Exercise 1

1. After eliminating left recursion, we get follows:
   S -> T$
   T -> abV
   V -> UV | lambda
   U -> aUbb | ab
   Then using factorization
   S -> T$
   T -> abV
   V -> UV | lambda
   U -> aW
   W -> Ubb | b

   The following is a deterministic PDA for the language:

   

   look-ahead:

   Alternative (3)/(4): choose (3) if next input symble is "a"; choose (4) if next input symble is "$"

   Alternative (6)/(7): choose (6) if next input symbol is "a"; choose (7) if next input symble is "b"

   The DPDA obtained with the technique of the look-ahead

   

   The recursive-descent parser is here.

Exercise 2