Abstract
We show that a deterministic Turing machine with one d-dimensional work tape and random access to the input cannot solve satisfiability in time n a for a < ( d + 2 ) / ( d + 1 ) . For conondeterministic machines, we obtain a similar lower bound for any a such that a 3 < 1 + a / ( d + 1 ) . The same bounds apply to almost all natural NP -complete problems known.
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