Green's conjecture and testing linear-invariant properties
Proceedings of the forty-first annual ACM symposium on Theory of computing
Finding maximum degrees in hidden bipartite graphs
Proceedings of the 2010 ACM SIGMOD International Conference on Management of data
Local graph exploration and fast property testing
ESA'10 Proceedings of the 18th annual European conference on Algorithms: Part I
Testing expansion in bounded-degree graphs
Combinatorics, Probability and Computing
Local Monotonicity Reconstruction
SIAM Journal on Computing
Property testing
Sublinear graph approximation algorithms
Property testing
Local property reconstruction and monotonicity
Property testing
Property testing
Sublinear graph approximation algorithms
Property testing
Local property reconstruction and monotonicity
Property testing
Testing permutation properties through subpermutations
Theoretical Computer Science
Inflatable graph properties and natural property tests
APPROX'11/RANDOM'11 Proceedings of the 14th international workshop and 15th international conference on Approximation, randomization, and combinatorial optimization: algorithms and techniques
Testing Eulerianity and connectivity in directed sparse graphs
Theoretical Computer Science
An Expansion Tester for Bounded Degree Graphs
SIAM Journal on Computing
Testing Fourier Dimensionality and Sparsity
SIAM Journal on Computing
Testing odd-cycle-freeness in Boolean functions
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
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
Untestable properties expressible with four first-order quantifiers
LATA'10 Proceedings of the 4th international conference on Language and Automata Theory and Applications
Exact and approximate algorithms for the most connected vertex problem
ACM Transactions on Database Systems (TODS)
Testable and untestable classes of first-order formulae
Journal of Computer and System Sciences
SIAM Journal on Discrete Mathematics
A note on permutation regularity
Discrete Applied Mathematics
Limits of permutation sequences
Journal of Combinatorial Theory Series B
Every locally characterized affine-invariant property is testable
Proceedings of the forty-fifth annual ACM symposium on Theory of computing
An algebraic characterization of testable boolean CSPs
ICALP'13 Proceedings of the 40th international conference on Automata, Languages, and Programming - Volume Part I
Proceedings of the 5th conference on Innovations in theoretical computer science
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The problem of characterizing all the testable graph properties is considered by many to be the most important open problem in the area of property testing. Our main result in this paper is a solution of an important special case of this general problem: Call a property tester oblivious if its decisions are independent of the size of the input graph. We show that a graph property ${\cal P}$ has an oblivious one-sided error tester if and only if ${\cal P}$ is semihereditary. We stress that any “natural” property that can be tested (either with one-sided or with two-sided error) can be tested by an oblivious tester. In particular, all the testers studied thus far in the literature were oblivious. Our main result can thus be considered as a precise characterization of the natural graph properties, which are testable with one-sided error. One of the main technical contributions of this paper is in showing that any hereditary graph property can be tested with one-sided error. This general result contains as a special case all the previous results about testing graph properties with one-sided error. More importantly, as a special case of our main result, we infer that some of the most well-studied graph properties, both in graph theory and computer science, are testable with one-sided error. Some of these properties are the well-known graph properties of being perfect, chordal, interval, comparability, permutation, and more. None of these properties was previously known to be testable.