Research
Research
Research
Research
20+ open-access research outputs.
This paper presents a novel AI-powered framework designed to streamline database management and query optimization for PostgreSQL systems. Structured in three phases: Natural Language to SQL Translati…
A major open problem in proof complexity is to demonstrate that random 3-CNFs with a linear number of clauses require super-polynomial size refutations in bounded-depth Frege systems. We take the firs…
For fixed integers $b\geq k$, the problem of perfect $(b,k)$-hashing asks for the asymptotic growth of largest subsets of $\{1,2,\ldots,b\}^n$ such that for any $k$ distinct elements in the set, there…
We prove a direct product theorem for the one-way entanglement-assisted quantum communication complexity of a general relation $f\subseteq\mathcal{X}\times\mathcal{Y}\times\mathcal{Z}$. For any $\vare…
In this paper, we look into the adaptive bitprobe model that stores subsets of size at most four from a universe of size m, and answers membership queries using two bitprobes. We propose a scheme that…
We are studying the adaptive bitprobe model to store an arbitrary subset S of size at most five from a universe U of size m and answer the membership queries of the form "Is x in S?" in two bitprobes.…
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…
We consider the non-adaptive bit-probe complexity of the set membership problem, where a set S of size at most n from a universe of size m is to be represented as a short bit vector in order to answer…
We consider space-efficient algorithms for two-coloring $n$-uniform hypergraphs $H=(V,E)$ in the streaming model, when the hyperedges arrive one at a time. It is known that any such hypergraph with at…
We prove a near optimal round-communication tradeoff for the two-party quantum communication complexity of disjointness. For protocols with $r$ rounds, we prove a lower bound of $\tilde{\Omega}(n/r + …
We continue the study of communication cost of computing functions when inputs are distributed among $k$ processors, each of which is located at one vertex of a network/graph called a terminal. Every …
We consider the bit-probe complexity of the set membership problem, where a set S of size at most n from a universe of size m is to be represented as a short bit vector in order to answer membership q…
We present a technique of proving lower bounds for noisy computations. This is achieved by a theorem connecting computations on a kind of randomized decision trees and sampling based algorithms. This …
We show a tight lower bound of $\Omega(N \log\log N)$ on the number of transmissions required to compute the parity of $N$ input bits with constant error in a noisy communication network of $N$ random…
This article focuses on an important piece of work of the world renowned Indian statistician, Calyampudi Radhakrishna Rao. In 1945, C. R. Rao (25 years old then) published a pathbreaking paper, which …
A fundamental ambition of grid and distributed systems is to be capable of sustaining evolution and allowing for adaptability ((F. Losavio et al., 2002), (S. Radhakrishnan, 2005)). Furthermore, as the…
We study probabilistic bit-probe schemes for the membership problem. Given a set A of at most n elements from the universe of size m we organize such a structure that queries of type "Is x in A?" can …
In this paper, we present near-optimal space bounds for Lp-samplers. Given a stream of updates (additions and subtraction) to the coordinates of an underlying vector x \in R^n, a perfect Lp sampler ou…
Weighted automata are nondeterministic automata with numerical weights on transitions. They can define quantitative languages~$L$ that assign to each word~$w$ a real number~$L(w)$. In the case of infi…
This paper makes three main contributions to the theory of communication complexity and stream computation. First, we present new bounds on the information complexity of AUGMENTED-INDEX. In contrast t…
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