title: Generating Sets via recursion - Language and strings (cs/logic)
body: <p>This is a general logic question, common to most introductory language and machines courses. However I've searched the internet and the forums for any help on this, but I cant seem to find a topic that details what the successive sets will contain. Here is an example question: (I have many HW problems like this, I just don't know where to start)</p>
  
  <p>Let L be the language over {a,b} generated by the following recursive definition
  basis: λ ∈ L
  recursive step: If w ∈ L then awbb is in L.
  closure: A string w ∈ L only if it can be obtained from the basis set by a finite number
  of applications of the recursive step.
  Part a. Give the sets L1; L2; and L3 generated by the recursive definition. Note that L0 = λ</p>
  
  <p>I get that The alphabet is {a,b}, Lo = the empty string, and if a string w is contained in L, then awbb is in L. But what does that mean for the next couple sets?</p>
  
  <p>I think L1 = {λ ,awbb} and then L2={λ , awbb, aawbbwbb}?</p>
  
  <p>Any help you could offer on this would be appreciated.</p>