Query-to-communication lifting for BPP using inner product

Arkadev Chattopadhyay; Yuval Filmus; Sajin Koroth; Or Meir; Toniann Pitassi

doi:10.4230/LIPIcs.ICALP.2019.35

Query-to-communication lifting for BPP using inner product

Arkadev Chattopadhyay
, Yuval Filmus
, Sajin Koroth
, Or Meir
, Toniann Pitassi

Department of Computer Science

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

Abstract

We prove a new query-to-communication lifting for randomized protocols, with inner product as gadget. This allows us to use a much smaller gadget, leading to a more efficient lifting. Prior to this work, such a theorem was known only for deterministic protocols, due to Chattopadhyay et al. [4] and Wu et al. [22]. The only query-to-communication lifting result for randomized protocols, due to Göös, Pitassi and Watson [13], used the much larger indexing gadget. Our proof also provides a unified treatment of randomized and deterministic lifting. Most existing proofs of deterministic lifting theorems use a measure of information known as thickness. In contrast, Göös, Pitassi and Watson [13] used blockwise min-entropy as a measure of information. Our proof uses the blockwise min-entropy framework to prove lifting theorems in both settings in a unified way.

Original language	English
Title of host publication	46th International Colloquium on Automata, Languages, and Programming, ICALP 2019
Editors	Christel Baier, Ioannis Chatzigiannakis, Paola Flocchini, Stefano Leonardi
Publisher	Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
Pages	35:1–35:15
ISBN (Electronic)	9783959771092
DOIs	https://doi.org/10.4230/LIPIcs.ICALP.2019.35
State	Published - 1 Jul 2019
Event	46th International Colloquium on Automata, Languages, and Programming, ICALP 2019 - Patras, Greece Duration: 9 Jul 2019 → 12 Jul 2019

Publication series

Name	Leibniz International Proceedings in Informatics, LIPIcs
Volume	132
ISSN (Print)	1868-8969

Conference

Conference	46th International Colloquium on Automata, Languages, and Programming, ICALP 2019
Country/Territory	Greece
City	Patras
Period	9/07/19 → 12/07/19

Bibliographical note

Funding Information:
Funding Yuval Filmus: Taub Fellow – supported by the Taub Foundations. The research was funded by ISF grant 1337/16. Sajin Koroth: Supported by the Israel Science Foundation (grant No. 1445/16) Or Meir: Partially supported by ISF grant by the Israel Science Foundation (grant No. 1445/16).

Funding Information:
Yuval Filmus: Taub Fellow - supported by the Taub Foundations. The research was funded by ISF grant 1337/16. Sajin Koroth: Supported by the Israel Science Foundation (grant No. 1445/16) Or Meir: Partially supported by ISF grant by the Israel Science Foundation (grant No. 1445/16).

Publisher Copyright:
© Arkadev Chattopadhyay, Yuval Filmus, Sajin Koroth, Or Meir, and Toniann Pitassi; licensed under Creative Commons License CC-BY

Keywords

BPP Lifting
Deterministic Lifting
Inner product
Lifting theorems

ASJC Scopus subject areas

Software

Access to Document

10.4230/LIPIcs.ICALP.2019.35

Cite this

Chattopadhyay, A., Filmus, Y., Koroth, S., Meir, O., & Pitassi, T. (2019). Query-to-communication lifting for BPP using inner product. In C. Baier, I. Chatzigiannakis, P. Flocchini, & S. Leonardi (Eds.), 46th International Colloquium on Automata, Languages, and Programming, ICALP 2019 (pp. 35:1–35:15). Article 35 (Leibniz International Proceedings in Informatics, LIPIcs; Vol. 132). Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing. https://doi.org/10.4230/LIPIcs.ICALP.2019.35

Chattopadhyay, Arkadev ; Filmus, Yuval ; Koroth, Sajin et al. / Query-to-communication lifting for BPP using inner product. 46th International Colloquium on Automata, Languages, and Programming, ICALP 2019. editor / Christel Baier ; Ioannis Chatzigiannakis ; Paola Flocchini ; Stefano Leonardi. Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing, 2019. pp. 35:1–35:15 (Leibniz International Proceedings in Informatics, LIPIcs).

