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Two Query PCP with Sub-Constant Error

2008
*
2008 49th Annual IEEE Symposium on Foundations of Computer Science
*

We show that the N P-Complete language 3SAT has a

doi:10.1109/focs.2008.60
dblp:conf/focs/MoshkovitzR08
fatcat:agpggrno5ncuxnvr4vimozvvfy
*PCP*verifier that makes*two**queries*to a proof of almost-linear size and achieves*sub*-*constant*probability of*error*o(1). ... There were also*PCP*Theorems*with**sub*-*constant**error*and almost-linear size, but a*constant*number of*queries*that is larger than 2 [26]. As a corollary, we obtain a host of new results. ... ., [3] ): Are there*PCP*Theorems*with**two**queries*and*sub*-*constant**error*? How about*two*-*query*projection tests and*sub*-*constant**error*? Are there such*PCPs**with*almost-linear size ? ...##
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Composition of Low-Error 2-Query PCPs Using Decodable PCPs

2009
*
2009 50th Annual IEEE Symposium on Foundations of Computer Science
*

The main result of this paper is a generic composition theorem for low

doi:10.1109/focs.2009.8
dblp:conf/focs/DinurH09
fatcat:4ymy3vyienguzmn4wgwobw3j4e
*error**two*-*query*probabilistically checkable proofs (*PCPs*). ... Prior to this work, composition of*PCPs*was wellunderstood only in the*constant**error*regime. ... Indeed, this is how one constructs*PCPs**with**sub*-*constant**error*and a*constant*number of*queries*for the entire range of Ω(1) ≤ |Σ| ≤ exp((log n) 1−ε ) [RS97, AS03, DFK + 99]. ...##
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Composition of Low-Error 2-Query PCPs Using Decodable PCPs

2013
*
SIAM journal on computing (Print)
*

The main result of this paper is a generic composition theorem for low

doi:10.1137/100788161
fatcat:3k2qhgnkvrahri42ynnykctyle
*error**two*-*query*probabilistically checkable proofs (*PCPs*). ... Prior to this work, composition of*PCPs*was wellunderstood only in the*constant**error*regime. ... Indeed, this is how one constructs*PCPs**with**sub*-*constant**error*and a*constant*number of*queries*for the entire range of Ω(1) ≤ |Σ| ≤ exp((log n) 1−ε ) [RS97, AS03, DFK + 99]. ...##
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Composition of Low-Error 2-Query PCPs Using Decodable PCPs
[chapter]

2010
*
Lecture Notes in Computer Science
*

The main result of this paper is a generic composition theorem for low

doi:10.1007/978-3-642-16367-8_21
fatcat:57tg7catbndm7dyeaelrfgee54
*error**two*-*query*probabilistically checkable proofs (*PCPs*). ... Prior to this work, composition of*PCPs*was wellunderstood only in the*constant**error*regime. ... Indeed, this is how one constructs*PCPs**with**sub*-*constant**error*and a*constant*number of*queries*for the entire range of Ω(1) ≤ |Σ| ≤ exp((log n) 1−ε ) [RS97, AS03, DFK + 99]. ...##
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Efficient Arguments without Short PCPs

2007
*
Proceedings - IEEE Conference on Computational Complexity
*

Current constructions of efficient argument systems combine a short (polynomial size)

doi:10.1109/ccc.2007.10
dblp:conf/coco/IshaiKO07
fatcat:cxpvnlwrw5clnmll6yhgmhuyse
*PCP**with*a cryptographic hashing technique. ... (JACM 1998) yields a simple argument system for NP in which the communication from the prover to the verifier only includes a*constant*number of short encryptions. ... We are grateful to Eli Ben-Sasson and Prahladh Harsha for enlightening discussions on the efficiency of short*PCPs*, and to Rafael Pass for pointing out the relevance of [33] . ...##
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Low-degree test with polynomially small error

2016
*
Computational Complexity
*

We show that the Sliding Scale Conjecture in

doi:10.1007/s00037-016-0149-4
fatcat:sgzrdmg7hzfmdfh323r54n7mhq
*PCP*, namely the conjecture that there are*PCP*verifiers whose*error*is exponentially small in their randomness, would follow from a derandomization of our parallel ... This is known as low degree testing, and is the core of the algebraic approach to construction of*PCP*. ...*With*small*constant*number of*queries*, we have*PCP*theorems*with*soundness*error*2 −(log n) β for some*constant*β > 0 and 3*queries*[38, 4] . ...##
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Rigid Matrices From Rectangular PCPs
[article]

2020
*
arXiv
*
pre-print

Our construction of rectangular

arXiv:2005.03123v4
fatcat:7icnjyt7fzfovixm5puja3fxui
*PCPs*starts*with*an analysis of how randomness yields*queries*in the Reed–Muller-based outer*PCP*of Ben-Sasson, Goldreich, Harsha, Sudan and Vadhan [SICOMP, 2006; CCC, 2005 ... We introduce a variant of*PCPs*, that we refer to as rectangular*PCPs*, wherein proofs are thought of as square matrices, and the random coins used by the verifier can be partitioned into*two*disjoint sets ... For every*constants*s ∈ (0, 1/2) and τ ∈ (0, 1), there exists a*constant*-*query*, smooth and τ -almost rectangular*PCP*for L over the Boolean alphabet*with*perfect completeness, soundness*error*s, proof ...##
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Short Locally Testable Codes and Proofs: A Survey in Two Parts
[chapter]

