Limits of preprocessing

Yuval Filmus, Yuval Ishai, Avi Kaplan, Guy Kindler

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

3 Scopus citations

Abstract

It is a classical result that the inner product function cannot be computed by an AC0 circuit [17, 1, 22]. 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/(logω(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.

Original languageAmerican English
Title of host publication35th Computational Complexity Conference, CCC 2020
EditorsShubhangi Saraf
PublisherSchloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
ISBN (Electronic)9783959771566
DOIs
StatePublished - 1 Jul 2020
Event35th Computational Complexity Conference, CCC 2020 - Virtual, Online, Germany
Duration: 28 Jul 202031 Jul 2020

Publication series

NameLeibniz International Proceedings in Informatics, LIPIcs
Volume169
ISSN (Print)1868-8969

Conference

Conference35th Computational Complexity Conference, CCC 2020
Country/TerritoryGermany
CityVirtual, Online
Period28/07/2031/07/20

Bibliographical note

Publisher Copyright:
© Yuval Filmus, Yuval Ishai, Avi Kaplan, and Guy Kindler; licensed under Creative Commons License CC-BY 35th Computational Complexity Conference (CCC 2020).

Keywords

  • Circuit
  • Communication complexity
  • IPPP
  • PRF
  • Preprocessing
  • Simultaneous messages

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