A time lower bound for satisfiability

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 α for a < √(d + 2)/(d + 1). For conondeterministic machines, we obtain a similar lower bound for any a such that a 3 < 1+α/(d+1). The same bounds apply to almost all natural NP-complete problems known.

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