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There is a problem I can't solve: Assume n is an integer. Prove that there exists a recursive language such that there is no Turing Machine which accepts it and makes a maximum of n steps for every input. I'll be glad to receive hints. Thanks!

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Note that this has been cross-posted at MO, although it looks likely to be closed there. – Old John Dec 29 '12 at 15:55
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Hint: In $n$ steps, a Turing machine can read from at most the first $n$ cells. So any Turing machine with this property depends only on the contents of the first $n$ cells of the input tape.

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