A hard-core predicate for all one-way functions
STOC '89 Proceedings of the twenty-first annual ACM symposium on Theory of computing
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
Probabilistic checking of proofs: a new characterization of NP
Journal of the ACM (JACM)
Recycling queries in PCPs and in linearity tests (extended abstract)
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
Proof verification and the hardness of approximation problems
Journal of the ACM (JACM)
A PCP characterization of NP with optimal amortized query complexity
STOC '00 Proceedings of the thirty-second annual ACM symposium on Theory of computing
On the power of unique 2-prover 1-round games
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
Locally Testable Codes and PCPs of Almost-Linear Length
FOCS '02 Proceedings of the 43rd Symposium on Foundations of Computer Science
Towards optimal lower bounds for clique and chromatic number
Theoretical Computer Science
Gowers uniformity, influence of variables, and PCPs
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
Near-optimal algorithms for unique games
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
Linearity testing in characteristic two
IEEE Transactions on Information Theory - Part 1
List-decoding reed-muller codes over small fields
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
Inverse conjecture for the gowers norm is false
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
Unconditional pseudorandom generators for low degree polynomials
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
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
Guest Column: correlation bounds for polynomials over {0 1}
ACM SIGACT News
Testing Fourier Dimensionality and Sparsity
ICALP '09 Proceedings of the 36th International Colloquium on Automata, Languages and Programming: Part I
A Hypergraph Dictatorship Test with Perfect Completeness
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
On the structure of cubic and quartic polynomials
Proceedings of the forty-second ACM symposium on Theory of computing
Local list-decoding and testing of random linear codes from high error
Proceedings of the forty-second ACM symposium on Theory of computing
Breaking the $\epsilon$-Soundness Bound of the Linearity Test over GF(2)
SIAM Journal on Computing
Pseudorandom Bits for Polynomials
SIAM Journal on Computing
Limitation on the rate of families of locally testable codes
Property testing
Query-efficient dictatorship testing with perfect completeness
Property testing
Some recent results on local testing of sparse linear codes
Property testing
Limitation on the rate of families of locally testable codes
Property testing
Query-efficient dictatorship testing with perfect completeness
Property testing
Some recent results on local testing of sparse linear codes
Property testing
Limits on the rate of locally testable affine-invariant codes
APPROX'11/RANDOM'11 Proceedings of the 14th international workshop and 15th international conference on Approximation, randomization, and combinatorial optimization: algorithms and techniques
Hard functions for low-degree polynomials over prime fields
MFCS'11 Proceedings of the 36th international conference on Mathematical foundations of computer science
Testing Fourier Dimensionality and Sparsity
SIAM Journal on Computing
Towards an optimal query efficient PCP?
Proceedings of the 4th conference on Innovations in Theoretical Computer Science
Hard Functions for Low-Degree Polynomials over Prime Fields
ACM Transactions on Computation Theory (TOCT)
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We define tests of boolean functions which distinguish between linear (or quadratic) polynomials, and functions which are very far, in an appropriate sense, from these polynomials. The tests have optimal or nearly optimal trade-offs between soundness and the number of queries. A central step in our analysis of quadraticity tests is the proof of aninverse theorem for the third Gowers uniformity norm of boolean functions. The last result implies that it ispossible to estimate efficiently the distance from the second-order Reed-Muller code on inputs lying far beyond its list-decoding radius. Our main technical tools are Fourier analysis on Z2n and methods from additive number theory. We observe that these methods can be used to give a tight analysis of the Abelian Homomorphism testing problemfor some families of groups, including powers of Zp.