Polynomial Time Deterministic Identity Testing Algorithm for Σ[3]ΠΣΠ[2] Circuits via Edelstein–Kelly Type Theorem for Quadratic Polynomials

Shir Peleg; Amir Shpilka

doi:10.1145/3406325.3451013

Polynomial Time Deterministic Identity Testing Algorithm for Σ^[3]ΠΣΠ^[2] Circuits via Edelstein–Kelly Type Theorem for Quadratic Polynomials

Shir Peleg, Amir Shpilka

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

9 Scopus citations

Abstract

In this work we resolve conjectures of Beecken, Mitmann and Saxena [BMS13] and Gupta [Gupta14], by proving an analog of a theorem of Edelstein and Kelly for quadratic polynomials. As immediate corollary we obtain the first deterministic polynomial time black-box algorithm for testing zeroness of ?[3]II?II[2] circuits.

Original language	English
Title of host publication	STOC 2021 - Proceedings of the 53rd Annual ACM SIGACT Symposium on Theory of Computing
Editors	Samir Khuller, Virginia Vassilevska Williams
Publisher	Association for Computing Machinery
Pages	259-271
Number of pages	13
ISBN (Electronic)	9781450380539
DOIs	https://doi.org/10.1145/3406325.3451013
State	Published - 15 Jun 2021
Event	53rd Annual ACM SIGACT Symposium on Theory of Computing, STOC 2021 - Virtual, Online, Italy Duration: 21 Jun 2021 → 25 Jun 2021

Publication series

Name	Proceedings of the Annual ACM Symposium on Theory of Computing
ISSN (Print)	0737-8017

Conference

Conference	53rd Annual ACM SIGACT Symposium on Theory of Computing, STOC 2021
Country/Territory	Italy
City	Virtual, Online
Period	21/06/21 → 25/06/21

Funding

Funders	Funder number
Blavatnik Family Foundation
Israel Science Foundation	514/20

Keywords

Algebraic computation
Computational complexity
Computational geometry
Identity testing

Access to Document

10.1145/3406325.3451013

Cite this

Peleg, S., & Shpilka, A. (2021). Polynomial Time Deterministic Identity Testing Algorithm for Σ^[3]ΠΣΠ^[2] Circuits via Edelstein–Kelly Type Theorem for Quadratic Polynomials. In S. Khuller, & V. V. Williams (Eds.), STOC 2021 - Proceedings of the 53rd Annual ACM SIGACT Symposium on Theory of Computing (pp. 259-271). (Proceedings of the Annual ACM Symposium on Theory of Computing). Association for Computing Machinery. https://doi.org/10.1145/3406325.3451013

Peleg, Shir ; Shpilka, Amir. / Polynomial Time Deterministic Identity Testing Algorithm for Σ^[3]ΠΣΠ^[2] Circuits via Edelstein–Kelly Type Theorem for Quadratic Polynomials. STOC 2021 - Proceedings of the 53rd Annual ACM SIGACT Symposium on Theory of Computing. editor / Samir Khuller ; Virginia Vassilevska Williams. Association for Computing Machinery, 2021. pp. 259-271 (Proceedings of the Annual ACM Symposium on Theory of Computing).

@inproceedings{fa29df333b1d4113815c922cf14771bc,

title = "Polynomial Time Deterministic Identity Testing Algorithm for Σ[3]ΠΣΠ[2] Circuits via Edelstein–Kelly Type Theorem for Quadratic Polynomials",

abstract = "In this work we resolve conjectures of Beecken, Mitmann and Saxena [BMS13] and Gupta [Gupta14], by proving an analog of a theorem of Edelstein and Kelly for quadratic polynomials. As immediate corollary we obtain the first deterministic polynomial time black-box algorithm for testing zeroness of ?[3]II?II[2] circuits.",

keywords = "Algebraic computation, Computational complexity, Computational geometry, Identity testing",

author = "Shir Peleg and Amir Shpilka",

note = "Publisher Copyright: {\textcopyright} 2021 ACM.; 53rd Annual ACM SIGACT Symposium on Theory of Computing, STOC 2021 ; Conference date: 21-06-2021 Through 25-06-2021",

