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- W2953008500 abstract "Let $mathcal{P}$ be a property of function $mathbb{F}_p^n to {0,1}$ for a fixed prime $p$. An algorithm is called a tester for $mathcal{P}$ if, given a query access to the input function $f$, with high probability, it accepts when $f$ satisfies $mathcal{P}$ and rejects when $f$ is far from satisfying $mathcal{P}$. In this paper, we give a characterization of affine-invariant properties that are (two-sided error) testable with a constant number of queries. The characterization is stated in terms of decomposition theorems, which roughly claim that any function can be decomposed into a structured part that is a function of a constant number of polynomials, and a pseudo-random part whose Gowers norm is small. We first give an algorithm that tests whether the structured part of the input function has a specific form. Then we show that an affine-invariant property is testable with a constant number of queries if and only if it can be reduced to the problem of testing whether the structured part of the input function is close to one of a constant number of candidates." @default.
- W2953008500 created "2019-06-27" @default.
- W2953008500 creator A5038701345 @default.
- W2953008500 date "2014-02-10" @default.
- W2953008500 modified "2023-09-26" @default.
- W2953008500 title "A Characterization of Locally Testable Affine-Invariant Properties via Decomposition Theorems" @default.
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- W2953008500 doi "https://doi.org/10.48550/arxiv.1402.2175" @default.
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