1. Given the following grammar S à 0A0 | 1B1 | BB; A à C; B à S | A; C à S | ε, (a) (Derivation)

Given a left-most and right-most derivation of a string 01001110 (b) (Parse tree) Draw the parse tree from step (a)

2. (Language to PDA) Design a PDA whose language is {a^mbⁿc^pd^q | m + n = p + q}.

3. (a) (Language to CFG, closure property) Construct CFG for the following language L = {bⁱ a²ⁱ | i >= 0} (b) (CFG to PDA) Design a PDA for the above grammar using a transition diagram and specifying the start/accept state(s), start symbol on the stack. (c) (PDA computation) Show the stack

content, state of the PDA in each step given an input string baa

4. (Pumping lemma) Use pumping lemma to show that the following language is not context free {0ⁱ1^j | i is not a multiple of j}

5. Show that the language L = {aⁱb^j |i  ≠ j) is context free.