Given,

CFG:

S aSbB S Aa A aA A SA A a B AB B bBC B b C abCS C

Construct the following using the above CFG:

a. a PDA simulating the leftmost derivation

b. The LL(1) parse table containing FIRST₁, FOLLOW_1, and LOOKAHEAD₁ sets and justify whether it's an LL(1) grammar

c. The LL(2) parse table containing FIRST2, FOLLOW_2, and LOOKAHEAD2 sets and justify whether it's an LL(2) grammar

d. Run the LL(2) parser on the input string aaaabbb to find an accepting computation. If the grammar in the above CFG is not LL(2), use a rule leading to acceptance when there are multiple choices as a nondeterministic PDA does.