turing machine, but there are some simple functions that they cannot compute. Counter machines with only a single counter can recognize a proper superset of the regular languages and a subset of the deterministic context free languages. [1]
Turochamp simulates a game of chess against the player by accepting the player's moves as input and outputting its move in response. The program's algorithm uses a heuristic to determine the best move to make, calculating all potential moves that it can make, then all of the potential player responses that could be made in turn, as well as further "considerable" moves, such as captures of ...