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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]
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 ...
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
Alan Turing in the 1930s. Alan Turing was an English mathematician, computer scientist, logician, cryptanalyst, philosopher and theoretical biologist. [5] Turing was highly influential in the development of theoretical computer science, providing a formalisation of the concepts of algorithm and computation with the Turing machine, which can be considered a model of a general-purpose computer.
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 ...
(This essentially simulates an infinite periodic tiling, and in the field of partial differential equations is sometimes referred to as periodic boundary conditions.) This can be visualized as taping the left and right edges of the rectangle to form a tube, then taping the top and bottom edges of the tube to form a torus (doughnut shape).
The Z3 was demonstrated in 1998 to be, in principle, Turing-complete. [13] However, because it lacked conditional branching, the Z3 only meets this definition by speculatively computing all possible outcomes of a calculation. Thanks to this machine and its predecessors, Konrad Zuse has often been suggested as the inventor of the computer.
For each m > 1, the set of m-tag systems is Turing-complete; i.e., for each m > 1, it is the case that for any given Turing machine T, there is an m-tag system that emulates T. In particular, a 2-tag system can be constructed to emulate a Universal Turing machine , as was done by Wang (1963) and by Cocke & Minsky (1964) .