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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

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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