flac-hw2

# flac-hw2 - A so that A 1 3 = x | for some yz | x | = 1 3 |...

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FLAC Assignment 2 Exercise 1. Use the construction given in class or in Theorem 1.39 to convert each of the two NFAs at the right into an equivalent DFA. Exercise 2. Are the following languages regular? For each language, either give an automaton 1 that recognizes it or give a proof that it is not regular. a. { a n b * c n } , for Σ = { a , b , c } b. { ww R | w Σ * } , for Σ = { 0 , 1 } c. { ww | w Σ * } , for Σ = { 0 , 1 } Exercise 3. Consider the set of strings that have an equal number of occurences of “01” and “10”. (For example, “010” is in this language but “0101” is not.) Under each of the following alphabets, is this language regular? For each alphabet, give an automaton that recognizes it or prove that it is not regular. a. Σ = { 0 , 1 } b. Σ = { 0 , 1 , # } Exercise 4. If A is a regular language, let A 1 3 be the set of all ﬁrst thirds of strings in
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Unformatted text preview: A so that A 1 3 = { x | for some yz, | x | = 1 3 | xyz | and xyz ∈ A } Similarly, let A 3 3 be the set of all last thirds of strings in A so that A 3 3 = { z | for some xy, | z | = 1 3 | xyz | and xyz ∈ A } Finally, let A 1 3 , 3 3 be the set of strings with their middle third deleted so that A 1 3 , 3 3 = { xz | for some y, | x | = | z | = 1 3 | xyz | and xyz ∈ A } a. Give an automaton that recognizes A 1 3 or prove that is not regular. b. Give an automaton that recognizes A 3 3 or prove that is not regular. c. Give an automaton that recognizes A 1 3 , 3 3 or prove that is not regular. 1 Give the state-transition diagram of the automaton; don’t give a tuple. Page 1...
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