All reports by Author Swagato Sanyal:

__
TR18-014
| 10th January 2018
__

Swagato Sanyal#### A Composition Theorem via Conflict Complexity

__
TR17-152
| 9th October 2017
__

Swagato Sanyal#### One-way Communication and Non-adaptive Decision Tree

Comments: 1

__
TR17-123
| 2nd August 2017
__

Dmitry Gavinsky, Rahul Jain, Hartmut Klauck, Srijita Kundu, Troy Lee, Miklos Santha, Swagato Sanyal, Jevgenijs Vihrovs#### Quadratically Tight Relations for Randomized Query Complexity

__
TR17-107
| 1st June 2017
__

Anurag Anshu, Dmitry Gavinsky, Rahul Jain, Srijita Kundu, Troy Lee, Priyanka Mukhopadhyay, Miklos Santha, Swagato Sanyal#### A Composition Theorem for Randomized Query complexity

Revisions: 1

__
TR16-103
| 6th July 2016
__

Jaikumar Radhakrishnan, Swagato Sanyal#### The zero-error randomized query complexity of the pointer function.

__
TR15-107
| 21st June 2015
__

Sagnik Mukhopadhyay, Swagato Sanyal#### Towards Better Separation between Deterministic and Randomized Query Complexity

__
TR14-088
| 13th July 2014
__

Swagato Sanyal#### Sub-linear Upper Bounds on Fourier dimension of Boolean Functions in terms of Fourier sparsity

Revisions: 1
,
Comments: 1

Swagato Sanyal

Let $\R(\cdot)$ stand for the bounded-error randomized query complexity. We show that for any relation $f \subseteq \{0,1\}^n \times \mathcal{S}$ and partial Boolean function $g \subseteq \{0,1\}^n \times \{0,1\}$, $\R_{1/3}(f \circ g^n) = \Omega(\R_{4/9}(f) \cdot \sqrt{\R_{1/3}(g)})$. Independently of us, Gavinsky, Lee and Santha \cite{newcomp} proved this result. By an example ... more >>>

Swagato Sanyal

Let $f$ be a Boolean function on $n$-bits, and $\mathsf{IP}$ the inner-product function on $2b$ bits. Let $f^{\mathsf{IP}}:=f \circ \mathsf{IP}^n$ be the two party function obtained by composing $f$ with $\mathsf{IP}$. In this work we bound the one-way communication complexity of $f^{\IP}$ in terms of the non-adaptive query complexity of ... more >>>

Dmitry Gavinsky, Rahul Jain, Hartmut Klauck, Srijita Kundu, Troy Lee, Miklos Santha, Swagato Sanyal, Jevgenijs Vihrovs

Let $f:\{0,1\}^n \rightarrow \{0,1\}$ be a Boolean function. The certificate complexity $C(f)$ is a complexity measure that is quadratically tight for the zero-error randomized query complexity $R_0(f)$: $C(f) \leq R_0(f) \leq C(f)^2$. In this paper we study a new complexity measure that we call expectational certificate complexity $EC(f)$, which is ... more >>>

Anurag Anshu, Dmitry 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 >>>

Jaikumar Radhakrishnan, Swagato Sanyal

The pointer function of G{\"{o}}{\"{o}}s, Pitassi and Watson

\cite{DBLP:journals/eccc/GoosP015a} and its variants have recently

been used to prove separation results among various measures of

complexity such as deterministic, randomized and quantum query

complexities, exact and approximate polynomial degrees, etc. In

particular, the widest possible (quadratic) separations between

deterministic and zero-error ...
more >>>

Sagnik Mukhopadhyay, Swagato Sanyal

We show that there exists a Boolean function $F$ which observes the following separations among deterministic query complexity $(D(F))$, randomized zero error query complexity $(R_0(F))$

and randomized one-sided error query complexity $(R_1(F))$: $R_1(F) = \widetilde{O}(\sqrt{D(F)})$ and $R_0(F)=\widetilde{O}(D(F))^{3/4}$. This refutes the conjecture made by

Saks and Wigderson that for any Boolean ...
more >>>

Swagato Sanyal

We prove that the Fourier dimension of any Boolean function with

Fourier sparsity $s$ is at most $O\left(s^{2/3}\right)$. Our proof

method yields an improved bound of $\widetilde{O}(\sqrt{s})$

assuming a conjecture of Tsang~\etal~\cite{tsang}, that for every

Boolean function of sparsity $s$ there is an affine subspace of

more >>>