All reports by Author Sourav Chakraborty:

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TR13-052
| 3rd April 2013
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Sourav Chakraborty, Raghav Kulkarni, Satyanarayana V. Lokam, Nitin Saurabh#### {Upper Bounds on Fourier Entropy

Revisions: 2

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TR10-093
| 3rd June 2010
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Sourav Chakraborty, David García Soriano, Arie Matsliah#### Nearly Tight Bounds for Testing Function Isomorphism

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TR10-067
| 14th April 2010
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Sourav Chakraborty, Eldar Fischer, Arie Matsliah#### Query Complexity Lower Bounds for Reconstruction of Codes

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TR10-048
| 24th March 2010
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David García Soriano, Arie Matsliah, Sourav Chakraborty, Jop Briet#### Monotonicity Testing and Shortest-Path Routing on the Cube

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TR08-040
| 3rd April 2008
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Sourav Chakraborty, Laszlo Babai#### Property Testing of Equivalence under a Permutation Group Action

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TR05-020
| 22nd November 2004
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Sourav Chakraborty#### On the Sensitivity of Cyclically-Invariant Boolean Functions

Sourav Chakraborty, Raghav Kulkarni, Satyanarayana V. Lokam, Nitin Saurabh

iven a function $f : \{0,1\}^n \to \reals$, its {\em Fourier Entropy} is defined to be $-\sum_S \fcsq{f}{S} \log \fcsq{f}{S}$, where $\fhat$ denotes the Fourier transform of $f$. This quantity arises in a number of applications, especially in the study of Boolean functions. An outstanding open question is a conjecture ... more >>>

Sourav Chakraborty, David García Soriano, Arie Matsliah

In this paper we study the problem of testing structural equivalence (isomorphism) between a pair of Boolean

functions $f,g:\zo^n \to \zo$. Our main focus is on the most studied case, where one of the functions is given (explicitly), and the other function can be queried.

We prove that for every ... more >>>

Sourav Chakraborty, Eldar Fischer, Arie Matsliah

We investigate the problem of {\em local reconstruction}, as defined by Saks and Seshadhri (2008), in the context of error correcting codes.

The first problem we address is that of {\em message reconstruction}, where given oracle access to a corrupted encoding $w \in \zo^n$ of some message $x \in \zo^k$ ... more >>>

David García Soriano, Arie Matsliah, Sourav Chakraborty, Jop Briet

We study the problem of monotonicity testing over the hypercube. As

previously observed in several works, a positive answer to a natural question about routing

properties of the hypercube network would imply the existence of efficient

monotonicity testers. In particular, if any $\ell$ disjoint source-sink pairs

on the directed hypercube ...
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Sourav Chakraborty, Laszlo Babai

For a permutation group $G$ acting on the set $\Omega$

we say that two strings $x,y\,:\,\Omega\to\boole$

are {\em $G$-isomorphic} if they are equivalent under

the action of $G$, \ie, if for some $\pi\in G$ we have

$x(i^{\pi})=y(i)$ for all $i\in\Omega$.

Cyclic Shift, Graph Isomorphism ...
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Sourav Chakraborty

In this paper we construct a cyclically invariant Boolean function

whose sensitivity is $\Theta(n^{1/3})$. This result answers two

previously published questions. Tur\'an (1984) asked if any

Boolean function, invariant under some transitive group of

permutations, has sensitivity $\Omega(\sqrt{n})$. Kenyon and Kutin

(2004) asked whether for a ``nice'' function the product ...
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