1. Consider the following grammar

S -> A
A -> aaB | bAA
B -> b | aB 

Suppose that a string generated by this grammar contains n occurrences of
"a" and m occurrences of "b".

1. What is the shortest string that this grammar generates?







2. Can n be greater than m?  If so, give an example that illustrates this.









3. Can n be less than m? If so, give an example that illustrates this.







4. Can n be equal to m?  If so, give an example that illustrates this.








5. Can this grammar be parsed by a top-down parser using one lookahead
   only?  Explain briefly.