Given Regular expression Accept all strings over alphabet {a,b} which end with either ba or bb.
Because,(a+b)*b(a+b)=(a+b)*(ba+bb).
So, to recognise this we have to see the strings which have ba or bb at end .
Below is the Required Dfa. and we can't further minimize it.
By equivalance theorem we have two sets of final and non-final states.
[a,b] [ba,bb]
[a] [b] [ba] [bb] //Because a,b goes to diffrent sets on a-transitions and ba,bb also goes to diffrent sets on a-transitions.