Torus polynomials: an algebraic approach to ACC lower bounds
Computational Complexity
2019-03-04 v3
Abstract
We propose an algebraic approach to proving circuit lower bounds for ACC0 by defining and studying the notion of torus polynomials. We show how currently known polynomial-based approximation results for AC0 and ACC0 can be reformulated in this framework, implying that ACC0 can be approximated by low-degree torus polynomials. Furthermore, as a step towards proving ACC0 lower bounds for the majority function via our approach, we show that MAJORITY cannot be approximated by low-degree symmetric torus polynomials. We also pose several open problems related to our framework.
Cite
@article{arxiv.1804.08176,
title = {Torus polynomials: an algebraic approach to ACC lower bounds},
author = {Abhishek Bhrushundi and Kaave Hosseini and Shachar Lovett and Sankeerth Rao},
journal= {arXiv preprint arXiv:1804.08176},
year = {2019}
}
Comments
15 pages, no figures