NDLI: Robust PCPs of Proximity, Shorter PCPs, and Applications to Coding

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

Robust PCPs of Proximity, Shorter PCPs, and Applications to Coding

Content Provider	Society for Industrial and Applied Mathematics (SIAM)
Author	BenSasson, Eli Harsha, Prahladh Vadhan, Salil Goldreich, Oded Sudan, Madhu
Copyright Year	2006
Abstract	We continue the study of the tradeoff between the length of probabilistically checkable proofs PCPs and their query complexity, establishing the following main results which refer to proofs of satisfiability of circuits of size n:1. We present PCPs of length $\exp(o(\log\log n)^2)\cdot n$ that can be verified by making $o(\log\log n)$ Boolean queries.2. For every \epsilon>0, we present PCPs of length $\exp(\log^\epsilon n)\cdot n$ that can be verified by making a constant number of Boolean queries.In both cases, false assertions are rejected with constant probability which may be set to be arbitrarily close to 1. The multiplicative overhead on the length of the proof, introduced by transforming a proof into a probabilistically checkable one, is just quasi polylogarithmic in the first case of query complexity $o(\log\log n)$), and is $2^{(\log n)^\epsilon}$, for any $\epsilon > 0$, in the second case (of constant query complexity. Our techniques include the introduction of a new variant of PCPs that we call robust PCPs of proximity. These new PCPs facilitate proof composition, which is a central ingredient in the construction of PCP systems. A related notion and its composition properties were discovered independently by Dinur and Reingold. Our main technical contribution is a construction of a lengthefficient robust PCP of proximity. While the new construction uses many of the standard techniques used in PCP constructions, it does differ from previous constructions in fundamental ways, and in particular does not use the parallelization step of Arora et al. J. ACM, 45 1998, pp. 501555. The alternative approach may be of independent interest. We also obtain analogous quantitative results for locally testable codes. In addition, we introduce a relaxed notion of locally decodable codes and present such codes mapping k information bits to codewords of length $k^{1+\epsilon}$ for any $\epsilon>0$.
Starting Page	889
Ending Page	974
Page Count	86
File Format	PDF
ISSN	00975397
DOI	10.1137/S0097539705446810
e-ISSN	10957111
Journal	SIAM Journal on Computing (SMJCAT)
Issue Number	4 (Special Issue on Randomness and Complexity)
Volume Number	36
Language	English
Publisher	Society for Industrial and Applied Mathematics
Publisher Date	2006-12-15
Access Restriction	Subscribed
Subject Keyword	probabilistically checkable proofs Computational difficulty of problems Coding and information theory locally decodable codes locally testable codes Other types of codes property testing PCP
Content Type	Text
Resource Type	Article
Subject	Mathematics Computer Science

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

Robust pcps of proximity, shorter pcps and applications to coding

Short PCPs with Polylog Query Complexity

Composition of Low-Error 2-Query PCPs Using Decodable PCPs

Combinatorial construction of locally testable codes

Combinatorial Construction of Locally Testable Codes

Simple PCPs with poly-log rate and query complexity

Randomness-efficient low degree tests and short PCPs via epsilon-biased sets

Combinatorial PCPs with Short Proofs

Combinatorial PCPs with Efficient Verifiers

Robust PCPs of Proximity, Shorter PCPs, and Applications to Coding

Similar Documents

Robust pcps of proximity, shorter pcps and applications to coding

Short PCPs with Polylog Query Complexity

Composition of Low-Error 2-Query PCPs Using Decodable PCPs

Combinatorial construction of locally testable codes

Combinatorial Construction of Locally Testable Codes

Simple PCPs with poly-log rate and query complexity

Randomness-efficient low degree tests and short PCPs via epsilon-biased sets

Combinatorial PCPs with Short Proofs

Combinatorial PCPs with Efficient Verifiers

Robust PCPs of Proximity, Shorter PCPs, and Applications to Coding