Pseudorandom generator designs When designing pseudorandom generators what should one consider? Here is an example pseudorandom generator $F^t : \{0,1\}^n \rightarrow \{0,1\}^{4n}$. I have no idea what it means, so what does it kindly mean? It is one proposal written in a book for the truly random compression function $t : \{0,1\}^{2n} \rightarrow \{0,1\}^n$

Like how would I design one for truly random compression function such as $t : \{0,1\}^{2n} \rightarrow \{0,1\}^n$?
It just defines a function that expands the input size with the output size four times, where the output depends on configuration value $t$ as well. The hash function compresses the input to an output that is half the size (which is not common, usually a hash function outputs a constant size hash).

Here ^ is not a power function. It simply shows how many elements there are sequentially taken from the input set $\{0, 1\}$ - properly formatted it reads $\{0, 1\}^{4 \cdot n}$. So the $x$ in $\{0, 1\}^x$ simply defines an input or output consisting of $x$ bits - with value $0$ or $1$ of course.