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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 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 Turing test, originally called the imitation game by Alan Turing in 1949, [2] is a test of a machine's ability to exhibit intelligent behaviour equivalent to that of a human. In the test, a human evaluator judges a text transcript of a natural-language conversation between a human and a machine. The evaluator tries to identify the machine ...
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 ...
A set of natural numbers is said to be a computable set (also called a decidable, recursive, or Turing computable set) if there is a Turing machine that, given a number n, halts with output 1 if n is in the set and halts with output 0 if n is not in the set.
A Turing degree is an equivalence class of the relation ≡ T. The notation [X] denotes the equivalence class containing a set X. The entire collection of Turing degrees is denoted . The Turing degrees have a partial order ≤ defined so that [X] ≤ [Y] if and only if X ≤ T Y. There is a unique Turing degree containing all the computable ...
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:
Extra-sensory perception: In 1950, extra-sensory perception was an active area of research and Turing chooses to give ESP the benefit of the doubt, arguing that conditions could be created in which mind-reading would not affect the test. Turing admitted to "overwhelming statistical evidence" for telepathy, likely referring to early 1940s ...