ass3 - MATH 239 Assignment 3 This assignment is due at noon...

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MATH 239 Assignment 3 This assignment is due at noon on Friday, June 12, 2009, in the drop boxes opposite the Tutorial Centre, MC 4067. 1. Let a and b be two distinct nonempty binary strings, and let A = { a,b } . Determine whether the following two statements are true or false, and prove your assertions. (a) If a and b have the same length, then strings of A * are uniquely created. (b) If a and b have different lengths, then strings of A * are uniquely created. 2. For each of the three parts in this quesion, i. find a decomposition that uniquely creates elements of S ; and ii. show that the generating function for S with respect to length is the given rational function. (a) i. S is the set of binary strings that do not contain “1000” as a substring. ii. Φ S ( x ) = 1 1 - 2 x + x 4 . (b) i. S is the set of binary strings where each block has odd length. ii. Φ S ( x ) = 1 + x - x 2 1 - x - x 2 . (c)
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