Design a DFA for the language L = {w | w contain 2 a’s at any position and greater than 3 b’s at any position, w ϵ {a.b}*}/

Question

I do not understand this question,because for saving Number of a's and b's memory is required,which FA does not provide.could anybody please explain this?

Answer 1

Hint. You just need to count the number of $a$'s up to $2$ and the number of $b$'s up to $3$. Just think of the languages $aaa^*$ and $bbbb^*$. First design a DFA for these languages and then use the same idea for your language.