Torus polynomials: an algebraic approach to ACC lower bounds

Abhishek Bhrushundi; Kaave Hosseini; Shachar Lovett; Sankeerth Rao

doi:10.4230/lipics.itcs.2019.13

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arXiv · 1804.08176

Torus polynomials: an algebraic approach to ACC lower bounds

Abhishek Bhrushundi·Kaave Hosseini·Shachar Lovett·Sankeerth Rao

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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.

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Abhishek Bhrushundi, Kaave Hosseini, Shachar Lovett, Sankeerth Rao. 2018-04-22. Torus polynomials: an algebraic approach to ACC lower bounds. https://doi.org/10.4230/lipics.itcs.2019.13

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