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In the recent movie called The Imitation Game, there is a affirmation that Turing was building his theoretical machine. That machine is the Bombe Machine. Is this machine really equivalent to a Turing Machine ?

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No, the bombe was very specific. It consisted of a bunch of enigma machines hooked together. It was very limited in its use. A more interesting question is whether the Colossus computer, also used in Bletchely Park, was Turing-complete.

When asking such a question, it should be understood that no physical computer is Turing-complete, since it cannot handle arbitrarily large inputs. But even if we abstract this issue away (in any reasonable way), bombes are not Turing-complete. It could be fun to come up with an appropriate model and determine the exact complexity class covered by bombes.

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  • $\begingroup$ So the Turing's work in second war doesn't have any relation with computability ?! Yes, would be fun :D Thank you! $\endgroup$ – Rafael Castro Feb 1 '15 at 3:49
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    $\begingroup$ @Rafael: building a special-purpose (not Turing-complete) computer certainly has connections with computability. $\endgroup$ – Peter Shor Feb 1 '15 at 18:05
  • $\begingroup$ Re the question about Colossus, its Wikipedia page links to dl.acm.org/citation.cfm?id=1612096 $\endgroup$ – Peter Taylor Feb 2 '15 at 12:04
  • $\begingroup$ It is not true that computers aren't Turing complete: they can use an unlimited amount of external storage. $\endgroup$ – reinierpost Feb 2 '15 at 22:27
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    $\begingroup$ @reinerpost: No, they can't. The amount of available storage is limited by the amount of available matter, which is limited to less than $10^{1000}$ elementary particles. $\endgroup$ – Jeffε Feb 7 '15 at 19:53

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