# ass4 - (c) S is the set of binary strings in which each...

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This assignment will not be marked. Do not hand in. Math 239 Assignment 4 1. For each of the following sets A , determine whether A * is uniquely created. Prove your assertion in each case. (Hint: to prove a set A * is uniquely created, try using induction on the length.) (a) A = { 00 , 010 , 0111 } (b) A = { 010 , 0010 , 01001 } . 2. For each of the following sets of binary string S , write a decomposition that precisely describes S , in which the elements are uniquely created. Justify why each has the uniquely created property. (a) S is the set of binary strings in which each occurrence of 0 must be immediately followed by at least four consecutive 1’s. (b) S is the set of binary strings in which each block of 0’s that immediately follows a block of 1’s has the same length as that block of 1’s.
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Unformatted text preview: (c) S is the set of binary strings in which each block of 0’s that immediately follows a block of 1’s is longer than that block of 1’s. 3. Let S be the set of binary strings (in which elements are uniquely created) given by S = { 11 } * ( { }{ 00 } * { 1 }{ 11 } * ∪ { 00 }{ 00 } * { 11 }{ 11 } * ) * { 00 } * . Find the generating function for S with respect to length, and describe in words the strings that belong to S . 4. For each of the following recursive deﬁnitions, describe in words the strings that belong to S , and explain why the strings of S are or are not uniquely created. (a) S = { ± } ∪ S { }{ } * { 1 }{ 1 } * (b) S = { ± } ∪ { , 1 } S { , 1 } ∪ SS ....
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## This note was uploaded on 08/13/2011 for the course MATH 239 taught by Professor M.pei during the Spring '09 term at Waterloo.

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