title: How should one proceed to prove (or find) if two regular expressions are same or equivalent?
body: <p>For example, in an assignment given to me, we were asked to find out if two regular expressions are equal or not.</p>
  
  <pre><code>(a+b+c)*  and ((ab)**c*)*
  </code></pre>
  
  <p>My question is how is one supposed to do that? If I draw the transition graphs for both and then run a few strings through it and show that both of the TGs are able to accept it, is that a sufficient proof ? If not, how do I do it? Is there a mathematical/axiomatic approach towards this?</p>
  
  <p>Thanks in advance.</p>
  
  <p>EDIT: There is another thing that I'd like to clear which is kind of related to this question. Are the two FAs depicted in the photo below the same? </p>
  
  <p><img src="https://i.stack.imgur.com/3Sok9.jpg" alt="enter image description here"></p>
  
  <p>i.e. Are (1) and (2) in the above picture the same? </p>