License: Creative Commons Attribution 4.0 International license (CC BY 4.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.FSTTCS.2022.10
URN: urn:nbn:de:0030-drops-174023
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2022/17402/
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Bisht, Pranav ; Volkovich, Ilya

On Solving Sparse Polynomial Factorization Related Problems

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LIPIcs-FSTTCS-2022-10.pdf (0.8 MB)

Abstract

In a recent result of Bhargava, Saraf and Volkovich [FOCS’18; JACM’20], the first factor sparsity bound for constant individual degree polynomials was shown. In particular, it was shown that any factor of a polynomial with at most s terms and individual degree bounded by d can itself have at most s^O(d²log n) terms. It is conjectured, though, that the "true" sparsity bound should be polynomial (i.e. s^poly(d)). In this paper we provide supporting evidence for this conjecture by presenting polynomial-time algorithms for several problems that would be implied by a polynomial-size sparsity bound. In particular, we give efficient (deterministic) algorithms for identity testing of Σ^[2]ΠΣΠ^[ind-deg d] circuits and testing if a sparse polynomial is an exact power. Hence, our algorithms rely on different techniques.

BibTeX - Entry

@InProceedings{bisht_et_al:LIPIcs.FSTTCS.2022.10,
  author =	{Bisht, Pranav and Volkovich, Ilya},
  title =	{{On Solving Sparse Polynomial Factorization Related Problems}},
  booktitle =	{42nd IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2022)},
  pages =	{10:1--10:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-261-7},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{250},
  editor =	{Dawar, Anuj and Guruswami, Venkatesan},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2022/17402},
  URN =		{urn:nbn:de:0030-drops-174023},
  doi =		{10.4230/LIPIcs.FSTTCS.2022.10},
  annote =	{Keywords: Sparse Polynomials, Identity Testing, Derandomization, Factor-Sparsity, Multivariate Polynomial Factorization}
}

Keywords: Sparse Polynomials, Identity Testing, Derandomization, Factor-Sparsity, Multivariate Polynomial Factorization
Collection: 42nd IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2022)
Issue Date: 2022
Date of publication: 14.12.2022

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