Given a set of discrete probability distributions, the minimum entropy coupling is the
minimum entropy joint distribution that has the input distributions as its marginals. This has …

Abstract The Sum of Square Roots (SSR) problem is the following computational problem:
Given positive integers a 1,…, ak, and signs δ1,…, δ k∈{-1, 1}, check if. The problem is …

We study the problem of generating the monomials of a black box polynomial in the context
of enumeration complexity. We present three new randomized algorithms for restricted …

This paper focuses on the study of the order of power series that are linear combinations of a
given finite set of power series. The order of a formal power series, known as, is defined as …

A set of multivariate polynomials, over a field of zero or large characteristic, can be tested for
algebraic independence by the well-known Jacobian criterion. For fields of other …

We present improved uniform TC 0 circuits for division, matrix powering, and related
problems, where the improvement is in terms of “majority depth”(as studied by Maciel and …

This thesis examines the concepts of linear and algebraic independence in algebraic
complexity theory. Arithmetic circuits, computing multivariate polynomials over a field, form …

We investigate the complexity of languages that correspond to algebraic real numbers, and
we present improved upper bounds on the complexity of these languages. Our key technical …

We study the Radical Identity Testing problem (RIT): Given an algebraic circuit representing
a polynomial and nonnegative integers a1,…, ak and d1,…, dk, written in binary, test …

In this paper, we consider the problem of finding how close two sums of mth roots can be to
each other. For integers m≥ 2, k≥ 1 and 0≤ s≤ k, let em (s, k)> 0 and E m (s, k)> 0 be the …