We prove that a $T(n)$ time-bounded, $S(n)$ space-bounded and $U(n)$ output-length-bounded Turing machine can be simulated in O(T(n) + (n + U(n))log log S(n)) time by a random access machine (with no multiplication or division instructions) under the logarithmic cost criterion.
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Katajainen et al. (1988) studied this question.
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