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# A4 - strings where each block of 1’s has length at least...

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Due: Friday, June 11 Math 239 Assignment 4 1. (a) (4 points) Prove that the elements of {011,1101,10110} * are uniquely created. (b) (4 points) Give an example of a set A of binary strings such that A 2 is uniquely created but A 3 is not. (c) (4 points (bonus)) Suppose M and S are sets of binary strings and ε S. If M = ε SM, (1) prove that M = S * . 2. For each of the following sets of strings, write down a decomposition that uniquely creates it. (a) (2 points) The set L of strings that do not contain 000 or 111. (b) (2 points) The set L of strings that do not contain 100. (c) (4 points) The strings where each odd block of 0’s is followed by an odd block of 1’s, and each even block of 0’s by an even block of 1’s. 3. (5 points) Use a decomposition to determine the generating series for the set of binary
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Unformatted text preview: strings where each block of 1’s has length at least three, and express it as a rational func-tion. 4. (a) (4 points) Use a block decomposition to describe the set L of binary strings where each 0 is followed by an odd number of 1’s. . (b) (3 points) Determine the generating series for L and express it as a rational function. 5. (5 points) Let L be the set of binary strings that do not contain 10101 as a substring. Let M be the set of all binary strings that contain exactly one copy of 10101, at the right hand end. Find the generating series for L and M, expressed as rational functions....
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