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Till date I have read that a Turing machine can do whatever a computer can.

Wikipedia Turing machine

mentions that since a real machine can have only a finite number of configurations it is equivalent to linear bounded automata.

Is this true?

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A machine bounded by $\Theta(1)$ memory is a finite state automaton (As a matter of fact, proving that $\textsf{DSPACE}(\Theta(1)) = \textsf{REG}$ is a classical exercise).

We say that "Turing machines can do whatever computers can" because, as long as we keep in mind that real computers are subject to limitations in computational power, it's more useful to think of computers as imperfect implementations of a universal Turing Machine rather than perfect implementations of a finite state automaton.

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  • $\begingroup$ It's not a finite state automaton, only equivalent to it in power. It is very unlike a finite state automaton, I would say, and much more like a Turing machine supplied with a finite tape. $\endgroup$ – reinierpost Jan 11 '18 at 23:33

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