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## §8.6: Highlight: Randomized decision tree complexity

A decision tree $T$ for $f : \{-1,1\}^n \to \{-1,1\}$ can be thought of as a deterministic algorithm which, given adaptive query access to the bits of an unknown string $x \in \{-1,1\}^n$, outputs $f(x)$. E.g., to describe a natural decision tree for $f = \mathrm{Maj}_3$ in words: “Query $x_1$, then $x_2$. If they [...]

## Chapter 7 notes

The study of property testing was initiated by Rubinfeld and Sudan [RS96] and significantly expanded by Goldreich, Goldwasser, and Ron [GGR98]; the stricter notion of local testability was introduced (in the context of error-correcting codes) by Friedl and Sudan [FS95]. The first local tester for dictatorship was given by Bellare, Goldreich, and Sudan [BGS95,BGS98] (as [...]