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Is the first bit preserving version of a PRG also a PRG?

Given that $G$ is a pseudorandom generator from $\{0,1\}^n$ to $\{0,1\}^{l(n)}$, $G'$ defined as follows: $G'(s) = \begin{cases} G(s) \space \text{if the first bit of s and G(s) are the same} \\ …
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