year = "2021",

month = jun,

day = "15",

doi = "10.1145/3406325.3451013",

language = "אנגלית",

series = "Proceedings of the Annual ACM Symposium on Theory of Computing",

publisher = "Association for Computing Machinery",

pages = "259--271",

editor = "Samir Khuller and Williams, {Virginia Vassilevska}",

booktitle = "STOC 2021 - Proceedings of the 53rd Annual ACM SIGACT Symposium on Theory of Computing",

address = "ארצות הברית",

}

Peleg, S & Shpilka, A 2021, Polynomial Time Deterministic Identity Testing Algorithm for Σ^[3]ΠΣΠ^[2] Circuits via Edelstein–Kelly Type Theorem for Quadratic Polynomials. in S Khuller & VV Williams (eds), STOC 2021 - Proceedings of the 53rd Annual ACM SIGACT Symposium on Theory of Computing. Proceedings of the Annual ACM Symposium on Theory of Computing, Association for Computing Machinery, pp. 259-271, 53rd Annual ACM SIGACT Symposium on Theory of Computing, STOC 2021, Virtual, Online, Italy, 21/06/21. https://doi.org/10.1145/3406325.3451013

Polynomial Time Deterministic Identity Testing Algorithm for Σ^[3]ΠΣΠ^[2] Circuits via Edelstein–Kelly Type Theorem for Quadratic Polynomials. / Peleg, Shir; Shpilka, Amir.
STOC 2021 - Proceedings of the 53rd Annual ACM SIGACT Symposium on Theory of Computing. ed. / Samir Khuller; Virginia Vassilevska Williams. Association for Computing Machinery, 2021. p. 259-271 (Proceedings of the Annual ACM Symposium on Theory of Computing).

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

TY - GEN

T1 - Polynomial Time Deterministic Identity Testing Algorithm for Σ[3]ΠΣΠ[2] Circuits via Edelstein–Kelly Type Theorem for Quadratic Polynomials

AU - Peleg, Shir

AU - Shpilka, Amir

PY - 2021/6/15

Y1 - 2021/6/15

N2 - In this work we resolve conjectures of Beecken, Mitmann and Saxena [BMS13] and Gupta [Gupta14], by proving an analog of a theorem of Edelstein and Kelly for quadratic polynomials. As immediate corollary we obtain the first deterministic polynomial time black-box algorithm for testing zeroness of ?[3]II?II[2] circuits.

AB - In this work we resolve conjectures of Beecken, Mitmann and Saxena [BMS13] and Gupta [Gupta14], by proving an analog of a theorem of Edelstein and Kelly for quadratic polynomials. As immediate corollary we obtain the first deterministic polynomial time black-box algorithm for testing zeroness of ?[3]II?II[2] circuits.

KW - Algebraic computation

KW - Computational complexity

KW - Computational geometry

KW - Identity testing

UR - http://www.scopus.com/inward/record.url?scp=85108165388&partnerID=8YFLogxK

U2 - 10.1145/3406325.3451013

DO - 10.1145/3406325.3451013

M3 - ???researchoutput.researchoutputtypes.contributiontobookanthology.conference???

AN - SCOPUS:85108165388

T3 - Proceedings of the Annual ACM Symposium on Theory of Computing

SP - 259

EP - 271

BT - STOC 2021 - Proceedings of the 53rd Annual ACM SIGACT Symposium on Theory of Computing

A2 - Khuller, Samir

A2 - Williams, Virginia Vassilevska

PB - Association for Computing Machinery

T2 - 53rd Annual ACM SIGACT Symposium on Theory of Computing, STOC 2021

Y2 - 21 June 2021 through 25 June 2021

ER -

Peleg S, Shpilka A. Polynomial Time Deterministic Identity Testing Algorithm for Σ^[3]ΠΣΠ^[2] Circuits via Edelstein–Kelly Type Theorem for Quadratic Polynomials. In Khuller S, Williams VV, editors, STOC 2021 - Proceedings of the 53rd Annual ACM SIGACT Symposium on Theory of Computing. Association for Computing Machinery. 2021. p. 259-271. (Proceedings of the Annual ACM Symposium on Theory of Computing). doi: 10.1145/3406325.3451013