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2IND_Luby_Widgerson - Pairwise Independence and...

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Pairwise Independence and Derandomization Foundations and Trends in Theoretical Computer Science 2005 Pairwise Independence and Derandomization

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Table of contents Introduction to Pairwise Independence Generating Pairwise Independent Bits Introduction to Derandomizatoin Brute Force Derandomization Derandomization via Pairwise Independence Application- MAXCUT A Complexity Theory Result Pairwise Independence and Derandomization
Pairwise Independent Events Consider the set of events A 1 , ..., A n The events A 1 , ..., A n are mutually independent if Pr [ A 1 A 2 ... A n ] = Pr [ A 1 ] Pr [ A 2 ] ... Pr [ A n ] The events A i and A j are pairwise independent if Pr [ A i A j ] = Pr [ A i ] Pr [ A j ] for all i , j Pairwise Independence and Derandomization

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Example of Pairwise Independent Events Consider the set Ω = { abc , acb , aaa , bac , bca , bbb , cab , cba , ccc } and probability of any of them being picked is 1 9 . Let event A k denote that the k th letter is a . Clearly Pr [ A k ] = 1 3 Pr [ A 1 A 2 ] = Pr [ A 2 A 3 ] = Pr [ A 3 A 1 ] = 1 9 Pr [ A 1 A 2 A 3 ] = 1 9 6 = Pr [ A 1 ] Pr [ A 2 ] Pr [ A 3 ] Thus, the events pairwise independent but not mutually independent Pairwise Independence is weaker than Mutual Independence Pairwise Independence and Derandomization
Generating Pairwise Independent Bits We know how to generate mutually independent bits (Coin Flips) Can we use mutually independent bits to generate pairwise independent bits? Construction of

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This note was uploaded on 10/23/2011 for the course CS 7520 taught by Professor Staff during the Spring '08 term at Georgia Tech.

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2IND_Luby_Widgerson - Pairwise Independence and...

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