A Pseudorandom Generator for Functions of Low-Degree Polynomial Threshold Functions
Year: 2025
Type: preprint
Abstract: 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 threshold functions (PTFs) over Gaussian space. Our main result is an explicit construction of PRG with seed length $\mathrm{poly}(k,d,1/ε)\cdot\log n$ that can fool any function of $k$ degree-$d$ PTFs with probability at least $1-\varepsilon$. More specifically, we show that the summation of $L$ independent $R$-moment-matching Gaussian vectors $ε$-fools functions of $k$ degree-$d$ PTFs, where $L=\mathrm{poly}( k, d, \frac{1}ε)$ and $R = O({\log \frac{kd}ε})$. The PRG is then obtained by applying an appropriate discretization to Gaussian vectors with bounded independence.
Source: arXiv (Cornell University)
Authors: Yao, Penghui, Zhao, Mingnan
Institution: Nanjing University
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W6948254164
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