Problem 1

From the Pumping Lemma for Context Free Languages given in the class notes, what length for a string u would suffice to gauruntee that u could be "pumped", i.e. that we could find repeated symbols, break up into v,w,x,y,z, etc?

Problem 2

Now consider the very much shorter string u = bbcaccbcaccb.

• Construct the parse tree for u using grammar G.
   
• There is a path containing repeated non-terminals. Identify the repeated non-terminals (on your parse tree from above).
   
• Give me the v,w,x,y,z such that u = vwxyz, not both w and y are the empty string, and vw^kxy^kz ∈ L(G).