## Turing machine |

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variants alternating turing machine differentiable neural computer nondeterministic turing machine quantum turing machine post–turing machine probabilistic turing machine read-only turing machine read-only right moving turing machines multitape turing machine multi-track turing machine symmetric turing machine total turing machine unambiguous turing machine universal turing machine zeno machine

science alan turing category:turing machine

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**turing machine**is a that defines anmathematical model of computation ,abstract machine ^{[1]}which manipulates symbols on a strip of tape according to a table of rules.^{[2]}despite the model's simplicity, given any , a turing machine capable of simulating that algorithm's logic can be constructed.computer algorithm ^{[3]}the machine operates on an infinite

^{[4]}memory tape divided into "cells".discrete ^{[5]}the machine positions its "head" over a cell and "reads" or "scans"^{[6]}the symbol there. then, as per the symbol and its present place in a "finite table"^{[7]}of user-specified instructions, the machine (i) writes a symbol (e.g., a digit or a letter from a finite alphabet) in the cell (some models allow symbol erasure or no writing),^{[8]}then (ii) either moves the tape one cell left or right (some models allow no motion, some models move the head),^{[9]}then (iii) (as determined by the observed symbol and the machine's place in the table) either proceeds to a subsequent instruction or halts the computation.^{[10]}the turing machine was invented in 1936 by

,alan turing ^{[11]}^{[12]}who called it an "a-machine" (automatic machine).^{[13]}with this model, turing was able to answer two questions in the negative: (1) 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); similarly, (2) does a machine exist that can determine whether any arbitrary machine on its tape ever prints a given symbol.^{[14]}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 of theuncomputability ('decision problem').entscheidungsproblem ^{[15]}thus, turing machines prove fundamental limitations on the power of mechanical computation.

^{[16]}while they can express arbitrary computations, their minimalist design makes them unsuitable for computation in practice: real-world are based on different designs that, unlike turing machines, usecomputers .random-access memory is the ability for a system of instructions to simulate a turing machine. 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.turing completeness - overview
- description
- formal definition
- additional details required to visualize or implement turing machines
- models equivalent to the turing machine model
- choice c-machines, oracle o-machines
- universal turing machines
- comparison with real machines
- history
- see also
- notes
- references
- external links

This article has an unclear citation style. (November 2019) ( |

A **Turing machine** is a ^{[1]} which manipulates symbols on a strip of tape according to a table of rules.^{[2]} Despite the model's simplicity, given any ^{[3]}

The machine operates on an infinite^{[4]} memory tape divided into ^{[5]} The machine positions its "head" over a cell and "reads" or "scans"^{[6]} the symbol there. Then, as per the symbol and its present place in a "finite table"^{[7]} of user-specified instructions, the machine (i) writes a symbol (e.g., a digit or a letter from a finite alphabet) in the cell (some models allow symbol erasure or no writing),^{[8]} then (ii) either moves the tape one cell left or right (some models allow no motion, some models move the head),^{[9]} then (iii) (as determined by the observed symbol and the machine's place in the table) either proceeds to a subsequent instruction or halts the computation.^{[10]}

The Turing machine was invented in 1936 by ^{[11]}^{[12]} who called it an "a-machine" (automatic machine).^{[13]} With this model, Turing was able to answer two questions in the negative: (1) 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); similarly, (2) does a machine exist that can determine whether any arbitrary machine on its tape ever prints a given symbol.^{[14]} 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 * Entscheidungsproblem* ('decision problem').

Thus, Turing machines prove fundamental limitations on the power of mechanical computation.^{[16]} While they can express arbitrary computations, their minimalist design makes them unsuitable for computation in practice: real-world