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Electronic Colloquium on Computational Complexity

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Reports tagged with Element Distinctness Problem:
TR95-063 | 19th December 1995
Dima Grigoriev, Marek Karpinski, Friedhelm Meyer auf der Heide, Roman Smolensky

A Lower Bound for Randomized Algebraic Decision Trees

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 ... more >>>

TR18-010 | 14th January 2018
Alexander A. Sherstov

Algorithmic polynomials

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 >>>

ISSN 1433-8092 | Imprint