title: Regular expression for a DFA that accepts the empty string as well as other strings
body: <p>For the following <s>DFA</s> NFA</p>
  
  <p><a href="https://i.stack.imgur.com/PTqGZ.png" rel="nofollow noreferrer"><img src="https://i.stack.imgur.com/PTqGZ.png" alt="enter image description here"></a></p>
  
  <p>I produced the RE</p>
  
  <pre><code>(a + b)(ab)*
  </code></pre>
  
  <p>However, I then realised that my RE doesn't accept the empty string as it only accepts strings beginning with an <code>a</code> or a <code>b</code>, yet the <s>DFA</s> NFA also accepts the empty string as the initial state is an accepting state.</p>
  
  <p>What is a valid RE for this <s>DFA</s> NFA? I would think something along the lines of</p>
  
  <pre><code>Ø + (a + b)(ab).*
  </code></pre>
  
  <p>but I doubt this syntax is accepted.</p>
  
  <p><strong>EDIT</strong></p>
  
  <p>I have also just realised that the example I have made is an NFA, but that is besides the point of the question.</p>