Sum of squares lower bounds from pairwise independence

Boaz Barak; Siu On Chan; Pravesh K. Kothari

doi:10.1145/2746539.2746625

Sum of squares lower bounds from pairwise independence

Boaz Barak, Siu On Chan, Pravesh K. Kothari

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

36 Scopus citations

Abstract

We prove that for every ∈ > 0 and predicate P : {0,1}^k → {0,1} that supports a pairwise independent distribution, there exists an instance I of the MaxP constraint satisfaction problem on n variables such that no assignment can satisfy more than a |P^-1(1)|/2^k + ∈ fraction of I's constraints but the degree Ω(n) Sum of Squares semidefinite programming hierarchy cannot certify that I is unsatisfiable. Similar results were previously only known for weaker hierarchies.

Original language	English (US)
Title of host publication	STOC 2015 - Proceedings of the 2015 ACM Symposium on Theory of Computing
Publisher	Association for Computing Machinery
Pages	97-106
Number of pages	10
ISBN (Electronic)	9781450335362
DOIs	https://doi.org/10.1145/2746539.2746625
State	Published - Jun 14 2015
Externally published	Yes
Event	47th Annual ACM Symposium on Theory of Computing, STOC 2015 - Portland, United States Duration: Jun 14 2015 → Jun 17 2015

Publication series

Name	Proceedings of the Annual ACM Symposium on Theory of Computing
Volume	14-17-June-2015
ISSN (Print)	0737-8017

Other

Other	47th Annual ACM Symposium on Theory of Computing, STOC 2015
Country/Territory	United States
City	Portland
Period	6/14/15 → 6/17/15

All Science Journal Classification (ASJC) codes

Software

Keywords

CSPs
Lower bounds
Sum of Squares Hierarchy

Access to Document

10.1145/2746539.2746625

Cite this

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title = "Sum of squares lower bounds from pairwise independence",

abstract = "We prove that for every ∈ > 0 and predicate P : {0,1}k → {0,1} that supports a pairwise independent distribution, there exists an instance I of the MaxP constraint satisfaction problem on n variables such that no assignment can satisfy more than a |P-1(1)|/2k + ∈ fraction of I's constraints but the degree Ω(n) Sum of Squares semidefinite programming hierarchy cannot certify that I is unsatisfiable. Similar results were previously only known for weaker hierarchies.",

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author = "Boaz Barak and Chan, {Siu On} and Kothari, {Pravesh K.}",

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doi = "10.1145/2746539.2746625",

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Barak, B, Chan, SO & Kothari, PK 2015, Sum of squares lower bounds from pairwise independence. in STOC 2015 - Proceedings of the 2015 ACM Symposium on Theory of Computing. Proceedings of the Annual ACM Symposium on Theory of Computing, vol. 14-17-June-2015, Association for Computing Machinery, pp. 97-106, 47th Annual ACM Symposium on Theory of Computing, STOC 2015, Portland, United States, 6/14/15. https://doi.org/10.1145/2746539.2746625

Sum of squares lower bounds from pairwise independence. / Barak, Boaz; Chan, Siu On; Kothari, Pravesh K.
STOC 2015 - Proceedings of the 2015 ACM Symposium on Theory of Computing. Association for Computing Machinery, 2015. p. 97-106 (Proceedings of the Annual ACM Symposium on Theory of Computing; Vol. 14-17-June-2015).

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

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AU - Kothari, Pravesh K.

PY - 2015/6/14

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N2 - We prove that for every ∈ > 0 and predicate P : {0,1}k → {0,1} that supports a pairwise independent distribution, there exists an instance I of the MaxP constraint satisfaction problem on n variables such that no assignment can satisfy more than a |P-1(1)|/2k + ∈ fraction of I's constraints but the degree Ω(n) Sum of Squares semidefinite programming hierarchy cannot certify that I is unsatisfiable. Similar results were previously only known for weaker hierarchies.

AB - We prove that for every ∈ > 0 and predicate P : {0,1}k → {0,1} that supports a pairwise independent distribution, there exists an instance I of the MaxP constraint satisfaction problem on n variables such that no assignment can satisfy more than a |P-1(1)|/2k + ∈ fraction of I's constraints but the degree Ω(n) Sum of Squares semidefinite programming hierarchy cannot certify that I is unsatisfiable. Similar results were previously only known for weaker hierarchies.

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ER -

Sum of squares lower bounds from pairwise independence

Abstract

Publication series

Other

All Science Journal Classification (ASJC) codes

Keywords

Access to Document

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