All reports by Author Zander Kelley:

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TR21-047
| 26th March 2021
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Zander Kelley, Raghu Meka#### Random restrictions and PRGs for PTFs in Gaussian Space

Revisions: 1

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TR20-182
| 3rd December 2020
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Zander Kelley#### An Improved Derandomization of the Switching Lemma

Revisions: 1

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TR18-147
| 19th August 2018
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Michael Forbes, Zander Kelley#### Pseudorandom Generators for Read-Once Branching Programs, in any Order

Zander Kelley, Raghu Meka

A polynomial threshold function (PTF) $f:\mathbb{R}^n \rightarrow \mathbb{R}$ is a function of the form $f(x) = sign(p(x))$ where $p$ is a polynomial of degree at most $d$. PTFs are a classical and well-studied complexity class with applications across complexity theory, learning theory, approximation theory, quantum complexity and more. We address ... more >>>

Zander Kelley

We prove a new derandomization of HÃ¥stad's switching lemma, showing how to efficiently generate restrictions satisfying the switching lemma for DNF or CNF formulas of size $m$ using only $\widetilde{O}(\log m)$ random bits. Derandomizations of the switching lemma have been useful in many works as a key building-block for constructing ... more >>>

Michael Forbes, Zander Kelley

A central question in derandomization is whether randomized logspace (RL) equals deterministic logspace (L). To show that RL=L, it suffices to construct explicit pseudorandom generators (PRGs) that fool polynomial-size read-once (oblivious) branching programs (roBPs). Starting with the work of Nisan, pseudorandom generators with seed-length $O(\log^2 n)$ were constructed. Unfortunately, ... more >>>