Automata and Computability

1. Given the grammar with production rules as follows: F(E)lalb Derive these strings and also draw parse trees for each string: (a) a (b) a+b (c) a+aa 2. Given the grammar G-(S), a, b), S, P), with productions Describe the language L(G) generated by this grammar. (Hint: derive a few words) 3. Show that the language L (a"b*e" n 20,k2 is not regular (Hint: Usete umping lemma). Show that the language L-(a": n is not a perfect square) is not regular (Hint: Use the pumping lemma)