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.