Let $G$ be a deterministic polynomial-time function from $\mathbb{N}^{<\omega}$ to $\mathbb{N}^{<\omega}$ with stretch function $l:\mathbb{N}\rightarrow\mathbb{N}$ , so that if $x$ has length $n$ then $G(x)$ has length $l(n)$ . Then let $G_n$ be the distribution on strings of length $l(n)$ defined by the output of $G$ on a randomly selected string of length $n$ selected by the uniform distribution.

Then we say $G$ is pseudorandom generator if $\{G_n\}_{n\in\mathbb{N}}$ is pseudorandom.

In effect, $G$ translates a random input of length $n$ to a pseudorandom output of length $l(n)$ . Assuming $l(n)>n$ , this expands a random sequence (and can be applied multiple times, since $G_n$ can be replaced by the distribution of $G(G(x))$ ).