Let $A(x)$ be an algorithm and $n=|x|$ denote the length of the binary encoding of its input $x$. We say that an event regarding $A$ and $x$ holds with negligible probability if it holds with probability $O(1/poly(n))$. We say the event holds with significant probability if it holds with probability $1-O(1/poly(n))$. Note that the property of being negligible or significant is closed under polynomial additions and multiplications. That is, the probability of the union and the interception of a polynomial number of negligible (resp.$\ $significant) events is still negligible (resp.$\ $significant).
We say that a PRG $G$ is predictable if given a random seed $k$, there is an efficient algorithm that can predict some $i$th bit of the output according to first $i-1$ bits with non-negligible probability.
We say that a PRG $G$ is insecure if given a random seed $k$, there is an efficient algorithm that can distinguish it from a true random number generator with non-negligible probability.
