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Journal of the ACM (JACM)
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Let k be a constant -&-ge; 2, and let us consider only deterministic k-tape Turing machines. We assume t2(n) -&-gt; n and t2 is computable in time t2. Then there is a language which is accepted in time t2, but not accepted in any time t1 with t1(n) -&-equil; o(t2(n)). Furthermore, we obtain a strong hierarchy (isomorphic to the rationals Q) for languages accepted in fixed space and variable time.