Find a DFA that accepts words with "aa" twice

[tomkoolen]

Hi everyone,

I have just started learning about DFA's and I have to solve the problem from the thread title with
Σ = {a,b}.

My attempts so far are in the attachments.

I am struggling as to what to do with the words in state 2 that have a b*a*b* substring before getting their second "aa". Can anyone help me with this?

NB: It was noted in the exercise that "aaa" is accepted by the DFA because it contains the substring "aa" twice as well.

 

[mfb]

Why do you have 4 and 0 and where is the difference between those states? What do they mean?
"abaaa" does not get accepted like that.

2b will need a new state I think.