A PRG for Boolean PTF of Degree 2 with Seed Length Subpolynomial in epsilon and Logarithmic in n

Authors Daniel Kane, Sankeerth Rao

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Daniel Kane
  • UC San Diego
Sankeerth Rao
  • UC San Diego

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Daniel Kane and Sankeerth Rao. A PRG for Boolean PTF of Degree 2 with Seed Length Subpolynomial in epsilon and Logarithmic in n. In 33rd Computational Complexity Conference (CCC 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 102, pp. 2:1-2:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)


We construct and analyze a pseudorandom generator for degree 2 boolean polynomial threshold functions. Random constructions achieve the optimal seed length of O(log n + log 1/epsilon), however the best known explicit construction of [Ilias Diakonikolas, 2010] uses a seed length of O(log n * epsilon^{-8}). In this work we give an explicit construction that uses a seed length of O(log n + (1/epsilon)^{o(1)}). Note that this improves the seed length substantially and that the dependence on the error epsilon is additive and only grows subpolynomially as opposed to the previously known multiplicative polynomial dependence. Our generator uses dimensionality reduction on a Nisan-Wigderson based pseudorandom generator given by Lu, Kabanets [Kabanets and Lu, 2018].

Subject Classification

ACM Subject Classification
  • Theory of computation → Pseudorandomness and derandomization
  • Pseudorandomness
  • Polynomial Threshold Functions


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