T4 - a substring Express Φ S x as a rational function As...

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Problem 1: Explain why the elements of { 0111 , 111 , 1110 , 00 } * are not uniquely created. Second, prove that the elements of { 0111 , 1110 , 00 } * are uniquely cre- ated. Problem 2: Let S be the set of all { 0 , 1 } -strings in which the substring ”01110” does not occur. Show that Φ S ( x ) = 1 + x 4 1 - 2 x + x 4 - x 5 where the weight of a string is its length. Problem 3: Let S be the set of binary strings that do not contain 00011 as
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Unformatted text preview: a substring. Express Φ S ( x ) as a rational function. As usual, the weight of a string is its length. Problem 4: Let A = { 01 , } and B = { 11 , 1 } . Are the elements of AB uniquely generated? How about the elements of BA ? (Here we use AB = ab : a ∈ A,b ∈ B } with usual string concatenation.) 1...
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