We introduce the notion of a Canonical Tester for a class of properties, that is, a tester strong and
general enough that ``a property is testable if and only if the
Canonical Tester tests it''. We construct a Canonical Tester
for the class of symmetric properties of one or two
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Estimating the second frequency moment of a stream up to $(1\pm\varepsilon)$ multiplicative error requires at most $O(\log n / \varepsilon^2)$ bits of space, due to a seminal result of Alon, Matias, and Szegedy. It is also known that at least $\Omega(\log n + 1/\varepsilon^{2})$ space is needed.
We prove an ... more >>>