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.CCC.2023.7
URN: urn:nbn:de:0030-drops-182774
URL: https://drops.dagstuhl.de/opus/volltexte/2023/18277/
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Impagliazzo, Russell ; Mouli, Sasank ; Pitassi, Toniann

Lower Bounds for Polynomial Calculus with Extension Variables over Finite Fields

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LIPIcs-CCC-2023-7.pdf (0.8 MB)


Abstract

For every prime p > 0, every n > 0 and κ = O(log n), we show the existence of an unsatisfiable system of polynomial equations over O(n log n) variables of degree O(log n) such that any Polynomial Calculus refutation over 𝔽_p with M extension variables, each depending on at most κ original variables requires size exp(Ω(n²)/10^κ(M + n log n))

BibTeX - Entry

@InProceedings{impagliazzo_et_al:LIPIcs.CCC.2023.7,
  author =	{Impagliazzo, Russell and Mouli, Sasank and Pitassi, Toniann},
  title =	{{Lower Bounds for Polynomial Calculus with Extension Variables over Finite Fields}},
  booktitle =	{38th Computational Complexity Conference (CCC 2023)},
  pages =	{7:1--7:24},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-282-2},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{264},
  editor =	{Ta-Shma, Amnon},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2023/18277},
  URN =		{urn:nbn:de:0030-drops-182774},
  doi =		{10.4230/LIPIcs.CCC.2023.7},
  annote =	{Keywords: Proof complexity, Algebraic proof systems, Polynomial Calculus, Extension variables, AC⁰\lbrackp\rbrack-Frege}
}

Keywords: Proof complexity, Algebraic proof systems, Polynomial Calculus, Extension variables, AC⁰[p]-Frege
Collection: 38th Computational Complexity Conference (CCC 2023)
Issue Date: 2023
Date of publication: 10.07.2023


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