All reports by Author Priyanka Mukhopadhyay:

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TR17-107
| 1st June 2017
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Anurag Anshu, Dmytro Gavinsky, Rahul Jain, Srijita Kundu, Troy Lee, Priyanka Mukhopadhyay, Miklos Santha, Swagato Sanyal#### A Composition Theorem for Randomized Query complexity

Revisions: 1

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TR17-054
| 22nd March 2017
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Anurag Anshu, Naresh Goud, Rahul Jain, Srijita Kundu, Priyanka Mukhopadhyay#### Lifting randomized query complexity to randomized communication complexity

Revisions: 4

Anurag Anshu, Dmytro Gavinsky, Rahul Jain, Srijita Kundu, Troy Lee, Priyanka Mukhopadhyay, Miklos Santha, Swagato Sanyal

Let the randomized query complexity of a relation for error probability $\epsilon$ be denoted by $\R_\epsilon(\cdot)$. We prove that for any relation $f \subseteq \{0,1\}^n \times \mathcal{R}$ and Boolean function $g:\{0,1\}^m \rightarrow \{0,1\}$, $\R_{1/3}(f\circ g^n) = \Omega(\R_{4/9}(f)\cdot\R_{1/2-1/n^4}(g))$, where $f \circ g^n$ is the relation obtained by composing $f$ and $g$. ... more >>>

Anurag Anshu, Naresh Goud, Rahul Jain, Srijita Kundu, Priyanka Mukhopadhyay

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 >>>