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We show that all languages accepted in time f(n) >= n^2 can be accepted inspace O(f(n)^{1/2})_and_ in time O(f(n)). The proof is carried out bysimulation, based on the idea of guessing the sequences of internal states ofthe simulated TM when entering certain critical cells, whose location is alsoguessed. Our method cannot be generalised easily to many-tapes TMs, and in nocase can it be relativised.

Is Space a Stronger Resource than Time? Positive Answer for the Nondeterministic at-Least-Quadratic Time Case