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

Dana Moshkovitz, Ran Raz
2008 SIAM journal on computing (Print)  
We design and analyze new 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.  ... 
doi:10.1137/060656838 fatcat:ggfdacgvsvdolbec3vkzk2fqg4

Sub-constant error low degree test of almost-linear size

Dana Moshkovitz, Ran Raz
2006 Proceedings of the thirty-eighth annual ACM symposium on Theory of computing - STOC '06  
We design and analyze new 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.  ... 
doi:10.1145/1132516.1132520 dblp:conf/stoc/MoshkovitzR06 fatcat:iew4s3or3fex7dkgigpjucztcy

Sub-Constant Error Probabilistically Checkable Proof of Almost-Linear Size

Dana Moshkovitz, Ran Raz
2009 Computational Complexity  
Its main ingredients are a recent 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.  ... 
doi:10.1007/s00037-009-0278-0 fatcat:vd5rlal3xfapjjmkahwtm5e46e

Low-degree test with polynomially small error

Dana Moshkovitz
2016 Computational Complexity  
We instantiate this theorem to obtain a 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] .  ... 
doi:10.1007/s00037-016-0149-4 fatcat:sgzrdmg7hzfmdfh323r54n7mhq

Non-interactive proofs of proximity

Tom Gur, Ron D. Rothblum
2016 Computational Complexity  
Thus, the verifier is only assured 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,  ... 
doi:10.1007/s00037-016-0136-9 fatcat:ny65uzg76zhg7do3yeq6gzkuee

Non-Interactive Proofs of Proximity

Tom Gur, Ron D. Rothblum
2015 Proceedings of the 2015 Conference on Innovations in Theoretical Computer Science - ITCS '15  
Thus, the verifier is only assured 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,  ... 
doi:10.1145/2688073.2688079 dblp:conf/innovations/GurR15 fatcat:mf5okdnhqrhp3ko256zesiqpty

Robust detection and verification of linear relationships to generate metabolic networks using estimates of technical errors

Frank Kose, Jan Budczies, Matthias Holschneider, Oliver Fiehn
2007 BMC Bioinformatics  
Results: The Bayesian law was applied for detecting 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.  ... 
doi:10.1186/1471-2105-8-162 pmid:17517139 pmcid:PMC1894643 fatcat:ymgl4far6rafjjhul5cc5qqrny

Locally testable codes and PCPs of almost-linear length

Oded Goldreich, Madhu Sudan
2006 Journal of the ACM  
Locally testable codes are 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.  ... 
doi:10.1145/1162349.1162351 fatcat:7dmnllyb35bmhm4hlds5qwetya

A practical local tomography reconstruction algorithm based on a known sub-region

Pierre Paleo, Michel Desvignes, Alessandro Mirone
2017 Journal of Synchrotron Radiation  
Using a coarse basis reduces the 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.  ... 
doi:10.1107/s1600577516016556 pmid:28009565 fatcat:nfk5gs53gvgjxosd5wramg4pjm

Development of a saturation and stress-dependent chord modulus model for unbound granular material

E van Aswegen, WJ vd M Steyn, HL Theyse
2015 Journal of the South African Institution of Civil Engineering  
Development 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%.  ... 
doi:10.17159/2309-8775/2015/v57n2a2 fatcat:msdqbp2zpfalfivfzwoesfwuje

Algebraic Methods in Computational Complexity (Dagstuhl Seminar 18391)

Markus Bläser, Valentine Kabanets, Jacobo Torán, Christopher Umans, Michael Wagner
2019 Dagstuhl Reports  
The Razborov-Smolensky polynomial-approximation method for proving 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  ... 
doi:10.4230/dagrep.8.9.133 dblp:journals/dagstuhl-reports/BlaserKTU18 fatcat:bqddvcedazgqngwix6ptk7syuq

Probabilistic Checking Against Non-Signaling Strategies from Linearity Testing

Alessandro Chiesa, Peter Manohar, Igor Shinkar, Michael Wagner
2018 Innovations in Theoretical Computer Science  
In this paper we prove that the exponential-length 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) .  ... 
doi:10.4230/lipics.itcs.2019.25 dblp:conf/innovations/ChiesaMS19 fatcat:7io7utcuhbb4pd6awocpevulqy

Two Query PCP with Sub-Constant Error

Dana Moshkovitz, Ran Raz
2008 2008 49th Annual IEEE Symposium on Foundations of Computer Science  
We show that the N P-Complete language 3SAT has a 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.  ...  Recently, sub-constant error was achieved simultaneously with almost-linear size: Theorem 8 (Sub-constant error PCP of almost-linear size, [27, 26] ).  ... 
doi:10.1109/focs.2008.60 dblp:conf/focs/MoshkovitzR08 fatcat:agpggrno5ncuxnvr4vimozvvfy

Two-query PCP with subconstant error

Dana Moshkovitz, Ran Raz
2010 Journal of the ACM  
We show that the N P-Complete language 3SAT has a 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.  ...  Recently, sub-constant error was achieved simultaneously with almost-linear size: Theorem 8 (Sub-constant error PCP of almost-linear size, [27, 26] ).  ... 
doi:10.1145/1754399.1754402 fatcat:nhhz2in55ngt3lo5kb6t73eb4e

Constructions of Low-degree and Error-Correcting ε-Biased Generators

Amir Shpilka
2009 Computational Complexity  
For any 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.  ... 
doi:10.1007/s00037-009-0281-5 fatcat:jgvml6jacjaetpmch2ihe2uwzi
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