• Corpus ID: 46797432

Nisan-Wigderson Pseudorandom Generators for Circuits with Polynomial Threshold Gates

@article{Kabanets2018NisanWigdersonPG,
  title={Nisan-Wigderson Pseudorandom Generators for Circuits with Polynomial Threshold Gates},
  author={Valentine Kabanets and Zhenjian Lu},
  journal={Electron. Colloquium Comput. Complex.},
  year={2018},
  volume={25},
  pages={12}
}
We show how the classical Nisan-Wigderson (NW) generator [NW94] yields a nontrivial pseudorandom generator (PRG) for circuits with sublinearly many polynomial threshold function (PTF) gates. For the special case of a single PTF of degree d on n inputs, our PRG for error has the seed size exp ( O (√ d · log n · log log(n/ ) )) ; this can give a super-polynomial stretch even for a sub-exponentially small error parameter = exp(−n), for any γ = o(1). In contrast, the best known PRGs for PTFs of… 
1 Citations
A PRG for Boolean PTF of Degree 2 with Seed Length Subpolynomial in and Logarithmic in n
TLDR
This work constructs and analyzes a pseudorandom generator for degree 2 boolean polynomial threshold functions and gives an explicit construction that uses a seed length of O(logn+( 1 ) o(1).

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