Testing Fourier Dimensionality and Sparsity
ICALP '09 Proceedings of the 36th International Colloquium on Automata, Languages and Programming: Part I
Lower bounds for testing triangle-freeness in Boolean functions
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
Local Monotonicity Reconstruction
SIAM Journal on Computing
Testing linear-invariant non-linear properties: a short report
Property testing
Local property reconstruction and monotonicity
Property testing
Testing linear-invariant non-linear properties: a short report
Property testing
Local property reconstruction and monotonicity
Property testing
Online geometric reconstruction
Journal of the ACM (JACM)
Testing Fourier Dimensionality and Sparsity
SIAM Journal on Computing
A note on the testability of ramsey's class
TAMC'10 Proceedings of the 7th annual conference on Theory and Applications of Models of Computation
Testable and untestable classes of first-order formulae
Journal of Computer and System Sciences
SIAM Journal on Discrete Mathematics
On the removal lemma for linear systems over Abelian groups
European Journal of Combinatorics
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Recent works of Alon–Shapira (A characterization of the (natural) graph properties testable with one-sided error. Available at: ) and Rödl–Schacht (Generalizations of the removal lemma, Available at: ) have demonstrated that every hereditary property of undirected graphs or hypergraphs is testable with one-sided error; informally, this means that if a graph or hypergraph satisfies that property “locally” with sufficiently high probability, then it can be perturbed (or “repaired”) into a graph or hypergraph which satisfies that property “globally.” In this paper we make some refinements to these results, some of which may be surprising. In the positive direction, we strengthen the results to cover hereditary properties of multiple directed polychromatic graphs and hypergraphs. In the case of undirected graphs, we extend the result to continuous graphs on probability spaces and show that the repair algorithm is “local” in the sense that it only depends on a bounded amount of data; in particular, the graph can be repaired in a time linear in the number of edges. We also show that local repairability also holds for monotone or partite hypergraph properties (this latter result is also implicitly in (Ishigamis work Removal lemma for infinitely-many forbidden hypergraphs and property testing. Available at: arXiv.org: math.CO-0612669)). In the negative direction, we show that local repairability breaks down for directed graphs or for undirected 3-uniform hypergraphs. The reason for this contrast in behavior stems from (the limitations of) Ramsey theory. © 2010 Wiley Periodicals, Inc. Random Struct. Alg., 2010