Related papers: Probabilistic results on the $2$-adic complexity

Building on previous results of Xing, we give new lower bounds on the rate of intersecting codes over large alphabets. The proof is constructive, and uses algebraic geometry, although nothing beyond the basic theory of linear systems on…

We prove the existence of a limit distribution for the normalized normality measure $\mathcal{N}(E_N)/\sqrt{N}$ (as $N \to \infty$) for random binary sequences $E_N$, by this means confirming a conjecture of Alon, Kohayakawa, Mauduit,…

Program sensitivity, also known as Lipschitz continuity, describes how small changes in a program's input lead to bounded changes in the output. We propose an average notion of program sensitivity for probabilistic programs---expected…

We introduce a mild generative variant of the classical neural operator model, which leverages Kolmogorov--Arnold networks to solve infinite families of second-order backward stochastic differential equations ($2$BSDEs) on regular bounded…

We investigate the AC conductivity of binary random impedance networks, with emphasis on its dependence on the ratio of the complex conductances of both phases. We propose an algorithm to determine the conductance of a finite network, in…

Given pseudo-random binary sequence of length $L$, assuming it consists of $k$ sub-sequences of length $N$. We estimate how $k$ scales with growing $N$ to obtain a {\it limiting} ergodic behaviour, to fulfill the basic definition of…

Let $P_n(x)=\frac1{n!}\sum\binom n{2i+1}(2i+1)^x$. This extends to a continuous function on the 2-adic integers, the $n$th 2-adic partial Stirling function. We show that $(-1)^{n+1}P_n$ is the only 2-adically continuous approximation to…

We prove that the binary complexity of solving ordinary polynomial differential equations in terms of Puiseux series is single exponential in the number of terms in the series. Such a bound was given by Grigoriev [10] for Riccatti…

We consider any fixed $d\in\mathbb{Z}_{>0}$ number of second class particles in the asymmetric simple exclusion process (ASEP), constructed via a basic coupling of two ASEPs. We give the joint distribution of the positions of the second…

Estimating the length of the longest increasing subsequence (LIS) in an array is a problem of fundamental importance. Despite the significance of the LIS estimation problem and the amount of attention it has received, there are important…

Since human randomness production has been studied and widely used to assess executive functions (especially inhibition), many measures have been suggested to assess the degree to which a sequence is random-like. However, each of them…

The complexities of self-dual normal bases, which are candidates for the lowest complexity basis of some defined extensions, are determined with the help of the number of all but the simple points in well chosen minimal Besicovitch…

We show that deciding whether a sparse univariate polynomial has a p-adic rational root can be done in NP for most inputs. We also prove a polynomial-time upper bound for trinomials with suitably generic p-adic Newton polygon. We thus…

We convert, within polynomial-time and sequential processing, NP-Complete Problems into a problem of deciding feasibility of a given system S of linear equations with constants and coefficients of binary-variables that are 0, 1, or -1. S is…

In this paper, we present a method for estimating the least common multiple of a large class of binary linear recurrence sequences. Let $P,Q,R_0$, and $R_1$ be fixed integers and let $\boldsymbol{R}=\left(R_n\right)_{n}$ be the recurrence…

Let $n,k,a$ and $c$ be positive integers and $b$ be a nonnegative integer. Let $\nu_2(k)$ and $s_2(k)$ be the 2-adic valuation of $k$ and the sum of binary digits of $k$, respectively. Let $S(n,k)$ be the Stirling number of the second kind.…

We present a deterministic distributed $2$-approximation algorithm for the Minimum Weight Vertex Cover problem in the CONGEST model whose round complexity is $O(\log n \log \Delta / \log^2 \log \Delta)$. This improves over the currently…

If $G$ is a finite Abelian group, define $s_{k}(G)$ to be the minimal $m$ such that a sequence of $m$ elements in $G$ always contains a $k$-element subsequence which sums to zero. Recently Bitz et al. proved that if $n = exp(G)$, then…

Let $O(2n+\ell)$ be the group of orthogonal matrices of size $\left(2n+\ell\right)\times \left(2n+\ell\right)$ equipped with the probability distribution given by normalized Haar measure. We study the probability \begin{equation*}…

The simplex method for linear programming is known to be highly efficient in practice, and understanding its performance from a theoretical perspective is an active research topic. The framework of smoothed analysis, first introduced by…