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.CCC.2020.17
URN: urn:nbn:de:0030-drops-125697
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2020/12569/
Go to the corresponding LIPIcs Volume Portal

Filmus, Yuval ; Ishai, Yuval ; Kaplan, Avi ; Kindler, Guy

Limits of Preprocessing

pdf-format:
LIPIcs-CCC-2020-17.pdf (0.6 MB)

Abstract

It is a classical result that the inner product function cannot be computed by an AC⁰ circuit [Merrick L. Furst et al., 1981; Miklós Ajtai, 1983; Johan Håstad, 1986]. It is conjectured that this holds even if we allow arbitrary preprocessing of each of the two inputs separately. We prove this conjecture when the preprocessing of one of the inputs is limited to output n + n/(log^{ω(1)} n) bits. Our methods extend to many other functions, including pseudorandom functions, and imply a (weak but nontrivial) limitation on the power of encoding inputs in low-complexity cryptography. Finally, under cryptographic assumptions, we relate the question of proving variants of the main conjecture with the question of learning AC⁰ under simple input distributions.

BibTeX - Entry

@InProceedings{filmus_et_al:LIPIcs:2020:12569,
  author =	{Yuval Filmus and Yuval Ishai and Avi Kaplan and Guy Kindler},
  title =	{{Limits of Preprocessing}},
  booktitle =	{35th Computational Complexity Conference (CCC 2020)},
  pages =	{17:1--17:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-156-6},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{169},
  editor =	{Shubhangi Saraf},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2020/12569},
  URN =		{urn:nbn:de:0030-drops-125697},
  doi =		{10.4230/LIPIcs.CCC.2020.17},
  annote =	{Keywords: circuit, communication complexity, IPPP, preprocessing, PRF, simultaneous messages}
}

Keywords: circuit, communication complexity, IPPP, preprocessing, PRF, simultaneous messages
Collection: 35th Computational Complexity Conference (CCC 2020)
Issue Date: 2020
Date of publication: 17.07.2020

DROPS-Home | Fulltext Search | Imprint | Privacy Published by LZI