# Tag Info

$F'_k(x)$ is not necessarily pseudo-random. Proof: Changing one output does not affect PRGness, so if there is a PRG that stretches by a factor of 2 then there is a PRG that stretches by a factor of 2 and sends all-zero strings to all-zero strings. For all $n$ and $k$ and $x$, if $G$ is such a PRG then $F'_k(x)$ is the string of $n$ zeros. For all $n$, ...