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A Pseudorandom Generator for Functions of Low-Degree Polynomial Threshold Functions

Authors Penghui Yao , Mingnan Zhao

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  • Theory of computation → Pseudorandomness and derandomization
Keywords
  • Pseudorandom generators
  • polynomial threshold functions

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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 poly(k, d, 1/ε)⋅log n that can fool any function of k degree-d PTFs with probability at least 1 - ε. 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 = poly(k, d, 1/ε) and R = O(log kd/ε). The PRG is then obtained by applying an appropriate discretization to Gaussian vectors with bounded independence.

Cite As Get BibTex

Penghui Yao and Mingnan Zhao. A Pseudorandom Generator for Functions of Low-Degree Polynomial Threshold Functions. In 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 334, pp. 134:1-134:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025) https://doi.org/10.4230/LIPIcs.ICALP.2025.134

Author Details

Penghui Yao
  • State Key Laboratory for Novel Software Technology, New Cornerstone Science Laboratory, Nanjing University, Nanjing 210023, China
  • Hefei National Laboratory, Hefei 230088, China
Mingnan Zhao
  • State Key Laboratory for Novel Software Technology, New Cornerstone Science Laboratory, Nanjing University, Nanjing 210023, China

Funding

PY and MZ were supported by National Natural Science Foundation of China (Grant Nos. 62332009 and 12347104), Innovation Program for Quantum Science and Technology (Grant No. 2021ZD0302901), NSFC/RGC Joint Research Scheme (Grant No. 12461160276), Natural Science Foundation of Jiangsu Province (Grant No. BK20243060), and New Cornerstone Science Foundation.

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