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Sub-Constant Error Low Degree Test of Almost-Linear Size

2008
*
SIAM journal on computing (Print)
*

We design and analyze new

doi:10.1137/060656838
fatcat:ggfdacgvsvdolbec3vkzk2fqg4
*low**degree*testers that have both*sub*-*constant**error*o(1) and*almost*-*linear**size*n 1+o(1) (where n = |F| m ). ... Previous constructions*of**almost*-*linear**size*testers obtained only*constant**error*[13, 7] . ... Our Contribution: Randomness-Efficient*Sub*-*Constant**Error*Testers We design and analyze two*low**degree*testers that have both*sub*-*constant**error*and*almost*-*linear**size*. ...##
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Sub-constant error low degree test of almost-linear size

2006
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Proceedings of the thirty-eighth annual ACM symposium on Theory of computing - STOC '06
*

We design and analyze new

doi:10.1145/1132516.1132520
dblp:conf/stoc/MoshkovitzR06
fatcat:iew4s3or3fex7dkgigpjucztcy
*low**degree*testers that have both*sub*-*constant**error*o(1) and*almost*-*linear**size*n 1+o(1) (where n = |F| m ). ... Previous constructions*of**almost*-*linear**size*testers obtained only*constant**error*[13, 7] . ... Our Contribution: Randomness-Efficient*Sub*-*Constant**Error*Testers We design and analyze two*low**degree*testers that have both*sub*-*constant**error*and*almost*-*linear**size*. ...##
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Sub-Constant Error Probabilistically Checkable Proof of Almost-Linear Size

2009
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Computational Complexity
*

Its main ingredients are a recent

doi:10.1007/s00037-009-0278-0
fatcat:vd5rlal3xfapjjmkahwtm5e46e
*low**degree**test*with both*sub*-*constant**error*and*almost*-*linear**size*[12] and a new method for constructing a short list*of*balanced curves. ... We show a construction*of*a P CP with both*sub*-*constant**error*and*almost*-*linear**size*. ... A step in this direction is taken in [12] , where a*low**degree**test**of**sub*-*constant**error*and*almost*-*linear**size*is constructed. ...##
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Low-degree test with polynomially small error

2016
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Computational Complexity
*

We instantiate this theorem to obtain a

doi:10.1007/s00037-016-0149-4
fatcat:sgzrdmg7hzfmdfh323r54n7mhq
*low**degree*tester whose*error*probability is polynomially small in the*size**of*the space. ... We prove a parallel repetition theorem for*low**degree**testing*achieving optimal exponential decay*of*the*error*probability. ... Acknowledgements This paper originally appeared as "An Approach To The Sliding Scale Conjecture Via Parallel Repetition For*Low**Degree**Testing*" [31] . ...##
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Non-interactive proofs of proximity

2016
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Computational Complexity
*

Thus, the verifier is only assured

doi:10.1007/s00037-016-0136-9
fatcat:ny65uzg76zhg7do3yeq6gzkuee
*of*the proximity*of*the statement to a correct one. Such proof-systems can be viewed as the N P (or more accurately MA) analogue*of*property*testing*. ... In addition, we show a natural problem that has a full and (*almost*) tight multiplicative trade-off between the length*of*the proof and the verifier's query complexity. ... We also thank Oded for multiple technical and conceptual suggestions that greatly improved both the results and presentation*of*this work, and for allowing us to include his generalization*of*[GS06, ...##
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Non-Interactive Proofs of Proximity

2015
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Proceedings of the 2015 Conference on Innovations in Theoretical Computer Science - ITCS '15
*

Thus, the verifier is only assured

doi:10.1145/2688073.2688079
dblp:conf/innovations/GurR15
fatcat:mf5okdnhqrhp3ko256zesiqpty
*of*the proximity*of*the statement to a correct one. Such proof-systems can be viewed as the N P (or more accurately MA) analogue*of*property*testing*. ... In addition, we show a natural problem that has a full and (*almost*) tight multiplicative trade-off between the length*of*the proof and the verifier's query complexity. ... We also thank Oded for multiple technical and conceptual suggestions that greatly improved both the results and presentation*of*this work, and for allowing us to include his generalization*of*[GS06, ...##
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Robust detection and verification of linear relationships to generate metabolic networks using estimates of technical errors

2007
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BMC Bioinformatics
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Results: The Bayesian law was applied for detecting

doi:10.1186/1471-2105-8-162
pmid:17517139
pmcid:PMC1894643
fatcat:ymgl4far6rafjjhul5cc5qqrny
*linearities*that are validated by explaining the residues by the*degree**of*technical measurement*errors*. ...*Test*statistics were developed and the algorithm was*tested*on simulated data using 3-150 samples and 0-100% technical*error*. ... Acknowledgements The work was funded by the NIEHS through the R01 project ES13932 granted to*OF*and by a fellowship granted to FK by the Max-Planck Society, Germany. ...##
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Locally testable codes and PCPs of almost-linear length

