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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).
Among other things, he developed a proof showing that the Rule 110 cellular automaton is Turing-complete. Cook presented his proof at the Santa Fe Institute conference CA98 before the publishing of Wolfram's book—an action that led Wolfram Research to accuse Cook of violating his NDA and resulted in the blocking of the publication of the ...
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]
The halting problem is a decision problem about properties of computer programs on a fixed Turing-complete model of computation, i.e., all programs that can be written in some given programming language that is general enough to be equivalent to a Turing machine. The problem is to determine, given a program and an input to the program, whether ...
[1] [2] The device has implications for nanotechnology. [ 3 ] [ 4 ] The game is advertised as Turing complete : an extension of the game that allows an infinitely large board and infinitely many pieces has been shown to be Turing complete via simulations of both Rule 110 for cellular automata , as well as of Turing machines .
The success of the Church–Turing thesis prompted variations of the thesis to be proposed. For example, the physical Church–Turing thesis states: "All physically computable functions are Turing-computable." [54]: 101 The Church–Turing thesis says nothing about the efficiency with which one model of computation can simulate another.
Arithmetic-based Turing-complete machines use an arithmetic operation and a conditional jump. Like the two previous universal computers, this class is also Turing-complete. The instruction operates on integers which may also be addresses in memory. Currently there are several known OISCs of this class, based on different arithmetic operations:
In 1936 Alan Turing published his seminal paper On Computable Numbers, with an Application to the Entscheidungsproblem [34] in which he modeled computation in terms of a one-dimensional storage tape, leading to the idea of the Universal Turing machine and Turing-complete systems.