NDLI: PCP Characterizations of NP: Toward a Polynomially-Small Error-Probability

Please wait, while we are loading the content...

PCP Characterizations of NP: Toward a Polynomially-Small Error-Probability

Content Provider	Springer Nature Link
Author	Fischer, Eldar Raz, Ran Kindler, Guy Safra, Shmuel Dinur, Irit
Copyright Year	2011
Abstract	This paper strengthens the low-error PCP characterization of NP, coming closer to the upper limit of the BGLR conjecture. Consider the task of verifying a written proof for the membership of a given input in an NP language. In this paper, this is achieved by making a constant number of accesses to the proof, obtaining error probability that is exponentially small in the total number of bits that are read.We show that the number of bits that are read in each access to the proof can be made as high as log β n , for any constant β < 1, where n is the length of the proof. The BGLR conjecture asserts the same for any constant β, for β smaller or equal to 1.Our results are in fact stronger, implying that the Gap-Quadratic-Solvability problem with a constant number of variables in each equation is NP-hard. That is, given a system of n quadratic equations over a field $${\mathcal{F}}$$ of size up to $$2^{\log^\beta n}$$ , where each equation depends on a constant number of variables, it is NP-hard to distinguish between the case where there is a common solution to all of the equations and the case where any assignment satisfies at most a $${2 / \|\mathcal{F}\|}$$ fraction of them.At the same time, our proof presents a direct construction of a low-degree test whose error-probability is exponentially small in the number of bits accessed. Such a result was previously known only relying on recursive applications of the entire PCP theorem.
Ending Page	504
Page Count	92
Starting Page	413
File Format	PDF
ISSN	10163328
e-ISSN	14208954
Journal	Computational complexity
Issue Number	3
Volume Number	20
Language	English
Publisher	SP Birkhäuser Verlag Basel
Publisher Date	2011-08-04
Publisher Place	Basel
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	NP consistent-reader Computational Mathematics and Numerical Analysis representation-procedure sum-check low-degree extension Computational difficulty of problems (lower bounds, completeness, difficulty of approximation, etc.) PCP Algorithm Analysis and Problem Complexity
Content Type	Text
Resource Type	Article
Subject	Theoretical Computer Science Computational Theory and Mathematics Computational Mathematics

Sl.	Authority	Responsibilities	Communication Details
1	Ministry of Education (GoI), Department of Higher Education	Sanctioning Authority	https://www.education.gov.in/ict-initiatives
2	Indian Institute of Technology Kharagpur	Host Institute of the Project: The host institute of the project is responsible for providing infrastructure support and hosting the project	https://www.iitkgp.ac.in
3	National Digital Library of India Office, Indian Institute of Technology Kharagpur	The administrative and infrastructural headquarters of the project	Dr. B. Sutradhar bsutra@ndl.gov.in
4	Project PI / Joint PI	Principal Investigator and Joint Principal Investigators of the project	Dr. B. Sutradhar bsutra@ndl.gov.in Prof. Saswat Chakrabarti will be added soon
5	Website/Portal (Helpdesk)	Queries regarding NDLI and its services	support@ndl.gov.in
6	Contents and Copyright Issues	Queries related to content curation and copyright issues	content@ndl.gov.in
7	National Digital Library of India Club (NDLI Club)	Queries related to NDLI Club formation, support, user awareness program, seminar/symposium, collaboration, social media, promotion, and outreach	clubsupport@ndl.gov.in
8	Digital Preservation Centre (DPC)	Assistance with digitizing and archiving copyright-free printed books	dpc@ndl.gov.in
9	IDR Setup or Support	Queries related to establishment and support of Institutional Digital Repository (IDR) and IDR workshops	idr@ndl.gov.in

PCP Characterizations of NP: Toward a Polynomially-Small Error-Probability

Property Testing Lower Bounds via Communication Complexity

On the questions P ?= NP $\cap$ co-NP and NP ?= co-NP for infinite time Turing machines

Recognizing when heuristics can approximate minimum vertex covers is complete for parallel access to NP

P != NP Proof

Choosing, Agreeing, and Eliminating in Communication Complexity

The Computational Complexity of Plethysm Coefficients

Lower Bounds for Depth-Three Arithmetic Circuits with small bottom fanin

The unbounded-error communication complexity of symmetric functions

PCP Characterizations of NP: Toward a Polynomially-Small Error-Probability

Similar Documents

PCP Characterizations of NP: Toward a Polynomially-Small Error-Probability

Property Testing Lower Bounds via Communication Complexity

On the questions P ?= NP $\cap$ co-NP and NP ?= co-NP for infinite time Turing machines

Recognizing when heuristics can approximate minimum vertex covers is complete for parallel access to NP

P != NP Proof

Choosing, Agreeing, and Eliminating in Communication Complexity

The Computational Complexity of Plethysm Coefficients

Lower Bounds for Depth-Three Arithmetic Circuits with small bottom fanin

The unbounded-error communication complexity of symmetric functions

PCP Characterizations of NP: Toward a Polynomially-Small Error-Probability