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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:
A related concept is that of Turing equivalence – two computers P and Q are called equivalent if P can simulate Q and Q can simulate P. [4] The Church–Turing thesis conjectures that any function whose values can be computed by an algorithm can be computed by a Turing machine, and therefore that if any real-world computer can simulate a ...
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]
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. Lambda calculus may be untyped or typed. In typed lambda calculus ...
The "Total Turing test" [3] variation of the Turing test, proposed by cognitive scientist Stevan Harnad, [107] adds two further requirements to the traditional Turing test. The interrogator can also test the perceptual abilities of the subject (requiring computer vision ) and the subject's ability to manipulate objects (requiring robotics ).
and a deterministic polynomial-time Turing machine is a deterministic Turing machine M that satisfies two conditions: M halts on all inputs w and there exists k ∈ N {\displaystyle k\in N} such that T M ( n ) ∈ O ( n k ) {\displaystyle T_{M}(n)\in O(n^{k})} , where O refers to the big O notation and
A universal constructor can be built which contains a Turing complete computer, and which can build many types of complex objects, including more copies of itself. [2] On November 23, 2013, Dave Greene built the first replicator in the Game of Life that creates a complete copy of itself, including the instruction tape. [48]
Such a machine is called queue machine and is Turing-complete. Tape memory: The inputs and outputs of automata are often described as input and output tapes. Some machines have additional working tapes, including the Turing machine, linear bounded automaton, and log-space transducer. Transition function