All reports by Author Swagato Sanyal:

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TR22-135
| 18th September 2022
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Rahul Chugh, Supartha Poddar, Swagato Sanyal#### Decision Tree Complexity versus Block Sensitivity and Degree

Comments: 1

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TR21-065
| 5th May 2021
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Nikhil Mande, Swagato Sanyal#### One-way communication complexity and non-adaptive decision trees

Revisions: 1

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TR20-119
| 1st August 2020
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Nikhil Mande, Swagato Sanyal#### On parity decision trees for Fourier-sparse Boolean functions

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TR18-014
| 10th January 2018
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Swagato Sanyal#### A Composition Theorem via Conflict Complexity

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TR17-152
| 9th October 2017
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Swagato Sanyal#### One-way Communication and Non-adaptive Decision Tree

Comments: 1

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TR17-123
| 2nd August 2017
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Dmytro Gavinsky, Rahul Jain, Hartmut Klauck, Srijita Kundu, Troy Lee, Miklos Santha, Swagato Sanyal, Jevgenijs Vihrovs#### Quadratically Tight Relations for Randomized Query Complexity

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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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TR16-103
| 6th July 2016
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Jaikumar Radhakrishnan, Swagato Sanyal#### The zero-error randomized query complexity of the pointer function.

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TR15-107
| 21st June 2015
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Sagnik Mukhopadhyay, Swagato Sanyal#### Towards Better Separation between Deterministic and Randomized Query Complexity

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TR14-088
| 13th July 2014
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Swagato Sanyal#### Sub-linear Upper Bounds on Fourier dimension of Boolean Functions in terms of Fourier sparsity

Revisions: 1
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Comments: 1

Rahul Chugh, Supartha Poddar, Swagato Sanyal

Relations between the decision tree complexity and various other complexity measures of Boolean functions is a thriving topic of research in computational complexity. While decision tree complexity is long known to be polynomially related with many other measures, the optimal exponents of many of these relations are not known. It ... more >>>

Nikhil Mande, Swagato Sanyal

We study the relationship between various one-way communication complexity measures of a composed function with the analogous decision tree complexity of the outer function. We consider two gadgets: the AND function on 2 inputs, and the Inner Product on a constant number of inputs. Let $IP$ denote Inner Product on ... more >>>

Nikhil Mande, Swagato Sanyal

We study parity decision trees for Boolean functions. The motivation of our study is the log-rank conjecture for XOR functions and its connection to Fourier analysis and parity decision tree complexity. Our contributions are as follows. Let $f : \mathbb{F}_2^n \to \{-1, 1\}$ be a Boolean function with Fourier support ... more >>>

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 >>>

Dmytro 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, 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 >>>

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 >>>