# Definition:Time-Constructible Function/Definition 2

Let $f$ be a function.
Let there exist a positive integer $n_0$ and a Turing machine $M$ such that:
Given a string $1^n$ consisting of $n$ instances of $1$, $M$ outputs the binary representation of $f \left({n}\right)$ in $O \left({f \left({n}\right)}\right)$ time.
Then $f$ is time-constructible.