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quiz1-solns - ECS 120 Theory of Computation UC Davis Phil...

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ECS 120: Theory of Computation Handout Quiz #1S UC Davis — Phil Rogaway April 18, 2010 Quiz 1 Solutions Questions 1–4 were graded out of 10 points; questions 5–13 were graded out of 25 points total; question 14 was graded out of 20 points. So the total possible was 85 points. 1. Complete the following, being mathematically precise and following the conventions of your text: An NFA is a five-tuple M = ( Q, Σ , δ, q 0 , F ) where: Q is a finite set, Σ is an alphabet, q 0 Q , F Q , and δ is a function having domain and range δ : Q × ∪ { ε } ) → P ( Q ) 2. Draw a DFA for the language: L = { x ∈ { a, b, c } : x contains at least one a and at least one b } Make your DFA use a minimal possible number of states. Don’t forget the c ’s. a b b a a, c a, b, c b, c c 3. List the first five strings, according to the lexicographic ordering, 1 of the language L = { x ∈ { a, b, c } : x contains at least one a and at least one b } . ab, ba, aab, aba, abb 1 Recall that in the lexicographic ordering of a language L we first list all length-0 stings in L
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