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Torus Polynomials: An Algebraic Approach to ACC Lower Bounds

Authors Abhishek Bhrushundi, Kaave Hosseini, Shachar Lovett, Sankeerth Rao

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Author Details

Abhishek Bhrushundi
  • Rutgers University, New Brunswick, USA
Kaave Hosseini
  • University of California, San Diego, USA
Shachar Lovett
  • University of California, San Diego, USA
Sankeerth Rao
  • University of California, San Diego, USA

Funding

Supported by NSF grant CCF-1614023.
  • Bhrushundi, Abhishek: Part of this work was done when the author was visiting the University of California, San Diego. Research supported in part by Rutgers AAUP-AFT TA-GA Professional Development Fund.

Cite As Get BibTex

Abhishek Bhrushundi, Kaave Hosseini, Shachar Lovett, and Sankeerth Rao. Torus Polynomials: An Algebraic Approach to ACC Lower Bounds. In 10th Innovations in Theoretical Computer Science Conference (ITCS 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 124, pp. 13:1-13:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019) https://doi.org/10.4230/LIPIcs.ITCS.2019.13

Abstract

We propose an algebraic approach to proving circuit lower bounds for ACC^0 by defining and studying the notion of torus polynomials. We show how currently known polynomial-based approximation results for AC^0 and ACC^0 can be reformulated in this framework, implying that ACC^0 can be approximated by low-degree torus polynomials. Furthermore, as a step towards proving ACC^0 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.

Subject Classification

ACM Subject Classification
  • Theory of computation → Circuit complexity
Keywords
  • Circuit complexity
  • ACC
  • lower bounds
  • polynomials

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