A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2017; you can also visit the original URL.
The file type is application/pdf.
Filters
Sub-Constant Error Probabilistically Checkable Proof of Almost-Linear Size
2009
Computational Complexity
Preserved Fulltext
We show a construction of a P CP with both sub-constant error and almost-linear size. ...
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. ...
Sub-Constant Error and Almost-Linear Size The question of whether there exist P CP s with both sub-constant error and almost-linear size was open. ...
doi:10.1007/s00037-009-0278-0
fatcat:vd5rlal3xfapjjmkahwtm5e46e
The tale of the PCP theorem
2012
XRDS Crossroads The ACM Magazine for Students
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2012; you can also visit the original URL.
The file type is application/pdf.
increase by more than a sub-linear factor to make the format probabilistically checkable. ...
Overall, the reduction from "is there a proof of size n?" to the gap problem is essentially equivalent to a transformation of a proof to a probabilistically checkable format. ...
doi:10.1145/2090276.2090286
fatcat:aim67yzrxrhsnjfs72dkfomzae
Page 2646 of Mathematical Reviews Vol. , Issue 2001D
[page]
2001
Mathematical Reviews
Preserved Fulltext
The Internet Archive has digitized a microfilm copy of this work. It may be possible to borrow a copy for reading.
(465-474 (electronic)); Ran Raz and Shmuel Safra, A sub-constant error-probability low-degree test, and a sub-constant error-probability PCP characterization of NP (475- 484 (electronic)); Sanjeev Arora ...
Yau, Eigenvalues, flows and separators of graphs (749 (electronic)); Lance Fortnow and Michael Sipser, Retraction of probabilistic computation and linear time (750 (electronic)). ...
Some Applications of Coding Theory in Computational Complexity
[article]
2004
arXiv
pre-print
Preserved Fulltext
The Internet Archive has a preservation copy of this work in our general collections.
The file type is application/pdf.
Locally testable codes are error-correcting codes with sub-linear time error-detection algorithms, and they are the combinatorial core of probabilistically checkable proofs. ...
Locally decodable codes are error-correcting codes with sub-linear time error-correcting algorithms. ...
Acknowledgements Most of my understanding of coding theory comes from Madhu Sudan. Working with Salil Vadhan on various research project has clarified connections to complexity. ...
arXiv:cs/0409044v1
fatcat:46gkw3tgnfbz7gfkwyrzgbw4wm
Sub-Constant Error Low Degree Test of Almost-Linear Size
2008
SIAM journal on computing (Print)
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2017; you can also visit the original URL.
The file type is application/pdf.
Previous constructions of almost-linear size testers obtained only constant error [13, 7] . ...
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 ). ...
However, at this point, these constructions achieve neither sub-constant error nor almost-linear size. ...
doi:10.1137/060656838
fatcat:ggfdacgvsvdolbec3vkzk2fqg4
Sub-constant error low degree test of almost-linear size
2006
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing - STOC '06
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2017; you can also visit the original URL.
The file type is application/pdf.
Previous constructions of almost-linear size testers obtained only constant error [13, 7] . ...
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 ). ...
However, at this point, these constructions achieve neither sub-constant error nor almost-linear size. ...
doi:10.1145/1132516.1132520
dblp:conf/stoc/MoshkovitzR06
fatcat:iew4s3or3fex7dkgigpjucztcy
Unconditional Lower Bounds against Advice
[chapter]
2009
Lecture Notes in Computer Science
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2017; you can also visit the original URL.
The file type is application/pdf.
We also consider the question of whether these lower bounds can be made to work on almost all input lengths rather than on infinitely many. ...
For the probabilistic classes, no lower bounds for uniform exponential time against advice were known before. ...
We also thank many other participants of Dagstuhl Seminar 08381 on the Computational Complexity of Discrete Problems, discussions with whom helped shape this paper. ...
doi:10.1007/978-3-642-02927-1_18
fatcat:t44e2glkrzd37dw4sviqs72gwy
Composition of Low-Error 2-Query PCPs Using Decodable PCPs
2009
2009 50th Annual IEEE Symposium on Foundations of Computer Science
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2017; you can also visit the original URL.
The file type is application/pdf.
The main result of this paper is a generic composition theorem for low error two-query probabilistically checkable proofs (PCPs). ...
In a recent breakthrough, Moshkovitz and Raz [In Proc. 49th IEEE Symp. on Foundations of Comp. Science (FOCS), 2008] constructed almost linear-sized low-error 2-query PCPs for every language in NP. ...
