Interactive proofs and the hardness of approximating cliques
Journal of the ACM (JACM)
STOC '97 Proceedings of the twenty-ninth annual ACM symposium on Theory of computing
Probabilistic checking of proofs: a new characterization of NP
Journal of the ACM (JACM)
Proof verification and the hardness of approximation problems
Journal of the ACM (JACM)
PCP characterizations of NP: towards a polynomially-small error-probability
STOC '99 Proceedings of the thirty-first annual ACM symposium on Theory of computing
Robust Characterizations of Polynomials withApplications to Program Testing
SIAM Journal on Computing
Locally Testable Codes and PCPs of Almost-Linear Length
FOCS '02 Proceedings of the 43rd Symposium on Foundations of Computer Science
Randomness-efficient low degree tests and short PCPs via epsilon-biased sets
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
Some improvements to total degree tests
ISTCS '95 Proceedings of the 3rd Israel Symposium on the Theory of Computing Systems (ISTCS'95)
Robust pcps of proximity, shorter pcps and applications to coding
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
Simple PCPs with poly-log rate and query complexity
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
The PCP theorem by gap amplification
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
ICALP '08 Proceedings of the 35th international colloquium on Automata, Languages and Programming, Part II
Local list-decoding and testing of random linear codes from high error
Proceedings of the forty-second ACM symposium on Theory of computing
Composition of low-error 2-query PCPs using decodable PCPs
Property testing
Some recent results on local testing of sparse linear codes
Property testing
Composition of low-error 2-query PCPs using decodable PCPs
Property testing
Some recent results on local testing of sparse linear codes
Property testing
Characterizations of locally testable linear-and affine-invariant families
COCOON'11 Proceedings of the 17th annual international conference on Computing and combinatorics
Characterizations of locally testable linear- and affine-invariant families
Theoretical Computer Science
Local decoding and testing for homomorphisms
APPROX'06/RANDOM'06 Proceedings of the 9th international conference on Approximation Algorithms for Combinatorial Optimization Problems, and 10th international conference on Randomization and Computation
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Given a function f:Fm→F over a finite field F, a low degree tester tests its agreement with an m-variate polynomial of total degree at most d over F. The tester is usually given access to an oracle A providing the supposed restrictions of f to affine subspaces of constant dimension (e.g., lines, planes, etc.). The tester makes very few (probabilistic) queries to f and to A (say, one query to f and one query to A), and decides whether to accept or reject based on the replies.We wish to minimize two parameters of a tester: its error and its size. The error bounds the probability that the tester accepts although the function is far from a low degree polynomial. The size is the number of bits required to write the oracle replies on all possible tester's queries.Low degree testing is a central ingredient in most constructions of probabilistically checkable proofs (PCPs) and locally testable codes (LTCs). The error of the low degree tester is related to the soundness of the PCP and its size is related to the size of the PCP (or the length of the LTC).We design and analyze new low degree testers that have both sub-constant error o(1) and almost-linear size n1+o(1) (where n=|F|m). Previous constructions of sub-constant error testers had polynomial size [13, 16]. These testers enabled the construction of PCPs with sub-constant soundness, but polynomial size [13, 16, 9]. Previous constructions of almost-linear size testers obtained only constant error [13, 7]. These testers were used to construct almost-linear size LTCs and almost-linear size PCPs with constant soundness [13, 7, 5, 6, 8].