Probabilistic Polynomials and Hamming Nearest Neighbors

@article{Alman2015ProbabilisticPA,
  title={Probabilistic Polynomials and Hamming Nearest Neighbors},
  author={Josh Alman and Ryan Williams},
  journal={2015 IEEE 56th Annual Symposium on Foundations of Computer Science},
  year={2015},
  pages={136-150}
}
  • Josh Alman, Ryan Williams
  • Published 2015
  • Computer Science, Mathematics
  • 2015 IEEE 56th Annual Symposium on Foundations of Computer Science
  • We show how to compute any symmetric Boolean function on n variables over any field (as well as '/ the integers) with a probabilistic polynomial of degree O( √nlog(1/ε)) and error at most ε. The degree dependence on n and ε is optimal, matching a lower bound of Razborov (1987) and Smolensky (1987) for the MAJORITY function. The proof is constructive: a low-degree polynomial can be efficiently sampled from the distribution. This polynomial construction is combined with other algebraic ideas to… CONTINUE READING

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