Special thanks to Oded Goldreich for many helpful comments on an earlier version of this manuscript. ...
doi:10.1109/focs.2009.8
dblp:conf/focs/DinurH09
fatcat:4ymy3vyienguzmn4wgwobw3j4e
The approximability of NP-hard problems
1998
Proceedings of the thirtieth annual ACM symposium on Theory of computing - STOC '98
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2017; you can also visit the original URL.
The file type is application/pdf.
in size-such that a probabilistic checker can verify their correctness by examining only a constant number of bits in them. ...
] and PH [92] , probabilistically checkable codes, zero-knowledge proofs, checkable VLSI computations, etc. ...
doi:10.1145/276698.276784
dblp:conf/stoc/Arora98
fatcat:yu5xnmrhsbd2xk7m6aanrb5ule
Probabilistic Proof Systems: A Primer
2007
Foundations and Trends® in Theoretical Computer Science
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2016; you can also visit the original URL.
The file type is application/pdf.
Probabilistically Checkable Proof Systems Probabilistically checkable proof systems can be viewed as standard (deterministic) proof systems that are augmented with a probabilistic procedure capable of ...
In this primer, we shall survey three types of probabilistic proof systems, called interactive proofs, zero-knowledge proofs, and probabilistic checkable proofs. ...
doi:10.1561/0400000023
fatcat:pcglbvm2xjfxnjm3w2p5ljzdem
Probabilistic Checking Against Non-Signaling Strategies from Linearity Testing
2018
Innovations in Theoretical Computer Science
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2022; you can also visit the original URL.
The file type is application/pdf.
A central tool for these applications is probabilistically checkable proofs (PCPs) that are 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) . ...
doi:10.4230/lipics.itcs.2019.25
dblp:conf/innovations/ChiesaMS19
fatcat:7io7utcuhbb4pd6awocpevulqy
Composition of Low-Error 2-Query PCPs Using Decodable PCPs
2013
SIAM journal on computing (Print)
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2017; you can also visit the original URL.
The file type is application/pdf.
The main result of this paper is a generic composition theorem for low error two-query probabilistically checkable proofs (PCPs). ...
Prior to this work, composition of PCPs was wellunderstood only in the constant error regime. ...
Special thanks to Oded Goldreich for many helpful comments on an earlier version of this manuscript. ...
doi:10.1137/100788161
fatcat:3k2qhgnkvrahri42ynnykctyle
Composition of Low-Error 2-Query PCPs Using Decodable PCPs
[chapter]
2010
Lecture Notes in Computer Science
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2017; you can also visit the original URL.
The file type is application/pdf.
The main result of this paper is a generic composition theorem for low error two-query probabilistically checkable proofs (PCPs). ...
Prior to this work, composition of PCPs was wellunderstood only in the constant error regime. ...
Special thanks to Oded Goldreich for many helpful comments on an earlier version of this manuscript. ...
doi:10.1007/978-3-642-16367-8_21
fatcat:57tg7catbndm7dyeaelrfgee54
Hard properties with (very) short PCPPs and their applications
[article]
2019
arXiv
pre-print
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2020; you can also visit the original URL.
The file type is application/pdf.
Other Versions
We show that there exist properties that are maximally hard for testing, while still admitting PCPPs with a proof size very close to linear. ...
proof size is O(n·log^(ℓ)n), where log^(ℓ) denotes the ℓ times iterated log function (e.g., log^(2)n = loglog n). ...
Introduction Probabilistically checkable proofs (PCPs) are one of the landmark achievements in theoretical computer science. ...
arXiv:1909.03255v2
fatcat:hfkyuaaeu5bjdhleu2w6bf2r7a
Improved 3LIN Hardness via Linear Label Cover
2019
International Workshop on Approximation Algorithms for Combinatorial Optimization
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2022; you can also visit the original URL.
The file type is application/pdf.
We prove that for every constant c and ε = (log n) −c , there is no polynomial time algorithm that when given an instance of 3-LIN with n variables where an (1 − ε)-fraction of the clauses are satisfiable ...
, finds an assignment that satisfies atleast ( 1 2 + ε)-fraction of clauses unless NP ⊆ BPP. ...
Later in a celebrated paper, Moshkovitz and Raz [12] gave an improved hardness of Label Cover that achieves sub-constant error under polynomial time reductions. ...
doi:10.4230/lipics.approx-random.2019.9
dblp:conf/approx/HarshaKLT19
fatcat:vjy5cuwaqbambgcza7ev3gjlu4
« Previous
Showing results 1 — 15 out of 342 results