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
Free Bits, PCPs, and Nonapproximability---Towards Tight Results
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A combinatorial characterization of the testable graph properties: it's all about regularity
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On the Query Complexity of Testing Orientations for Being Eulerian
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Foundations and Trends® in Machine Learning
On proximity oblivious testing
Proceedings of the forty-first annual ACM symposium on Theory of computing
Algorithmic and Analysis Techniques in Property Testing
Foundations and Trends® in Theoretical Computer Science
Proximity oblivious testing and the role of invariances
APPROX'11/RANDOM'11 Proceedings of the 14th international workshop and 15th international conference on Approximation, randomization, and combinatorial optimization: algorithms and techniques
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We present a general notion of properties that are characterized by local conditions that are invariant under a sufficiently rich class of symmetries. Our framework generalizes two popular models of testing graph properties as well as the algebraic invariances studied by Kaufman and Sudan (STOC'08). Our focus is on the case that the property is characterized by a constant number of local conditions and a rich set of invariances. We show that, in the aforementioned models of testing graph properties, characterization by such invariant local conditions is closely related to proximity oblivious testing (as defined by Goldreich and Ron, STOC'09). In contrast to this relation, we show that, in general, characterization by invariant local conditions is neither necessary nor sufficient for proximity oblivious testing. Furthermore, we show that easy testability is not guaranteed even when the property is characterized by local conditions that are invariant under a 1-transitive group of permutations.