In the context of formal language theory, a Turing machine ( automaton) is capable of enumerating some arbitrary subset of valid strings of an alphabet. Typically, the sequential memory is represented as a tape of infinite length on which the machine can perform read and write operations. A programming language that is Turing complete is theoretically capable of expressing all tasks accomplishable by computers nearly all programming languages are Turing complete if the limitations of finite memory are ignored.Ī Turing machine is an idealised model of a central processing unit (CPU) that controls all data manipulation done by a computer, with the canonical machine using sequential memory to store data. Turing completeness is the ability for a computational model or a system of instructions to simulate a Turing machine. While they can express arbitrary computations, their minimalist design makes them too slow for computation in practice: real-world computers are based on different designs that, unlike Turing machines, use random-access memory. Turing machines proved the existence of fundamental limitations on the power of mechanical computation. Thus by providing a mathematical description of a very simple device capable of arbitrary computations, he was able to prove properties of computation in general-and in particular, the uncomputability of the Entscheidungsproblem ('decision problem'). Does a machine exist that can determine whether any arbitrary machine on its tape ever prints a given symbol?.Does a machine exist that can determine whether any arbitrary machine on its tape is 'circular' (e.g., freezes, or fails to continue its computational task)?.With this model, Turing was able to answer two questions in the negative: It was Turing's doctoral advisor, Alonzo Church, who later coined the term 'Turing machine' in a review. The Turing machine was invented in 1936 by Alan Turing, who called it an 'a-machine' (automatic machine). Like a real computer program, it is possible for a Turing machine to go into an infinite loop which will never halt. The choice of which replacement symbol to write, which direction to move the head, and whether to halt is based on a finite table that specifies what to do for each combination of the current state and the symbol that is read. Then, based on the symbol and the machine's own present state, the machine writes a symbol into the same cell, and moves the head one step to the left or the right, or halts the computation. At each step of its operation, the head reads the symbol in its cell. It has a 'head' that, at any point in the machine's operation, is positioned over one of these cells, and a 'state' selected from a finite set of states. The machine operates on an infinite memory tape divided into discrete cells, each of which can hold a single symbol drawn from a finite set of symbols called the alphabet of the machine. Despite the model's simplicity, it is capable of implementing any computer algorithm.

(Clicking on each layer gets an article on that subject)Ī Turing machine is a mathematical model of computation describing an abstract machine that manipulates symbols on a strip of tape according to a table of rules.

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