UW-Madison
Computer Sciences Dept.

CS 880 - Pseudorandomness and Derandomization

Spring 2013
Instructors: Holger Dell and Dieter van Melkebeek

Lecture Notes

Below you can find the lecture notes of this course. For information on how to write up your scribe notes in LaTeX, check out these guidelines.

# Date Topic Scribe
011/23Introduction [PDF] [TEX]
randomized algorithms, statistical distance, pseudorandom distributions
Gautam Prakriya
021/28Pseudorandom Generators and Extractors [PDF] [TEX]
definition, use, connection with hardness, finite fields
Nick Pappas
031/30Error Correcting Codes [PDF] [TEX]
Hamming code, Hadamard code, Reed-Solomon code, code concatenation
Xi Wu
042/4k-Wise Uniform Generators [PDF] [TEX]
definition, connection with ECCs, construction
Alexi Brooks
052/6Applications of k-Wise Uniform Generators [PDF] [TEX]
Chebyshev's inequality, concentration bounds, list decoding the Hadamard code, hashing
Lubos Krcal
062/11Small-Bias Generators [PDF] [TEX]
definition, connection with ECCs, construction, PRGs for low-degree polynomials
Kevin Kowalski
072/13Harmonic Analysis [PDF] [TEX]
Fourier transform, Parseval's equality, list decoding the Hadamard code
Gautam Prakriya
082/18Applications of Small-Bias Generators [PDF] [TEX]
almost k-wise uniform generators, hardness of approximation
Gautam Prakriya
092/20Expanders [PDF] [TEX]
vertex expansion, edge expansion, quasi-randomness, rapid mixing, spectral expansion
Adam Everspaugh
103/4Expander Constructions [PDF] [TEX]
Cayley graph, Schreier graph, replacement product, zig-zag product
Xi Wu
112/25-27Applications of Expanders [PDF] [TEX]
deterministic and randomness-efficient confidence boosting, Chernoff bound
Mahnaz Akbari and Nick Pappas
12-
133/6Derandomized Squaring [PDF] [TEX] (draft from Jul 19, 8:43pm)Alexi Brooks
143/11Undirected Connectivity in Logarithmic Space [PDF] [TEX] (draft from Jul 16, 4:09pm)
Random walk algorithm, iterared derandomized squaring, INW-generator for undirected connectivity
Adam Everspaugh
153/13Pseudorandomness for Logarithmic Space [PDF] [TEX] (draft from Jul 16, 4:09pm)
Branching programs, INW generator, Nisan's generator
Gautam Prakriya
163/18BPL in L^1.5 [PDF] [TEX] (draft from Jul 16, 4:26pm)
Random perturbation, Rounding, Saks & Zhou
Lubos Krcal
173/20Randomness Extractors [PDF] [TEX] (draft from Aug 2, 2:33pm)
Extractors, Seeded Extractors, Existence
Mahnaz Akbari
184/1Construction of Extractors [PDF] [TEX] (draft from Apr 15, 9:44pm)
Expander walk extractor, GUV-extractor
Kevin Kowalski
194/3Extractor-based PRGs [PDF] [TEX] (draft from Apr 8, 7:32am)
Extractor-based INW generator
Alexi Brooks
204/8Pseudorandomness for Regular Branching Programs [PDF] [TEX] (draft from Feb 27, 11:43pm)Nick Pappas
214/10Randomness and Space [PDF] [TEX] (draft from Apr 26, 11:34am)
NZ-generator
Adam Everspaugh
224/15Pseudorandomness from Average-Case Hardness [PDF] [TEX] (draft from Apr 29, 8:04am)Mahnaz Akbari
234/17Pseudorandomness from Worst-Case Hardness [PDF] [TEX] (draft from Apr 22, 12:00pm)Kevin Kowalski
244/22Pseudorandomness for Bounded-Depth Circuits [PDF] [TEX] (draft from Apr 26, 11:32am)
Local list decoding, Reed-Muller code
Xi Wu
254/24Shrinkage [PDF] [TEX] (draft from May 1, 6:38pm)
Random restrictions, concentration bounds for k-wise independence
Lubos Krcal
264/29Pseudorandomness from Shrinkage [PDF] [TEX] (draft from May 22, 8:09pm)Gautam Prakriya
275/1Pseudorandomness for Half-spaces [PDF] [TEX] (draft from May 6, 12:59pm)
Sandwiching technique, invariance principle
Alexi Brooks
285/6Pseudorandomness for Half-spaces [PDF] [TEX] (draft from May 9, 7:41am)Nick Pappas
295/8PRGs from Communication Complexity [PDF] [TEX] (draft from Oct 22, 11:38am)Xi Wu

 
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