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Electronic Colloquium on Computational Complexity

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TR10-116 | 21st July 2010 02:00

Testing linear-invariant non-linear properties: A short report


Authors: Arnab Bhattacharyya, Victor Chen, Madhu Sudan, Ning Xie
Publication: 21st July 2010 02:03
Downloads: 1451


The rich collection of successes in property testing raises a natural question: Why are so many different properties turning out to be locally testable? Are there some broad "features" of properties that make them testable? Kaufman and Sudan (STOC 2008) proposed the study of the relationship between the invariances satisfied by a property and its testability. Particularly, they studied properties that were invariant under linear transformations of the domain and gave a characterization of testability in certain settings. However, the properties that they examined were also linear. This led us to investigate
linear-invariant properties that are not necessarily linear. Here we describe some of the resulting works which consider natural linear-invariant properties, specifically properties that are described by forbidden patterns of values that a function can take,
and show testability under various settings.

ISSN 1433-8092 | Imprint