For any PRG $G$:$\{0,1{\}}^{}\{0,1{\}}^{+l}$ there will be many strings in $\{0,1{\}}^{+l}$ that are

impossible to get as output of $G.$ Let $S$ be any such set of impossible $G-$outputs, and

consider the following adversary that has $S$ hard$-$coded:

$[A],[x$:$=$QUERY$()],[$ return $n^{?}S]$

What is the advantage of $A$ in distinguishing $L_{prg-\text{r}\text{e}\text{a}\text{l}}^G$ from $L_{prg-\text{r}\text{a}\text{n}\text{d}}^G?$ Why does an ad$-$

versary like this one not automatically break every PRG$?$