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- W2963721000 abstract "Let {fi: Fip → {0, 1}} be a sequence of functions, where p is a fixed prime and Fp is the finite field of order p. The limit of the sequence can be syntactically defined using the notion of ultralimit. Inspired by the Gowers norm, we introduce a metric over limits of function sequences, and study properties of it. One application of this metric is that it provides a simpler characterization of affine-invariant parameters of functions that are constant-query estimable than the previous one obtained by Yoshida (STOC'14). Using this characterization, we show that the property of being a function of a constant number of low-degree polynomials and a constant number of factored polynomials (of arbitrary degrees) is constant-query testable if it is closed under blowing-up. Examples of this property include the property of having a constant spectral norm and degree-structural properties with rank conditions." @default.
- W2963721000 created "2019-07-30" @default.
- W2963721000 creator A5038701345 @default.
- W2963721000 date "2016-01-10" @default.
- W2963721000 modified "2023-09-23" @default.
- W2963721000 title "Gowers norm, function limits, and parameter estimation" @default.
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- W2963721000 doi "https://doi.org/10.5555/2884435.2884531" @default.
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