Let {fiβ:Fpiββ{0,1}} be a sequence of functions, where
p is a fixed prime and Fpβ 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 characterization of affine-invariant parameters of
functions that are constant-query estimable. 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.Comment: arXiv admin note: text overlap with arXiv:1212.3849, arXiv:1308.4108
by other author