License: Creative Commons Attribution 3.0 Unported license (CC-BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.FSTTCS.2019.25
URN: urn:nbn:de:0030-drops-115879
URL: https://drops.dagstuhl.de/opus/volltexte/2019/11587/
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Potukuchi, Aditya

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

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LIPIcs-FSTTCS-2019-25.pdf (0.6 MB)


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.

BibTeX - Entry

@InProceedings{potukuchi:LIPIcs:2019:11587,
  author =	{Aditya Potukuchi},
  title =	{{On the AC^0[oplus] Complexity of Andreev's Problem}},
  booktitle =	{39th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2019)},
  pages =	{25:1--25:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-131-3},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{150},
  editor =	{Arkadev Chattopadhyay and Paul Gastin},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2019/11587},
  URN =		{urn:nbn:de:0030-drops-115879},
  doi =		{10.4230/LIPIcs.FSTTCS.2019.25},
  annote =	{Keywords: List Recovery, Sharp Threshold, Fourier Analysis}
}

Keywords: List Recovery, Sharp Threshold, Fourier Analysis
Collection: 39th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2019)
Issue Date: 2019
Date of publication: 04.12.2019


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