math239-26052008

Section 1(c sloss math 239 introduction to binary

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Unformatted text preview: Section 1 (C. Sloss) MATH 239: May 26, 2008 Introduction to Binary Strings Unique generation 6. Star of a set Definition : A * ; = { } ∪ A ∪ AA ∪ AAA ∪ ··· = ∪ k ≥ A k . For binary strings, A k is the concatenation product unless otherwise indicated. By convention, A = { } . The set of all binary strings is { , 1 } * . Section 1 (C. Sloss) MATH 239: May 26, 2008 Introduction to Binary Strings Unique generation 7. Generating series for A * Definition : A * is uniquely generated if | A * | = { } ∪ A ∪ A × A ∪ A × A × A ∪ ··· . If A * is uniquely generated, then Φ A * ( x ) = 1 1- Φ A ( x ) . Section 1 (C. Sloss) MATH 239: May 26, 2008 Introduction to Binary Strings Unique generation 8. Examples of Unique Generation Questions Let A = { 00 , 001 , 10 , 110 } . Are the elements of A * uniquely generated? Let B = { 00 , 101 , 11 } . Are the elements of B * uniquely generated? { , 1 , 11 } * is not uniquely generated, but { , 1 , 11 } * = { , 1 } * , which is uniquely generated. Section 1 (C. Sloss) MATH 239: May 26, 2008 Introduction to Binary Strings Unique generation Reading Assignment Read Section 2.4, pages 47-49 Try Question 1 in Section 2.5. Reading ahead : Remainder of Section 2.4 Section 1 (C. Sloss) MATH 239: May 26, 2008...
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Section 1(C Sloss MATH 239 Introduction to Binary Strings...

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