Dima Grigoriev, Marek Karpinski, Friedhelm Meyer auf der Heide, Roman Smolensky

We extend the lower bounds on the depth of algebraic decision trees

to the case of {\em randomized} algebraic decision trees (with

two-sided error) for languages being finite unions of hyperplanes

and the intersections of halfspaces, solving a long standing open

problem. As an application, among ...
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Alexander A. Sherstov

The approximate degree of a Boolean function $f(x_{1},x_{2},\ldots,x_{n})$ is the minimum degree of a real polynomial that approximates $f$ pointwise within $1/3$. Upper bounds on approximate degree have a variety of applications in learning theory, differential privacy, and algorithm design in general. Nearly all known upper bounds on approximate degree ... more >>>