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    $\begingroup$ Is it $\mathsf{TIME}[g(n)] = \mathsf{TIME}[f(g(n))]$? otherwise the statement is not interesting: just choose $g(n) = n$. $\endgroup$ Commented Jul 14, 2011 at 3:31
  • $\begingroup$ @Sasho, it appears so. The statement of Borodin's gap theorem (via the link) says as much. $\endgroup$ Commented Jul 23, 2011 at 16:05