2006
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Journal of the ACM
*

Locally testable codes are

doi:10.1145/1162349.1162351
fatcat:7dmnllyb35bmhm4hlds5qwetya
*error*-correcting codes that admit very efficient codeword*tests*. ... Specifically, using a*constant*number*of*(random) queries, non-codewords are rejected with probability proportional to their distance from the code. ... , and a direct construction*of*locally testable (*linear*) codes*of**sub*-exponential length. ...##
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A practical local tomography reconstruction algorithm based on a known sub-region

2017
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Journal of Synchrotron Radiation
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Using a coarse basis reduces the

doi:10.1107/s1600577516016556
pmid:28009565
fatcat:nfk5gs53gvgjxosd5wramg4pjm
*degrees**of*freedom*of*the problem while actually correcting the cupping effect. ... The coefficients*of*this basis are found by optimizing iteratively a fidelity term under the constraint*of*a known*sub*-region. ... Capturing the*low*frequencies*of*the*error*in the known zone The reconstruction*error*in is first approximated as a*linear*combination*of*Gaussian functions. ...##
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Development of a saturation and stress-dependent chord modulus model for unbound granular material

2015
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Journal of the South African Institution of Civil Engineering
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Development

doi:10.17159/2309-8775/2015/v57n2a2
fatcat:msdqbp2zpfalfivfzwoesfwuje
*of*a saturation and stress-dependent chord modulus model for unbound granular material. ... Stress stiffening occurred with increasing stress ratio at*low*and intermediate*degrees**of*saturation, but not at the highest*degree**of*saturation where the chord modulus remained*almost**constant*with ... b or*sub*-variable α 2 The*sub*-variable appears to reach a plateau for*degree**of*saturation below 40% and then rapidly decreases to a lower level plateau at a*degree**of*saturation above 60%. ...##
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Algebraic Methods in Computational Complexity (Dagstuhl Seminar 18391)

2019
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Dagstuhl Reports
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The Razborov-Smolensky polynomial-approximation method for proving

doi:10.4230/dagrep.8.9.133
dblp:journals/dagstuhl-reports/BlaserKTU18
fatcat:bqddvcedazgqngwix6ptk7syuq
*constant*-depth circuit lower bounds, the PCP characterization*of*NP, and the Agrawal-Kayal-Saxena polynomial-time primality*test*are some ... There have been similar successes concerning the related problems*of*polynomial identity*testing*and circuit reconstruction in the algebraic model (and these are tied to central questions regarding the ... Ramprasad Saptharishi showed that by barely improving the trivial (s + 1) n*size*hitting set even for n-variate*degree*s,*size*s algebraic circuits, we could get an*almost*complete derandomization*of*PIT ...##
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Probabilistic Checking Against Non-Signaling Strategies from Linearity Testing

2018
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Innovations in Theoretical Computer Science
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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. ... non-signaling analogue*of*the PCP Theorem. ...*sub*-*constant*soundness*error**of*2 −O(log S) . ...##
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Two Query PCP with Sub-Constant Error

2008
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2008 49th Annual IEEE Symposium on Foundations of Computer Science
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We show that the N P-Complete language 3SAT has a PCP verifier that makes two queries to a proof

doi:10.1109/focs.2008.60
dblp:conf/focs/MoshkovitzR08
fatcat:agpggrno5ncuxnvr4vimozvvfy
*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. ... Recently,*sub*-*constant**error*was achieved simultaneously with*almost*-*linear**size*: Theorem 8 (*Sub*-*constant**error*PCP*of**almost*-*linear**size*, [27, 26] ). ...##
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Two-query PCP with subconstant error

2010
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Journal of the ACM
*

We show that the N P-Complete language 3SAT has a PCP verifier that makes two queries to a proof

doi:10.1145/1754399.1754402
fatcat:nhhz2in55ngt3lo5kb6t73eb4e
*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. ... Recently,*sub*-*constant**error*was achieved simultaneously with*almost*-*linear**size*: Theorem 8 (*Sub*-*constant**error*PCP*of**almost*-*linear**size*, [27, 26] ). ...##
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Constructions of Low-degree and Error-Correcting ε-Biased Generators

2009
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Computational Complexity
*

For any

doi:10.1007/s00037-009-0281-5
fatcat:jgvml6jacjaetpmch2ihe2uwzi
*constant*k we get that n = Ω(m/ log(1/ )) k , which is nearly optimal. ... The paper also contains an appendix by Venkatesan Guruswami that provides an explicit construction*of*a family*of**error*correcting codes*of*rate 1/2 that has efficient encoding and decoding algorithms ... Acknowledgements I would like to thank Adam Smith for introducing me to the problem*of*constructing -biased good*error*correcting codes and for many valuable discussions. ...
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