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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 {ambncpdq | 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 {0i1j | i is not a multiple of j}
5. Show that the language L = {aibj |i ≠ j) is context free.
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Alec is a picky eater. He will only eat pizza that contains pineapple, tuna, or both mushrooms and ham, but he will refuse to eat any pizza that contains pepperoni or tomato sauce.
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