相关论文: New coins from old, smoothly

We study the power of classical and quantum algorithms equipped with nonuniform advice, in the form of a coin whose bias encodes useful information. This question takes on particular importance in the quantum case, due to a surprising…

We consider the probability distributions of values in the complex plane attained by Fourier sums of the form \sum_{j=1}^n a_j exp(-2\pi i j nu) /sqrt{n} when the frequency nu is drawn uniformly at random from an interval of length 1. If…

Coin-flipping is a cryptographic task in which two physically separated, mistrustful parties wish to generate a fair coin-flip by communicating with each other. Chailloux and Kerenidis (2009) designed quantum protocols that guarantee…

HMC sets are hereditarily at most countable sets. We rework a substantial part of univariate real analysis in a form in which only HMC real functions are used. In such countable real analysis we carry out Hilbert's proof of transcendence of…

An algorithm is presented that, taking a sequence of independent Bernoulli random variables with parameter $1/2$ as inputs and using only rational arithmetic, simulates a Bernoulli random variable with possibly irrational parameter $\tau$.…

Consider a real algebraic curve with set of real points $R\neq\emptyset$ and complexification $P\supset R$. Let $f$ be an algebraic function on $P$ with devisor of critical points $D\subset P$. We prove that $f$ is real after a…

Let $f(n)$ be a Steinhaus random multiplicative function. Let $A\subset [1, N]$ be a finite set of integers. We show that \[\frac{1}{\sqrt{|A|}} \sum_{n\in A} f(n) \xrightarrow[]{d} \mathcal{CN}(0,1)\] forces that $|A|=o(N)$. We prove that…

We present a new generalization of the bin covering problem that is known to be a strongly NP-hard problem. In our generalization there is a positive constant $\Delta$, and we are given a set of items each of which has a positive size. We…

The algebraic degree is an important parameter of Boolean functions used in cryptography. When a function in a large number of variables is not given explicitly in algebraic normal form, it might not be feasible to compute its degree.…

In this work, we establish a nontrivial level of distribution for densities on $\{1,\ldots, N\}$ obtained by a biased coin convolution. As a consequence of sieving theory, one then derives the expected lower bound for the weight of such…

A hypothesis testing algorithm is replicable if, when run on two different samples from the same distribution, it produces the same output with high probability. This notion, defined by by Impagliazzo, Lei, Pitassi, and Sorell [STOC'22],…

While it is well known that a Turing machine equipped with the ability to flip a fair coin cannot compute more that a standard Turing machine, we show that this is not true for a biased coin. Indeed, any oracle set $X$ may be coded as a…

For a nonempty polyhedral set $P\subset \mathbb R^d$, let $\mathcal F(P)$ denote the set of faces of $P$, and let $N(P,F)$ be the normal cone of $P$ at the nonempty face $F\in\mathcal F(P)$. We prove that the function $\sum_{F\in\mathcal…

We study the power of randomness in the Number-on-Forehead (NOF) model in communication complexity. We construct an explicit 3-player function $f:[N]^3 \to \{0,1\}$, such that: (i) there exist a randomized NOF protocol computing it that…

This study actually draws from and builds on an earlier paper (Kumar and Bhattacharya, 2002). Here we have basically added a neutrosophic dimension to the problem of determining the conditional probability that a financial fraud has been…

Given a set $P$ of $n$ points in the plane, we study the computation of the probability distribution function of both the area and perimeter of the convex hull of a random subset $S$ of $P$. The random subset $S$ is formed by drawing each…

Two players alternate tossing a biased coin where the probability of getting heads is p. The current player is awarded alpha points for tails and alpha+beta for heads. The first player reaching n points wins. For a completely unfair coin…

Coin-flipping is a fundamental task in two-party cryptography where two remote mistrustful parties wish to generate a shared uniformly random bit. While quantum protocols promising near-perfect security exist for weak coin-flipping -- when…

We present an algorithm for testing halfspaces over arbitrary, unknown rotation-invariant distributions. Using $\tilde O(\sqrt{n}\epsilon^{-7})$ random examples of an unknown function $f$, the algorithm determines with high probability…

Let $f$ be a Rademacher or a Steinhaus random multiplicative function. Let $\varepsilon>0$ small. We prove that, as $x\rightarrow +\infty$, we almost surely have $$\bigg|\sum_{\substack{n\leq x\\…