Self-testing/correcting with applications to numerical problems
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Property testing and its connection to learning and approximation
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Regular Languages are Testable with a Constant Number of Queries
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A characterization of easily testable induced subgraphs
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Property testing in hypergraphs and the removal lemma
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Every minor-closed property of sparse graphs is testable
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
The maximum edit distance from hereditary graph properties
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APPROX '07/RANDOM '07 Proceedings of the 10th International Workshop on Approximation and the 11th International Workshop on Randomization, and Combinatorial Optimization. Algorithms and Techniques
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Foundations and Trends® in Machine Learning
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ICALP '09 Proceedings of the 36th International Colloquium on Automata, Languages and Programming: Part I
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Foundations and Trends® in Theoretical Computer Science
Indistinguishability and first-order logic
TAMC'08 Proceedings of the 5th international conference on Theory and applications of models of computation
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Lower bounds for testing triangle-freeness in Boolean functions
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Introduction to testing graph properties
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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 P has an oblivious one-sided error tester, if and only if P is (semi) hereditary. 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. These include the results of [17] and [5] about testing k-colorability, the characterization of [18] of the graph-partition problems that are testable with 1-sided error, the induced vertex colorability properties of [3], the induced edge colorability properties of [13], a transformation from 2-sided to 1-sided error testing [18], as well as a recent result about testing monotone graph properties [10]. 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 and more. None of these properties was previously known to be testable.