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)
Robust Characterizations of Polynomials withApplications to Program Testing
SIAM Journal on Computing
Extremal problems on set systems
Random Structures & Algorithms
Testing subgraphs in directed graphs
Journal of Computer and System Sciences - Special issue: STOC 2003
Regularity lemma for k-uniform hypergraphs
Random Structures & Algorithms
Quasirandomness, Counting and Regularity for 3-Uniform Hypergraphs
Combinatorics, Probability and Computing
The counting lemma for regular k-uniform hypergraphs
Random Structures & Algorithms
A variant of the hypergraph removal lemma
Journal of Combinatorial Theory Series A
Green's conjecture and testing linear-invariant properties
Proceedings of the forty-first annual ACM symposium on Theory of computing
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A system of l linear equations in p unknowns M x = b is said to have the removal property if every set S ⊆ {1, . . . , n} which contains o(np-l) solutions of M x = b can be turned into a set S′ containing no solution of M x = b, by the removal of o(n) elements. Green [GAFA 2005] proved that a single homogenous linear equation always has the removal property, and conjectured that every set of homogenous linear equations has the removal property. In this paper we confirm Green's conjecture by showing that every set of linear equations (even non-homogenous) has the removal property. We also discuss some applications of our result in theoretical computer science, and in particular, use it to resolve a conjecture of Bhattacharyya, Chen, Sudan and Xie [4] related to algorithms for testing properties of boolean functions.