> When I say subclass of inputs, I literally mean inputs, so if say f is
> a function in NP, there is some subclass of x, S, such that for all x
> in S, T(f(x)) = O(|x|^n).
>

Such subclasses are known and studied. For example, the reason
that SAT works so well in real life is because almost all real-life
problems fall into the subclass!  But this is well-known, now, and
research has moved on to trying to identify if there are more
subclasses which have been missed so far (and/or for which some
other algo might be effective).

--linas

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