ECS 120, Summer II 2013, Prof. Franklin, Midterm 8/19/13 1. (10 points) This question is about the proof in the book of the equivalence of DFA's and NFA's. a. If M is a DFA with |Q| = 20 and |F| = 1, then how many states and final states are in the equivalent NFA? Explain. b. If N is a NFA with |Q| = 20 and |F| = 1, then how many states and final states are in the equivalent DFA? Explain. 2. (10 points) This question is about DFA's for pattern matching over the alphabet Sigma = {a, b, c}. a. Construct a DFA for {w | w contains substring aba}. b. Construct a DFA for {w | w does not contain substring aba}. 3. (10 points) Sketch the main ideas in the proof of the Pumping Lemma for context free languages. 4. (10 points) This question is about a CFG over the alphabet Sigma = {0} with the following rules: S -> 000S, S -> S000, S -> epsilon. a. Is this CFG ambiguous? Explain. b. Give the nondeterministic pushdown automaton for this CFG given by the prof in the book of the equivalence of CFG's and nondeterministic PDA's.