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 algorithmic aspects of the regularity lemma
Journal of Algorithms
On a class of O(n2) problems in computational geometry
Computational Geometry: Theory and Applications
Property testing and its connection to learning and approximation
Journal of the ACM (JACM)
Lower bounds for linear satisfiability problems
Proceedings of the sixth annual ACM-SIAM symposium on Discrete algorithms
Robust Characterizations of Polynomials withApplications to Program Testing
SIAM Journal on Computing
Extremal problems on set systems
Random Structures & Algorithms
A Lower Bound for Testing 3-Colorability in Bounded-Degree Graphs
FOCS '02 Proceedings of the 43rd Symposium on Foundations of Computer Science
Testing subgraphs in large graphs
Random Structures & Algorithms - Special issue: Proceedings of the tenth international conference "Random structures and algorithms"
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
Testing subgraphs in directed graphs
Journal of Computer and System Sciences - Special issue: STOC 2003
Regularity lemma for k-uniform hypergraphs
Random Structures & Algorithms
Some 3CNF Properties Are Hard to Test
SIAM Journal on Computing
Almost Orthogonal Linear Codes are Locally Testable
FOCS '05 Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science
Quasirandomness, Counting and Regularity for 3-Uniform Hypergraphs
Combinatorics, Probability and Computing
The counting lemma for regular k-uniform hypergraphs
Random Structures & Algorithms
A combinatorial characterization of the testable graph properties: it's all about regularity
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
A Characterization of Easily Testable Induced Subgraphs
Combinatorics, Probability and Computing
A variant of the hypergraph removal lemma
Journal of Combinatorial Theory Series A
Testing versus Estimation of Graph Properties
SIAM Journal on Computing
Subquadratic Algorithms for 3SUM
Algorithmica
A Characterization of the (Natural) Graph Properties Testable with One-Sided Error
SIAM Journal on Computing
Algebraic property testing: the role of invariance
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
Lower bounds for testing triangle-freeness in Boolean functions
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
Invariance in property testing
Property testing
Testing linear-invariant non-linear properties: a short report
Property testing
Green's conjecture and testing linear invariant properties
Property testing
Invariance in property testing
Property testing
Testing linear-invariant non-linear properties: a short report
Property testing
Green's conjecture and testing linear invariant properties
Property testing
Testing odd-cycle-freeness in Boolean functions
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
SIAM Journal on Discrete Mathematics
Every locally characterized affine-invariant property is testable
Proceedings of the forty-fifth annual ACM symposium on Theory of computing
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Given a set of linear equations Mx=b, we say that a set of integers S is (M,b)-free if it contains no solution to this system of equations. Motivated by questions related to testing linear-invariant properties of boolean functions, as well as recent investigations in additive number theory, the following conjecture was raised (implicitly) by Green and by Bhattacharyya, Chen, Sudan and Xie: we say that a set of integers S ⊆ [n], is ε-far from being (M,b)-free if one needs to remove at least ε n elements from S in order to make it (M,b)-free. The above conjecture states that for any system of homogenous linear equations Mx=0 and for any ε 0 there is a constant time algorithm that can distinguish with high probability between sets of integers that are (M,0)-free from sets that are ε-far from being (M,0)-free. Or in other words, that for any M there is an efficient testing algorithm for the property of being (M,0)-free. In this paper we confirm the above conjecture by showing that such a testing algorithm exists even for non-homogenous linear equations. As opposed to most results on testing boolean functions, which rely on algebraic and analytic arguments, our proof relies on results from extremal hypergraph theory, such as the recent removal lemmas of Gowers, Rodl et al. and Austin and Tao.