Related papers: Van Lambalgen's Theorem for uniformly relative Sch…

In the same sense as classical logic is a formal theory of truth, the recently initiated approach called computability logic is a formal theory of computability. It understands (interactive) computational problems as games played by a…

Rohatgi and the author recently proved a shuffling theorem for lozenge tilings of `doubly-dented hexagons' (arXiv:1905.08311). The theorem can be considered as a hybrid between two classical theorems in the enumeration of tilings:…

We introduce two notions of effective reducibility for set-theoretical statements, based on computability with Ordinal Turing Machines (OTMs), one of which resembles Turing reducibility while the other is modelled after Weihrauch…

A type-2 computable real function is necessarily continuous; and this remains true for relative, i.e. oracle-based computations. Conversely, by the Weierstrass Approximation Theorem, every continuous f:[0,1]->R is computable relative to…

The algebraic polynomial interpolation on uniformly distributed nodes is affected by the Runge phenomenon, also when the function to be interpolated is analytic. Among all techniques that have been proposed to defeat this phenomenon, there…

We examine the convergence properties of sequences of nonnegative real numbers that satisfy a particular class of recursive inequalities, from the perspective of proof theory and computability theory. We first establish a number of results…

We improve on Gonek-Montgomery's quantitative version of Kronecker's approximation theorem.

We show that given any non-computable left-c.e. real $\alpha$ there exists a left-c.e. real $\beta$ such that $\alpha\neq \beta+\gamma$ for all left-c.e. reals and all right-c.e. reals $\gamma$. The proof is non-uniform, the dichotomy being…

The pseudoinverse of a matrix, a generalized notion of the inverse, is of fundamental importance in linear algebra and, thereby, in many different fields. Despite its proven existence, an algorithmic approach is typically necessary to…

We study functions from reals to reals which are uniformly degree-invariant from Turing-equivalence to many-one equivalence, and compare them "on a cone." We prove that they are in one-to-one correspondence with the Wadge degrees, which can…

This paper is a contribution to the growing investigation of strong reducibilities between $\Pi^1_2$ statements of second-order arithmetic, viewed as an extension of the traditional analysis of reverse mathematics. We answer several…

We initiate a systematic investigation of distribution testing in the framework of algorithmic replicability. Specifically, given independent samples from a collection of probability distributions, the goal is to characterize the sample…

In this article we study asymptotic behavior of the probability that a random monic polynomial with integer coefficients is irreducible over the integers. We consider the cases where the coefficients grow together with the degree of the…

In this article we take a probabilistic look at H\"older's inequality, considering the ratio of terms in the classical H\"older inequality for random vectors in $\mathbb{R}^n$. We prove a central limit theorem for this ratio, which then…

We give an uncountability proof of the reals which relies on their order completeness instead of their sequential completeness. We use neither a form of the axiom of choice nor the law of excluded middle, therefore the proof applies to the…

We characterize the variation functions of computable Lipschitz functions. We show that a real z is computably random if and only if every computable Lipschitz function is differentiable at z. Beyond these principal results, we show that a…

Necessary and sufficient conditions are given for the similarity between two perturbations of the (backward) shift by rank one operators, under certain assumptions on the perturbations. The proof of similarity is based on an explicit…

We introduce the notion of finitary computable reducibility on equivalence relations on the natural numbers. This is a weakening of the usual notion of computable reducibility, and we show it to be distinct in several ways. In particular,…

The existence of incompatibility is one of the most fundamental features of quantum theory, and can be found at the core of many of the theory's distinguishing features, such as Bell inequality violations and the no-broadcasting theorem. A…

In applied probability, the normal approximation is often used for the distribution of data with assumed additive structure. This tradition is based on the central limit theorem for sums of (independent) random variables. However, it is…