@inproceedings{6b16bc740b904f22aee6bedd9761ad48,

title = "Query-to-communication lifting for BPP using inner product",

abstract = "We prove a new query-to-communication lifting for randomized protocols, with inner product as gadget. This allows us to use a much smaller gadget, leading to a more efficient lifting. Prior to this work, such a theorem was known only for deterministic protocols, due to Chattopadhyay et al. [4] and Wu et al. [22]. The only query-to-communication lifting result for randomized protocols, due to G{\"o}{\"o}s, Pitassi and Watson [13], used the much larger indexing gadget. Our proof also provides a unified treatment of randomized and deterministic lifting. Most existing proofs of deterministic lifting theorems use a measure of information known as thickness. In contrast, G{\"o}{\"o}s, Pitassi and Watson [13] used blockwise min-entropy as a measure of information. Our proof uses the blockwise min-entropy framework to prove lifting theorems in both settings in a unified way.",

keywords = "BPP Lifting, Deterministic Lifting, Inner product, Lifting theorems",

author = "Arkadev Chattopadhyay and Yuval Filmus and Sajin Koroth and Or Meir and Toniann Pitassi",

note = "Funding Information: Funding Yuval Filmus: Taub Fellow – supported by the Taub Foundations. The research was funded by ISF grant 1337/16. Sajin Koroth: Supported by the Israel Science Foundation (grant No. 1445/16) Or Meir: Partially supported by ISF grant by the Israel Science Foundation (grant No. 1445/16). Funding Information: Yuval Filmus: Taub Fellow - supported by the Taub Foundations. The research was funded by ISF grant 1337/16. Sajin Koroth: Supported by the Israel Science Foundation (grant No. 1445/16) Or Meir: Partially supported by ISF grant by the Israel Science Foundation (grant No. 1445/16). Publisher Copyright: {\textcopyright} Arkadev Chattopadhyay, Yuval Filmus, Sajin Koroth, Or Meir, and Toniann Pitassi; licensed under Creative Commons License CC-BY; 46th International Colloquium on Automata, Languages, and Programming, ICALP 2019 ; Conference date: 09-07-2019 Through 12-07-2019",

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Chattopadhyay, A, Filmus, Y, Koroth, S, Meir, O & Pitassi, T 2019, Query-to-communication lifting for BPP using inner product. in C Baier, I Chatzigiannakis, P Flocchini & S Leonardi (eds), 46th International Colloquium on Automata, Languages, and Programming, ICALP 2019., 35, Leibniz International Proceedings in Informatics, LIPIcs, vol. 132, Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing, pp. 35:1–35:15, 46th International Colloquium on Automata, Languages, and Programming, ICALP 2019, Patras, Greece, 9/07/19. https://doi.org/10.4230/LIPIcs.ICALP.2019.35

Query-to-communication lifting for BPP using inner product. / Chattopadhyay, Arkadev; Filmus, Yuval; Koroth, Sajin et al.
46th International Colloquium on Automata, Languages, and Programming, ICALP 2019. ed. / Christel Baier; Ioannis Chatzigiannakis; Paola Flocchini; Stefano Leonardi. Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing, 2019. p. 35:1–35:15 35 (Leibniz International Proceedings in Informatics, LIPIcs; Vol. 132).

