On the AC^0[oplus] Complexity of Andreev’s Problem

Author Aditya Potukuchi



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Aditya Potukuchi
  • Department of Computer Science, Rutgers University, USA

Acknowledgements

I would like to thank Swastik Kopparty for the discussions that led to Section 5, and Bhargav Narayanan for the discussions that led to Theorem 8.

Cite AsGet BibTex

Aditya Potukuchi. On the AC^0[oplus] Complexity of Andreev’s Problem. In 39th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 150, pp. 25:1-25:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)
https://doi.org/10.4230/LIPIcs.FSTTCS.2019.25

Abstract

Andreev’s Problem is the following: Given an integer d and a subset of S subset F_q x F_q, is there a polynomial y = p(x) of degree at most d such that for every a in F_q, (a,p(a)) in S? We show an AC^0[oplus] lower bound for this problem. This problem appears to be similar to the list recovery problem for degree-d Reed-Solomon codes over F_q which states the following: Given subsets A_1,...,A_q of F_q, output all (if any) the Reed-Solomon codewords contained in A_1 x *s x A_q. In particular, we study this problem when the lists A_1, ..., A_q are randomly chosen, and are of a certain size. This may be of independent interest.

Subject Classification

ACM Subject Classification
  • Theory of computation → Circuit complexity
Keywords
  • List Recovery
  • Sharp Threshold
  • Fourier Analysis

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