# hw2 - is never visited twice Part C Every DFA-acceptable...

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ECS 120: Introduction to the Theory of Computation Homework 2 Problem 1. Given a DFA M = ( Q, Σ , δ, q 0 , F ), prove that if ˆ δ ( q, xz ) F and ˆ δ ( q, yz ) 6∈ F then ˆ δ ( q, x ) 6 = ˆ δ ( q, y ), for x, y, z Σ * . Problem 2. Find the smallest (in terms of number of states) DFA for the language L = { 01 * 0 } . Prove that there is no DFA smaller than yours. Problem 3. Part A. Every DFA-acceptable language can be accepted by a DFA with an even number of states. Part B. Every DFA-acceptable language can be accepted by a DFA whose start state
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Unformatted text preview: is never visited twice. Part C. Every DFA-acceptable language can be accepted by a DFA no state of which is ever visited more than once. Part D. Every DFA-acceptable language can be accepted by a DFA with only a single ﬁnal state. Problem 4. Give two substantially diﬀerent proofs of the following: if L 1 and L 2 are DFA-acceptable then L 1 ⊕ L 2 = { w : w is in exactly one of L 1 and L 2 } is DFA-acceptable. 1...
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