Small-bias probability spaces: efficient constructions and applications
STOC '90 Proceedings of the twenty-second annual ACM symposium on Theory of computing
Checking computations in polylogarithmic time
STOC '91 Proceedings of the twenty-third annual ACM symposium on Theory of computing
Approximations of general independent distributions
STOC '92 Proceedings of the twenty-fourth annual ACM symposium on Theory of computing
A well-characterized approximation problem
Information Processing Letters
Self-testing/correcting with applications to numerical problems
Journal of Computer and System Sciences - Special issue: papers from the 22nd ACM symposium on the theory of computing, May 14–16, 1990
The probabilistic method yields deterministic parallel algorithms
Proceedings of the 30th IEEE symposium on Foundations of computer science
Nearly-linear size holographic proofs
STOC '94 Proceedings of the twenty-sixth annual ACM symposium on Theory of computing
&egr;-discrepancy sets and their application for interpolation of sparse polynomials
Information Processing Letters
STOC '97 Proceedings of the twenty-ninth annual ACM symposium on Theory of computing
Improved low-degree testing and its applications
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)
Free Bits, PCPs, and Nonapproximability---Towards Tight Results
SIAM Journal on Computing
Property testing and its connection to learning and approximation
Journal of the ACM (JACM)
On the efficiency of local decoding procedures for error-correcting codes
STOC '00 Proceedings of the thirty-second annual ACM symposium on Theory of computing
Some optimal inapproximability results
Journal of the ACM (JACM)
Robust Characterizations of Polynomials withApplications to Program Testing
SIAM Journal on Computing
Simple analysis of graph tests for linearity and PCP
Random Structures & Algorithms
Some improvements to total degree tests
ISTCS '95 Proceedings of the 3rd Israel Symposium on the Theory of Computing Systems (ISTCS'95)
Probabilistically checkable proofs and the testing of hadamard-like codes
Probabilistically checkable proofs and the testing of hadamard-like codes
IEEE Transactions on Information Theory - Part 1
Linearity testing in characteristic two
IEEE Transactions on Information Theory - Part 1
Robust pcps of proximity, shorter pcps and applications to coding
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
Derandomizing homomorphism testing in general groups
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
A new family of Cayley expanders (?)
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
Pseudorandom generators for low degree polynomials
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
Proceedings of the thirty-seventh 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
Correcting errors without leaking partial information
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
Almost Orthogonal Linear Codes are Locally Testable
FOCS '05 Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science
Sub-constant error low degree test of almost-linear size
Proceedings of the thirty-eighth 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
Robust locally testable codes and products of codes
Random Structures & Algorithms
Locally testable codes and PCPs of almost-linear length
Journal of the ACM (JACM)
The PCP theorem by gap amplification
Journal of the ACM (JACM)
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
Non-Abelian homomorphism testing, and distributions close to their self-convolutions
Random Structures & Algorithms
Unconditional pseudorandom generators for low degree polynomials
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
Small Sample Spaces Cannot Fool Low Degree Polynomials
APPROX '08 / RANDOM '08 Proceedings of the 11th international workshop, APPROX 2008, and 12th international workshop, RANDOM 2008 on Approximation, Randomization and Combinatorial Optimization: Algorithms and Techniques
Breaking the ε-Soundness Bound of the Linearity Test over GF(2)
APPROX '08 / RANDOM '08 Proceedings of the 11th international workshop, APPROX 2008, and 12th international workshop, RANDOM 2008 on Approximation, Randomization and Combinatorial Optimization: Algorithms and Techniques
On the Randomness Complexity of Property Testing
APPROX '07/RANDOM '07 Proceedings of the 10th International Workshop on Approximation and the 11th International Workshop on Randomization, and Combinatorial Optimization. Algorithms and Techniques
Guest Column: correlation bounds for polynomials over {0 1}
ACM SIGACT News
Hardness of Solving Sparse Overdetermined Linear Systems: A 3-Query PCP over Integers
ACM Transactions on Computation Theory (TOCT)
ACM Transactions on Computation Theory (TOCT)
Tolerant Linearity Testing and Locally Testable Codes
APPROX '09 / RANDOM '09 Proceedings of the 12th International Workshop and 13th International Workshop on Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques
Pseudorandom Bit Generators That Fool Modular Sums
APPROX '09 / RANDOM '09 Proceedings of the 12th International Workshop and 13th International Workshop on Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques
On the Power of Small-Depth Computation
Foundations and Trends® in Theoretical Computer Science
Two-query PCP with subconstant error
Journal of the ACM (JACM)
Derandomizing graph tests for homomorphism
TAMC'08 Proceedings of the 5th international conference on Theory and applications of models of computation
On the derandomization of the graph test for homomorphism over groups
Theoretical Computer Science
Breaking the $\epsilon$-Soundness Bound of the Linearity Test over GF(2)
SIAM Journal on Computing
Pseudorandom Bits for Polynomials
SIAM Journal on Computing
Short locally testable codes and proofs: a survey in two parts
Property testing
Symmetric LDPC codes and local testing
Property testing
Short locally testable codes and proofs: a survey in two parts
Property testing
Symmetric LDPC codes and local testing
Property testing
Short locally testable codes and proofs
Studies in complexity and cryptography
Characterizations of locally testable linear-and affine-invariant families
COCOON'11 Proceedings of the 17th annual international conference on Computing and combinatorics
Cryptography in constant parallel time
Cryptography in constant parallel time
Characterizations of locally testable linear- and affine-invariant families
Theoretical Computer Science
On pseudorandom generators with linear stretch in NC0
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
Robust local testability of tensor products of LDPC codes
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
Theoretical Computer Science
SIAM Journal on Discrete Mathematics
Proceedings of the 4th conference on Innovations in Theoretical Computer Science
On the concrete efficiency of probabilistically-checkable proofs
Proceedings of the forty-fifth annual ACM symposium on Theory of computing
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We present the first explicit construction of Probabilistically Checkable Proofs (PCPs) and Locally Testable Codes (LTCs) of fixed constant query complexity which have almost-linear (= n * 2Õ(√log n)) size. Such objects were recently shown to exist (nonconstructively) by Goldreich and Sudan[17]. Previous explicit constructions required size n1 + Ω(ε) with 1/ε queries. The key to these constructions is a nearly optimal randomness-efficient version of the low degree test[32]. In a similar way we give a randomness-efficient version of the BLR linearity test[13] (which is used, for instance, in locally testing the Hadamard code). The derandomizations are obtained through ε-biased sets for vector spaces over finite fields. The analysis of the derandomized tests rely on alternative views of ε-biased sets --- as generating sets of Cayley expander graphs for the low degree test, and as defining linear error-correcting codes for the linearity test.