$($b$)$ Let $G$:$\{,1{\}}^{}\{,1{\}}^{+l}$ be a candidate PRG$.$ Suppose there is a polynomial$-$time

algorithm $V$ with the property that it inverts $G$ with non$-$negligible probability. That

is$,$

$P{r}_{\text{s}\text{l}\text{a}\text{r}\text{r}\{\begin{array}{cc}[,& 1{\}}^{}\end{array}}[V(G(s))=s]is$ non$-$negligible.

Show that if an algorithm $V$ exists with this property, then $G$ is not a secure PRG$.$ In

other words, construct a distinguisher contradicting the PRG$-$security of $G$ and show

that it achieves non$-$negligible distinguishing advantage.

Note: Don't assume anything about the output of $V$ other than the property shown

above. In particular, $V$ might very frequently output the "wrong" thing.