Refinement of Hierarchies of Time Bounded Computations
Juris Hartmanis, John E. Hopcroft · eCommons (Cornell University) · 1968
It is shown that for any "slowly growing" time function $T(n)$ and any $\epsilon > 0$ there exists a computation which can be performed by a multitape Turing machine in time $T(n)\log^{\epsilon}T(n)$ and cannot be performed by any multitape Turing machine in time $T(n)$.