I was just thinking about the powerset construction and it is clear to me that the powerset construction will result into a DFA $D$ with possibly redundant states, as the NFA $N$ is not minimized. But in case where $N$ is minimal will $D$ will also be minimal?
So is there a DFA $D'$ with less states for the same Language $L$, assuming that only accessible states are added to $D$? I think it cannot be, since a redundant state in $D$ would result into a redundant edge in $N$ and this would contradict the assumption, but I am not sure.
Thanks.
