Category:Time-Constructible Functions

This category contains results about Time-Constructible Functions.
Definitions specific to this category can be found in Definitions/Time-Constructible Functions.

Definition 1

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 $1$, $M$ stops after exactly $f \left({n}\right)$ steps for all $n \ge n_0$.

Then $f$ is time-constructible.

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 $\map f n$ in $\map \OO {\map f n}$ time.

Then $f$ is time-constructible.