Related papers: Fractional Pseudorandom Generators from Any Fourie…
We establish new correlation bounds and pseudorandom generators for a collection of computation models. These models are all natural generalizations of structured low-degree $F_2$-polynomials that we did not have correlation bounds for…
We study the natural question of constructing pseudorandom generators (PRGs) for low-degree polynomial threshold functions (PTFs). We give a PRG with seed-length log n/eps^{O(d)} fooling degree d PTFs with error at most eps. Previously, no…
Developing explicit pseudorandom generators (PRGs) for prominent categories of Boolean functions is a key focus in computational complexity theory. In this paper, we investigate the PRGs against the functions of degree-$d$ polynomial…
We show a new PRG construction fooling depth-$d$, size-$m$ $\mathsf{AC}^0$ circuits within error $\varepsilon$, which has seed length $O(\log^{d-1}(m)\log(m/\varepsilon)\log\log(m))$. Our PRG improves on previous work (Trevisan and Xue…
Pseudorandom generators (PRGs) for low-degree polynomials are a central object in pseudorandomness, with applications to circuit lower bounds and derandomization. Viola's celebrated construction gives a PRG over the binary field, but with…
We present a new approach to constructing unconditional pseudorandom generators against classes of functions that involve computing a linear function of the inputs. We give an explicit construction of a pseudorandom generator that fools the…
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)…
The problem of constructing pseudorandom generators that fool halfspaces has been studied intensively in recent times. For fooling halfspaces over the hypercube with polynomially small error, the best construction known requires seed-length…
A polynomial threshold function (PTF) $f:\mathbb{R}^n \rightarrow \mathbb{R}$ is a function of the form $f(x) = \mathsf{sign}(p(x))$ where $p$ is a polynomial of degree at most $d$. PTFs are a classical and well-studied complexity class…
We devise a new pseudorandom generator against degree 2 polynomial threshold functions in the Gaussian setting. We manage to achieve $\epsilon$ error with seed length polylogarithmic in $\epsilon$ and the dimension, and exponential…
In a recent work, O'Donnell, Servedio and Tan (STOC 2019) gave explicit pseudorandom generators (PRGs) for arbitrary $m$-facet polytopes in $n$ variables with seed length poly-logarithmic in $m,n$, concluding a sequence of works in the last…
Halfspaces or linear threshold functions are widely studied in complexity theory, learning theory and algorithm design. In this work we study the natural problem of constructing pseudorandom generators (PRGs) for halfspaces over the sphere,…
We study correlation bounds and pseudorandom generators for depth-two circuits that consist of a $\mathsf{SYM}$-gate (computing an arbitrary symmetric function) or $\mathsf{THR}$-gate (computing an arbitrary linear threshold function) that…
We develop a pseudo-random generator to fool degree-$d$ polynomial threshold functions with respect to the Gaussian distribution. For $c>0$ any constant, we construct a pseudo-random generator that fools such functions to within $\epsilon$…
A sliding-window algorithm of window size $t$ is an algorithm whose current operation depends solely on the last $t$ symbols read. We construct pseudorandom generators (PRGs) for low-space randomized sliding-window algorithms that have…
We develop a pseudorandom generator that fools degree-$d$ polynomial threshold functions in $n$ variables with respect to the Gaussian distribution and has seed length $O_{c,d}(\log(n) \epsilon^{-c})$.
We give the best known pseudorandom generators for two touchstone classes in unconditional derandomization: an $\varepsilon$-PRG for the class of size-$M$ depth-$d$ $\mathsf{AC}^0$ circuits with seed length $\log(M)^{d+O(1)}\cdot…
We construct pseudorandom generators of seed length $\tilde{O}(\log(n)\cdot \log(1/\epsilon))$ that $\epsilon$-fool ordered read-once branching programs (ROBPs) of width $3$ and length $n$. For unordered ROBPs, we construct pseudorandom…
We present an iterative approach to constructing pseudorandom generators, based on the repeated application of mild pseudorandom restrictions. We use this template to construct pseudorandom generators for combinatorial rectangles and…
We construct explicit pseudorandom generators that fool $n$-variate polynomials of degree at most $d$ over a finite field $\mathbb{F}_q$. The seed length of our generators is $O(d \log n + \log q)$, over fields of size exponential in $d$…