title: How to convert (ab u aab u aba)* into a NFA?
body: <p><strong>(ab u aab u aba)*</strong></p>
  
  <p>I did it but I would like some feedback on its correctness:</p>
  
  <p>If it is correct: Can we simplify (ab u aab u aba)* any further?</p>
  
  <p>If not: What did I miss?</p>
  
  <p>EDIT: It seems I am missing e-transitions from all 3 final states back to the initial state and I need a new state that is initial and final which will go to the old initial state on e-transition. (Kleene Star rule).</p>
  
  <p><img src="https://i.stack.imgur.com/3QQT3.png" alt="enter image description here"></p>
  
  <p>P.S. Can we also simplify <code>(a u b)*aabab</code> and <code>(a u b)*a(a u b)(a u b)(a u b)(a u b)</code>.</p>
  
  <p>The reason why I ask because if there's no way to simplify/minimize, it will be a ridiculously long DFA...</p>