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Nonclassical Polynomials as a Barrier to Polynomial Lower Bounds by Bhowmick, Abhishek; Lovett, Shachar is a scholarly article available to read on EtoBox.

What is Nonclassical Polynomials as a Barrier to Polynomial Lower Bounds about?

The problem of constructing explicit functions which cannot be approximated by low degree polynomials has been extensively studied in computational complexity, motivated by applications in circuit lower bounds, pseudo-randomness, constructions of Ramsey graphs and locally decodable codes. Still, most of the known lower bounds become trivial for polynomials of super-logarithmic degree. Here, we suggest a new barrier explaining this phenomenon. We show that many of the existing lower bound proof techniques extend to nonclassical polynomials, an extension of classical polynomials which arose in higher order Fourier analysis. Moreover, these techniques are tight for nonclassical polynomials of logarithmic degree.

Author

Bhowmick, Abhishek; Lovett, Shachar

Published

2014

Language

EN