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

TY - GEN

T1 - Query-to-communication lifting for BPP using inner product

AU - Chattopadhyay, Arkadev

AU - Filmus, Yuval

AU - Koroth, Sajin

AU - Meir, Or

AU - Pitassi, Toniann

N1 - Funding Information: Funding Yuval Filmus: Taub Fellow – supported by the Taub Foundations. The research was funded by ISF grant 1337/16. Sajin Koroth: Supported by the Israel Science Foundation (grant No. 1445/16) Or Meir: Partially supported by ISF grant by the Israel Science Foundation (grant No. 1445/16). Funding Information: Yuval Filmus: Taub Fellow - supported by the Taub Foundations. The research was funded by ISF grant 1337/16. Sajin Koroth: Supported by the Israel Science Foundation (grant No. 1445/16) Or Meir: Partially supported by ISF grant by the Israel Science Foundation (grant No. 1445/16). Publisher Copyright: © Arkadev Chattopadhyay, Yuval Filmus, Sajin Koroth, Or Meir, and Toniann Pitassi; licensed under Creative Commons License CC-BY

PY - 2019/7/1

Y1 - 2019/7/1

N2 - We prove a new query-to-communication lifting for randomized protocols, with inner product as gadget. This allows us to use a much smaller gadget, leading to a more efficient lifting. Prior to this work, such a theorem was known only for deterministic protocols, due to Chattopadhyay et al. [4] and Wu et al. [22]. The only query-to-communication lifting result for randomized protocols, due to Göös, Pitassi and Watson [13], used the much larger indexing gadget. Our proof also provides a unified treatment of randomized and deterministic lifting. Most existing proofs of deterministic lifting theorems use a measure of information known as thickness. In contrast, Göös, Pitassi and Watson [13] used blockwise min-entropy as a measure of information. Our proof uses the blockwise min-entropy framework to prove lifting theorems in both settings in a unified way.

AB - We prove a new query-to-communication lifting for randomized protocols, with inner product as gadget. This allows us to use a much smaller gadget, leading to a more efficient lifting. Prior to this work, such a theorem was known only for deterministic protocols, due to Chattopadhyay et al. [4] and Wu et al. [22]. The only query-to-communication lifting result for randomized protocols, due to Göös, Pitassi and Watson [13], used the much larger indexing gadget. Our proof also provides a unified treatment of randomized and deterministic lifting. Most existing proofs of deterministic lifting theorems use a measure of information known as thickness. In contrast, Göös, Pitassi and Watson [13] used blockwise min-entropy as a measure of information. Our proof uses the blockwise min-entropy framework to prove lifting theorems in both settings in a unified way.

KW - BPP Lifting

KW - Deterministic Lifting

KW - Inner product

KW - Lifting theorems

UR - https://www.scopus.com/pages/publications/85069185435

U2 - 10.4230/LIPIcs.ICALP.2019.35

DO - 10.4230/LIPIcs.ICALP.2019.35

M3 - Conference contribution

AN - SCOPUS:85069185435

T3 - Leibniz International Proceedings in Informatics, LIPIcs

SP - 35:1–35:15

BT - 46th International Colloquium on Automata, Languages, and Programming, ICALP 2019

A2 - Baier, Christel

A2 - Chatzigiannakis, Ioannis

A2 - Flocchini, Paola

A2 - Leonardi, Stefano

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

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Y2 - 9 July 2019 through 12 July 2019

ER -

Chattopadhyay A, Filmus Y, Koroth S, Meir O, Pitassi T. Query-to-communication lifting for BPP using inner product. In Baier C, Chatzigiannakis I, Flocchini P, Leonardi S, editors, 46th International Colloquium on Automata, Languages, and Programming, ICALP 2019. Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing. 2019. p. 35:1–35:15. 35. (Leibniz International Proceedings in Informatics, LIPIcs). doi: 10.4230/LIPIcs.ICALP.2019.35

Query-to-communication lifting for BPP using inner product

Abstract

Publication series

Conference

Bibliographical note

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Query-to-Communication Lifting Using Low-Discrepancy Gadgets

Cite this

Query-to-communication lifting for BPP using inner product

Abstract

Publication series

Conference

Bibliographical note

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Related research output

Query-to-Communication Lifting Using Low-Discrepancy Gadgets

Cite this