regular expression from DFA

Question

..

Design regular expression for no 2  a's should come together , what i did i draw a dfa for 2 a's come together and then took complement of it , now iam using state elimination method but iam not getting correct regular expression from this  , correct regular expression is given below in image 

Comments

you can write like this -

(ab+b)*(epsilon+a)   OR   (epsilon+a)(ba+b)*

---

(epsilon+a) Will come due to a path is forming in between A to F(final state) as you shift  (a+b) to the A state as a loop but there will still another path exist between A to B on transition 'a' and B to F epsilon so (epsilon+a) .

---

Hi,

I have a doubt, in the DFA for Let 2a's come together, in state 'C' you are accepting any strings of a and b. i.e your DFA is saying that only one occurrence of 'aa' is sufficient. But shouldn't the complement of ' no 2  a's should come together' be that '2  a's should always come together'?