Consider the language of all words over {a, b} that either begins and ends with aa or bb (but both are the same within each word). That is, {ccycc | c ∈ {a, b}, y ∈ Σ ∗}
I have drawn the resulting NFA for the language described above, what would the corresponding DFA look like? What would the steps look like to get from an NFA to a DFA?
In this case you are very close to a DFA already. First add a 'dead state' (non-final) with additional transitions to it from q1, q2, q5, and q6 on symbols b, a, b, and a, respectively, plus an arrow from the state to itself on a and b. Second, split q7 into two final states q8, q9, with q5->q8 on a and q6->q9 on b, and add loops q8->q8 on a, q9->q9 on b, and cross-transitions q8->q6 on b, q9->q5 on a.