
Extractors for Sum of Two Sources
We consider the problem of extracting randomness from sumset sources, a ...
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SanthaVazirani sources, deterministic condensers and very strong extractors
The notion of semirandom sources, also known as SanthaVazirani (SV) so...
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An explicit twosource extractor with minentropy near 4/9
In 2005 Bourgain gave the first explicit construction of a twosource ex...
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Neural networks are a priori biased towards Boolean functions with low entropy
Understanding the inductive bias of neural networks is critical to expla...
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Asymptotic Synchronization for FiniteState Sources
We extend a recent synchronization analysis of exact finitestate source...
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On Entropy and Bit Patterns of Ring Oscillator Jitter
Thermal jitter (phase noise) from a freerunning ring oscillator is a co...
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An explicit twosource extractor with minentropy rate near 4/9
In 2005 Bourgain gave the first explicit construction of a twosource ex...
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Average Bias and Polynomial Sources
We identify a new notion of pseudorandomness for randomness sources, which we call the average bias. Given a distribution Z over {0,1}^n, its average bias is: b_av(Z) =2^n∑_c ∈{0,1}^n E_z ∼ Z(1)^〈 c, z〉. A source with average bias at most 2^k has minentropy at least k, and so low average bias is a stronger condition than high minentropy. We observe that the inner product function is an extractor for any source with average bias less than 2^n/2. The notion of average bias especially makes sense for polynomial sources, i.e., distributions sampled by lowdegree nvariate polynomials over F_2. For the wellstudied case of affine sources, it is easy to see that minentropy k is exactly equivalent to average bias of 2^k. We show that for quadratic sources, minentropy k implies that the average bias is at most 2^Ω(√(k)). We use this relation to design dispersers for separable quadratic sources with a minentropy guarantee.
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