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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 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 ...
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 ...
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:
The output function may be extended similarly into ¯ (,), which gives the complete output of the machine when run on word from state . Acceptor In order to study an automaton with the theory of formal languages , an automaton may be considered as an acceptor , replacing the output alphabet and function Γ {\displaystyle \Gamma } and λ ...
Turing complete set, a related notion from recursion theory; Completeness (knowledge bases), found in knowledge base theory; Complete search algorithm, a search algorithm that is guaranteed to find a solution if there is one; Incomplete database, a compact representation of a set of possible worlds
Lambda calculus is Turing complete, that is, it is a universal model of computation that can be used to simulate any Turing machine. [3] Its namesake, the Greek letter lambda (λ), is used in lambda expressions and lambda terms to denote binding a variable in a function.