In his answer to a previous question, Sadeq Dousti recalled the following terminology:$f(n) = n^{\omega(1)}$ is called super-polynomial. (e.g. $n^{\log n}, 2^n, 2^{2^n}$.)$f(n) = 2^{n^{\Theta(1)}}$ is called exponential. (e.g. $2^n, 3^{n^4}$.)$f(n) = 2^{n^{o(1)}}$ is called sub-exponential. (e.g. $2^{n^{1/n}}, n^{\log n}$.)Is this standard terminology? In particular, I am interested to know whether it is OK to call $2^{\sqrt{n}}$ and other functions in $2^{n^{\Theta(1)}}$ exponential or not.Edited after 1st answer: Yes! The issue is when you have a $2^{\sqrt{n}}$ lower bound. Can you say that this is an exponential lower bound? I am thinking here of a lower bound for a combinatorial value, not for some time complexity where one has standard definitions for $\mathsf{E}$ and $\mathsf{EXPTIME}$. I now realize I probably picked the wrong keywords.
Is it right to call $2^{\sqrt{n}}$ exponential?
complexity classes;terminology