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Electronic Colloquium on Computational Complexity

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Reports tagged with randomized query complexity:
TR11-033 | 8th March 2011
Rahul Jain, Shengyu Zhang

The influence lower bound via query elimination

We give a simpler proof, via query elimination, of a result due to O'Donnell, Saks, Schramm and Servedio, which shows a lower bound on the zero-error randomized query complexity of a function $f$ in terms of the maximum influence of any variable of $f$. Our lower bound also applies to ... more >>>

TR17-054 | 22nd March 2017
Anurag Anshu, Naresh Goud, Rahul Jain, Srijita Kundu, Priyanka Mukhopadhyay

Lifting randomized query complexity to randomized communication complexity

Revisions: 4

We show that for any (partial) query function $f:\{0,1\}^n\rightarrow \{0,1\}$, the randomized communication complexity of $f$ composed with $\mathrm{Index}^n_m$ (with $m= \poly(n)$) is at least the randomized query complexity of $f$ times $\log n$. Here $\mathrm{Index}_m : [m] \times \{0,1\}^m \rightarrow \{0,1\}$ is defined as $\mathrm{Index}_m(x,y)= y_x$ (the $x$th bit ... more >>>

TR17-150 | 26th September 2017
Andris Ambainis, Martins Kokainis, Krisjanis Prusis, Jevgenijs Vihrovs

All Classical Adversary Methods are Equivalent for Total Functions

Revisions: 2

We show that all known classical adversary lower bounds on randomized query complexity are equivalent for total functions, and are equal to the fractional block sensitivity $\text{fbs}(f)$. That includes the Kolmogorov complexity bound of Laplante and Magniez and the earlier relational adversary bound of Aaronson. For partial functions, we show ... more >>>

TR20-128 | 3rd September 2020
Alexander A. Sherstov, Andrey Storozhenko, Pei Wu

An Optimal Separation of Randomized and Quantum Query Complexity

Revisions: 1

We prove that for every decision tree, the absolute values of the Fourier coefficients of given order $\ell\geq1$ sum to at most $c^{\ell}\sqrt{{d\choose\ell}(1+\log n)^{\ell-1}},$ where $n$ is the number of variables, $d$ is the tree depth, and $c>0$ is an absolute constant. This bound is essentially tight and settles a ... more >>>

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