Replication Function

Definition¹

A vector-valued Boolean function like the following is called a cloning function.

$$ \text{cl} : \left\{ 0, 1 \right\} \to \left\{ 0, 1 \right\}^{2} $$

$$ \text{cl}(a) = (a, a) $$

Explanation

As the name suggests, it is a function that clones truth values. Unlike quantum computers, it is easy to clone signals on classical computers, so it can be used without restrictions. The $\text{NAND}$ gate is necessary to prove that it is functionally complete.