2010
*
Lecture Notes in Computer Science
*

We survey known results regarding locally testable codes and locally testable proofs (known as

doi:10.1007/978-3-642-16367-8_6
fatcat:x4strlpapzhcxdulsd3qjzbfje
*PCPs*),*with*emphasis on the length of these constructs. ... The survey consists of*two*independent (i.e., self-contained) parts that cover the same material at different levels of rigor and detail. ... Applying this reduction log log n times yields a*PCP*of*query*complexity poly(log n) and length O(n), which in turn yields a 3-*query*"*PCP**with*soundness*error*1 − 1/poly(log n)". ...##
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Universal Arguments and their Applications

2009
*
SIAM journal on computing (Print)
*

indistinguishable proof systems,

doi:10.1137/070709244
fatcat:hfvkr5g455hhdiawk3v7rksaaq
*error*-correcting codes, tree hashing. ... Furthermore, these protocols have a*constant*number of rounds and are of the public-coin type. ... Loosely speaking, such a commitment scheme is an e cient*two*-phase*two*-party protocol through which one party, called the sender, can commit itself to a value so the following*two*con icting requirements ...##
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On Efficient Zero-Knowledge PCPs
[chapter]

2012
*
Lecture Notes in Computer Science
*

Simplifying Bounded-

doi:10.1007/978-3-642-28914-9_9
fatcat:by5mj3efbnb6xdqvdkvcgtp5qa
*Query*ZK-*PCPs*. The bounded-*query*zeroknowledge*PCP*of Kilian et al. starts from a weakly-sound boundedquery ZK-*PCP*of Dwork et al. ... The existence of ZK-*PCPs*for NP*with*efficient oracles and arbitrary polynomial-time malicious verifiers was left open. ... [40] gave an elegant way of using locking schemes to convert a ZK-*PCP**with*1−1/ poly(k) soundness*error*into a standard ZK-*PCP*of*constant*or even negligible*error*. ...##
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Probabilistic Checking Against Non-Signaling Strategies from Linearity Testing

2018
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Innovations in Theoretical Computer Science
*

In this paper we prove that the exponential-length

doi:10.4230/lipics.itcs.2019.25
dblp:conf/innovations/ChiesaMS19
fatcat:7io7utcuhbb4pd6awocpevulqy
*constant*-*query**PCP*construction due to Arora et al. (JACM 1998) is sound against non-signaling strategies. ... Our result offers a new length-vs-*query*tradeoff when compared to the non-signaling*PCP*of Kalai, Raz, and Rothblum (STOC 2013 and 2014) and, moreover, may serve as an intermediate step to a proof of a ...*sub*-*constant*soundness*error*of 2 −O(log S) . ...##
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Subquadratic SNARGs in the Random Oracle Model
[article]

2021
*
IACR Cryptology ePrint Archive
*

We present a SNARG in the ROM

dblp:journals/iacr/ChiesaY21a
fatcat:5urql44a7bbchfmfjd4x2lmlle
*with*a*sub*-quadratic argument size: Õ(log(t/ ) • log t). Our construction relies on a strong soundness notion for*PCPs*and a weak binding notion for commitments. ... A SNARG in the ROM is (t, )-secure if every t-*query*malicious prover can convince the verifier of a false statement*with*probability at most . ... For example, a*PCP**with*this soundness*error*can be obtained by repeating O(log(t/ )) times the verifier of any*constant*-*query**constant*-soundness base*PCP*. ...##
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Robust PCPs of Proximity, Shorter PCPs, and Applications to Coding

2006
*
SIAM journal on computing (Print)
*

In both cases, false assertions are rejected

doi:10.1137/s0097539705446810
fatcat:lzcftg6gvngmhbdw7gnkmltwlu
*with**constant*probability (which may be set to be arbitrarily close to 1). ... For every ε > 0, we present*PCPs*of length exp(log ε n) · n that can be verified by making a*constant*number of Boolean*queries*. ... Acknowledgments We are grateful to Avi Wigderson for collaborating*with*us at early stages of this research and to Irit Dinur for inspiring discussions at late stages of this research. ...##
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Robust pcps of proximity, shorter pcps and applications to coding

2004
*
Proceedings of the thirty-sixth annual ACM symposium on Theory of computing - STOC '04
*

In both cases, false assertions are rejected

doi:10.1145/1007352.1007361
dblp:conf/stoc/Ben-SassonGHSV04
fatcat:l7iua5ues5gwvc54mpdzjvcjqa
*with**constant*probability (which may be set to be arbitrarily close to 1). ... For every ε > 0, we present*PCPs*of length exp(log ε n) · n that can be verified by making a*constant*number of Boolean*queries*. ... Acknowledgments We are grateful to Avi Wigderson for collaborating*with*us at early stages of this research and to Irit Dinur for inspiring discussions at late stages of this research. ...##
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Derandomized Parallel Repetition via Structured PCPs

2011
*
Computational Complexity
*

In this work we construct such

doi:10.1007/s00037-011-0013-5
fatcat:d66hpe5weje6hbpic5twqtf5re
*PCP*verifiers, i.e.,*PCPs*that make only*two**queries*and have*sub*-*constant*soundness*error*. ... Constructing*PCPs**with**sub*-*constant*soundness*error*and, at the same time, a minimal number of*queries*into the proof (namely*two*) is especially important due to applications for inapproximability. ... In this work we give a new construction of a*PCP**with**sub*-*constant*soundness*error*and*two**queries*. This setting is particularly important for inapproximability, as will be discussed shortly below. ...
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