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I have been hearing the phrases quasipolynomial, superpolynomial and subexponential.

I think know what quasipolynomial and subexponential is. I believe these are functions respectively of form $n^{\log^c n}$ and $n^{n^{1/c}}$ for some $c>1$.

What does superpolynomial mean?

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    $\begingroup$ Google "define: superpolynomial" answers this instantly. See wikipedia. $\endgroup$ – David Richerby Dec 12 '15 at 12:20
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Superpolynomial means $n^{\omega(1)}$, that is, growing faster than any polynomial. More clearly, $n^{f(n)}$ for some function $f$ satisfying $\lim_{n\to\infty} f(n) = \infty$.

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  • $\begingroup$ So superpoly contains both quasipoly and subexponential? $\endgroup$ – T.... Dec 12 '15 at 19:27
  • $\begingroup$ @Turbo That's right. $\endgroup$ – Yuval Filmus Dec 12 '15 at 19:52

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