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
Property testing and its connection to learning and approximation
Journal of the ACM (JACM)
The importance of being biased
STOC '02 Proceedings of the thiry-fourth 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
Algebraic testing and weight distributions of codes
Theoretical Computer Science
Robust pcps of proximity, shorter pcps and applications to coding
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
Testing Polynomials over General Fields
FOCS '04 Proceedings of the 45th Annual IEEE Symposium on Foundations of Computer Science
Testing Low-Degree Polynomials over Prime Fields
FOCS '04 Proceedings of the 45th Annual IEEE Symposium on Foundations of Computer Science
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
Tolerant property testing and distance approximation
Journal of Computer and System Sciences
Sparse Random Linear Codes are Locally Decodable and Testable
FOCS '07 Proceedings of the 48th Annual IEEE Symposium on Foundations of Computer Science
Distribution-Free Property-Testing
SIAM Journal on Computing
Combinatorial construction of locally testable codes
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
Algebraic property testing: the role of invariance
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
Tolerant locally testable codes
APPROX'05/RANDOM'05 Proceedings of the 8th international workshop on Approximation, Randomization and Combinatorial Optimization Problems, and Proceedings of the 9th international conference on Randamization and Computation: algorithms and techniques
Low rate is insufficient for local testability
APPROX/RANDOM'10 Proceedings of the 13th international conference on Approximation, and 14 the International conference on Randomization, and combinatorial optimization: algorithms and techniques
Distribution-free testing algorithms for monomials with a sublinear number of queries
APPROX/RANDOM'10 Proceedings of the 13th international conference on Approximation, and 14 the International conference on Randomization, and combinatorial optimization: algorithms and techniques
Guest column: testing linear properties: some general theme
ACM SIGACT News
Some recent results on local testing of sparse linear codes
Property testing
Some recent results on local testing of sparse linear codes
Property testing
SIAM Journal on Discrete Mathematics
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We study tolerant linearity testing under general distributions. Given groups G and H , a distribution μ on G , and oracle access to a function f :G ***H , we consider the task of approximating the smallest μ -distance of f to a homomorphism h :G ***H , where the μ -distance between f and h is the probability that $f(x) \ne h(x)$ when x is drawn according to the distribution μ . This question is intimately connected to local testability of linear codes. In this work, we give a general sufficient condition on the distribution μ for linearity to be tolerantly testable with a constant number of queries. Using this condition we show that linearity is tolerantly testable for several natural classes of distributions including low bias, symmetric and product distributions. This gives a new and simple proof of a result of Kaufman and Sudan which shows that sparse, unbiased linear codes over are locally testable.