title: Exhibiting an algorithm that determines if L = L*, given any regular language L
body: <p>I am studying membership algorithms and I am working on this particular problem which says the following:</p>
  
  <p><strong>Exhibit an algorithm that, given any regular language L, determines whether or not L = L*</strong></p>
  
  <p>So, my first thought was, we have L* which is Kleene star of L and to determine if L = L*, well couldn't we just say that since L is regular, we know L* is by definition which states that the family of regular languages is closed under star-closure. 
  Therefore L will always be equal to L*? </p>
  
  <p>I feel like there is definitely a lot more to it, there is probably something I am missing. Any help would be appreciated. Thanks again.</p>