A function T:N→N is time constructible if T(n)≥n and there is a Turing Machine M that computes the function x↦└T(|x|)┘ in time T(n). (└T(|x|)┘ denotes the binary representation of the number T(|x|).)
--Arora, Barak
I was going through the following link.
But the statement about "f(n)=c, f(n)=n are not time-constructible" I am heavily confused about this statement. As the wiki page says that f(n)= n is a time-constructible function.
Firstly how is f(n)=c a non-time constructible function and secondly is f(n)=n a time/non-time constructible function?