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arXiv · 1010.4925

Property Testing via Set-Theoretic Operations

Victor Chen·Madhu Sudan·Ning Xie
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Abstract

Given two testable properties $\mathcal{P}_{1}$ and $\mathcal{P}_{2}$, under what conditions are the union, intersection or set-difference of these two properties also testable? We initiate a systematic study of these basic set-theoretic operations in the context of property testing. As an application, we give a conceptually different proof that linearity is testable, albeit with much worse query complexity. Furthermore, for the problem of testing disjunction of linear functions, which was previously known to be one-sided testable with a super-polynomial query complexity, we give an improved analysis and show it has query complexity $O(1/\eps^2)$, where $\eps$ is the distance parameter.

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Victor Chen, Madhu Sudan, Ning Xie. 2010-10-24. Property Testing via Set-Theoretic Operations. https://arxiv.org/abs/1010.4925

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