Pairwise Independence and Derandomization
Michael Luby and Avi Wigderson
July 1995
This set of notes gives several applications of the
following paradigm. The paradigm consists of two
complementary parts. The first part is to design a
probabilistic algorithm described by a sequence of random
variables so that the analysis is valid assuming limited
independence between the random variables. The second part
is the design of a small probability space for the random
variables such that they are somewhat independent of each other.
Thus, the analysis of the algorithm holds even when the
random variables used by the algorithm are generated
according to the small space.
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Approximately 60 pages.
Reference as one of the following:
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ICSI TR-95-035
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UC Berkeley UCB/CSD-95-880
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Ecole Normale Superieure LIENS-95-22
Table of Contents
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Lecture 1: Pairwise Independence
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Lecture 2: Constructing Hash Functions
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Lecture 3: Derandomization Applications
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Lecture 4: Hashing
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Lecture 5: RP and BPP
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Lecture 6: Complexity of Unique Solutions
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Lecture 7: BPP is a subset of Sigma2
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Lecture 8: AM = IP
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Lecture 9: Deterministic Amplification
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Lecture 10: Chor-Goldreich Generator
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Lecture 11: Nisan's Generator
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Lecture 12: Impagliazzo-Zuckerman Generator
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Lecture 13: The Expander Mixing Lemma
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Lecture 14: Karp-Pippenger-Sipser Generator
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Lecture 15: Ajtai-Komlos-Szemeredi Generator
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Lecture 16: Limited Independence Probability Spaces
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Lecture 17: One-Way Functions
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Lecture 18: Hidden Bit Theorem
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Lecture 19: Pseudo-Random Generators
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Lecture 20: #P and Approximate Counting
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Lecture 21: DNF Counting
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Lecture 22: GF[2] Polynomial Counting
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Lecture 23: Bounded Depth Circuit Counting
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References