title: State Elimination DFA to Regular Expression
body: <p>I have a few questions regarding state elimination and the terminology. </p>
  
  <p><a href="https://i.stack.imgur.com/Hib12.jpg" rel="nofollow noreferrer"><img src="https://i.stack.imgur.com/Hib12.jpg" alt="enter image description here"></a></p>
  
  <p>In the example above is a DFA with a accepting state where you must start with symbol 0 and end with 1.</p>
  
  <p>If I were to convert it to regular expression, the upper would be 
  <a href="https://i.stack.imgur.com/1bsOC.jpg" rel="nofollow noreferrer"><img src="https://i.stack.imgur.com/1bsOC.jpg" alt="enter image description here"></a></p>
  
  <p>and the bottom would be
  <a href="https://i.stack.imgur.com/leFPV.jpg" rel="nofollow noreferrer"><img src="https://i.stack.imgur.com/leFPV.jpg" alt="enter image description here"></a></p>
  
  <p>Here is my problem, I have no idea how to add the top part and the bottom part into on single expression. I am also not totally sure how to eliminate q2 symbol 1 further.</p>
  
  <p>Would it be 0(0*(0+1))1* ?</p>
  
  <p>Thank you to anyone who could help!</p>