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Electronic Colloquium on Computational Complexity

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Reports tagged with direct sum theorems:
TR13-067 | 2nd May 2013
Oded Goldreich

On Multiple Input Problems in Property Testing

Revisions: 1

We consider three types of multiple input problems in the context of property testing.
Specifically, for a property $\Pi\subseteq\{0,1\}^n$, a proximity parameter $\epsilon$, and an integer $m$, we consider the following problems:

\item Direct $m$-Sum Problem for $\Pi$ and $\epsilon$:
Given a sequence of $m$ inputs, output a sequence ... more >>>

TR20-124 | 3rd August 2020
Joshua Brody, JaeTak Kim, Peem Lerdputtipongporn, Hariharan Srinivasulu

A Strong XOR Lemma for Randomized Query Complexity

We give a strong direct sum theorem for computing $XOR \circ g$. Specifically, we show that the randomized query complexity of computing the XOR of $k$ instances of $g$ satisfies $\bar{R}_\varepsilon(XOR \circ g)=\Theta(\bar{R}_{\varepsilon/k}(g))$. This matches the naive success amplification bound and answers a question of Blais and Brody.

As a ... more >>>

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