A homework question asks me to a draw a DFA for the regular expression
$((aa^*)^*b)^*$
I'm having trouble with this because I'm not sure how to express the idea of $a$ followed by $0$ or many $a$'s many times, in terms of a DFA.
I would guess it that $(aa^*)^*$ should be the same thing as $\lambda + a^*$ but I'm not sure if I can formally say that. If I could, it would make my DFA simply