Limits of preprocessing

Yuval Filmus; Yuval Ishai; Avi Kaplan; Guy Kindler

doi:10.4230/LIPIcs.CCC.2020.17

Limits of preprocessing

Yuval Filmus, Yuval Ishai, Avi Kaplan, Guy Kindler

The Rachel and Selim Benin School of Engineering and Computer Science

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

2 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/(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.

Original language	American English
Title of host publication	35th Computational Complexity Conference, CCC 2020
Editors	Shubhangi Saraf
Publisher	Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
ISBN (Electronic)	9783959771566
DOIs	https://doi.org/10.4230/LIPIcs.CCC.2020.17
State	Published - 1 Jul 2020
Event	35th Computational Complexity Conference, CCC 2020 - Virtual, Online, Germany Duration: 28 Jul 2020 → 31 Jul 2020

Publication series

Name	Leibniz International Proceedings in Informatics, LIPIcs
Volume	169
ISSN (Print)	1868-8969

Conference

Conference	35th Computational Complexity Conference, CCC 2020
Country/Territory	Germany
City	Virtual, Online
Period	28/07/20 → 31/07/20

Bibliographical note

Funding Information:
Funding Yuval Filmus: Supported by the European Union’s Horizon 2020 research and innovation programme under grant agreement No 802020-ERC-HARMONIC. Yuval Ishai: Supported by ERC Project NTSC (742754), NSF-BSF grant 2015782, BSF grant 2018393, and a grant from the Ministry of Science and Technology, Israel and Department of Science and Technology, Government of India. Avi Kaplan: Supported by the European Union’s Horizon 2020 research and innovation programme under grant agreement No 802020-ERC-HARMONIC, and ERC Project NTSC (742754).

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

Access to Document

10.4230/LIPIcs.CCC.2020.17

Cite this

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title = "Limits of preprocessing",

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.",

keywords = "Circuit, Communication complexity, IPPP, PRF, Preprocessing, Simultaneous messages",

author = "Yuval Filmus and Yuval Ishai and Avi Kaplan and Guy Kindler",

note = "Funding Information: Funding Yuval Filmus: Supported by the European Union{\textquoteright}s Horizon 2020 research and innovation programme under grant agreement No 802020-ERC-HARMONIC. Yuval Ishai: Supported by ERC Project NTSC (742754), NSF-BSF grant 2015782, BSF grant 2018393, and a grant from the Ministry of Science and Technology, Israel and Department of Science and Technology, Government of India. Avi Kaplan: Supported by the European Union{\textquoteright}s Horizon 2020 research and innovation programme under grant agreement No 802020-ERC-HARMONIC, and ERC Project NTSC (742754). Publisher Copyright: {\textcopyright} Yuval Filmus, Yuval Ishai, Avi Kaplan, and Guy Kindler; licensed under Creative Commons License CC-BY 35th Computational Complexity Conference (CCC 2020).; 35th Computational Complexity Conference, CCC 2020 ; Conference date: 28-07-2020 Through 31-07-2020",

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doi = "10.4230/LIPIcs.CCC.2020.17",

language = "American English",

series = "Leibniz International Proceedings in Informatics, LIPIcs",

publisher = "Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing",

editor = "Shubhangi Saraf",

booktitle = "35th Computational Complexity Conference, CCC 2020",

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}

Filmus, Y, Ishai, Y, Kaplan, A & Kindler, G 2020, Limits of preprocessing. in S Saraf (ed.), 35th Computational Complexity Conference, CCC 2020., 17, Leibniz International Proceedings in Informatics, LIPIcs, vol. 169, Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing, 35th Computational Complexity Conference, CCC 2020, Virtual, Online, Germany, 28/07/20. https://doi.org/10.4230/LIPIcs.CCC.2020.17

Limits of preprocessing. / Filmus, Yuval; Ishai, Yuval; Kaplan, Avi et al.
35th Computational Complexity Conference, CCC 2020. ed. / Shubhangi Saraf. Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing, 2020. 17 (Leibniz International Proceedings in Informatics, LIPIcs; Vol. 169).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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AU - Filmus, Yuval

AU - Ishai, Yuval

AU - Kaplan, Avi

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N1 - Funding Information: Funding Yuval Filmus: Supported by the European Union’s Horizon 2020 research and innovation programme under grant agreement No 802020-ERC-HARMONIC. Yuval Ishai: Supported by ERC Project NTSC (742754), NSF-BSF grant 2015782, BSF grant 2018393, and a grant from the Ministry of Science and Technology, Israel and Department of Science and Technology, Government of India. Avi Kaplan: Supported by the European Union’s Horizon 2020 research and innovation programme under grant agreement No 802020-ERC-HARMONIC, and ERC Project NTSC (742754). Publisher Copyright: © Yuval Filmus, Yuval Ishai, Avi Kaplan, and Guy Kindler; licensed under Creative Commons License CC-BY 35th Computational Complexity Conference (CCC 2020).

PY - 2020/7/1

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N2 - 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.

AB - 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.

KW - Circuit

KW - Communication complexity

KW - IPPP

KW - PRF

KW - Preprocessing

KW - Simultaneous messages

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DO - 10.4230/LIPIcs.CCC.2020.17

M3 - Conference contribution

AN - SCOPUS:85089370285

T3 - Leibniz International Proceedings in Informatics, LIPIcs

BT - 35th Computational Complexity Conference, CCC 2020

A2 - Saraf, Shubhangi

PB - Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing

T2 - 35th Computational Complexity Conference, CCC 2020

Y2 - 28 July 2020 through 31 July 2020

ER -

Limits of preprocessing

Abstract

Publication series

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Bibliographical note

Keywords

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