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convert a turing machine to oblivious turing machine

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Hi

I have an assignment question which I have no clue on how to start.I am posting the question. I would really appreciate if someone could guide me on how to solve it.

 

Question:

  1. Show that for every time-constructible T: N N, if L DTIME(T(n)), then there is an oblivious TM that decides L in time O(T (n) log T (n)).

Any material that will help solve it or any similar examples would be highly appreciated.

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