Related papers: Some Quantitative Aspects of Fractional Computabil…

We continue the study of the effective content of $K$-theory for C*-algebras, with a focus on AF algebras. We show that from a c.e. presentation of an AF algebra it is possible to compute a representation of the algebra as an inductive…

We present characterisations of "exact" gap-definable classes, in terms of indeterministic models of computation which slightly modify the standard model of quantum computation. This follows on work of Aaronson [arXiv:quant-ph/0412187], who…

Density functional theory is a successful branch of numerical simulations of quantum systems. While the foundations are rigorously defined, the universal functional must be approximated resulting in a `semi'-ab initio approach. The search…

This paper studies the expressive and computational power of discrete Ordinary Differential Equations (ODEs), a.k.a. (Ordinary) Difference Equations. It presents a new framework using these equations as a central tool for computation and…

We prove two new results about the randomized query complexity of composed functions. First, we show that the randomized composition conjecture is false: there are families of partial Boolean functions $f$ and $g$ such that $R(f\circ g)\ll…

In a recently launched research program for developing logic as a formal theory of (interactive) computability, several very interesting logics have been introduced and axiomatized. These fragments of the larger Computability Logic aim not…

The functional linear model is an important extension of the classical regression model allowing for scalar responses to be modeled as functions of stochastic processes. Yet, despite the usefulness and popularity of the functional linear…

In this paper, we investigate the problem of synthesizing computable functions of infinite words over an infinite alphabet (data omega-words). The notion of computability is defined through Turing machines with infinite inputs which can…

We provide an implicit characterization of polynomial time computation in terms of ordinary differential equations: we characterize the class $\operatorname{PTIME}$ of languages computable in polynomial time in terms of differential…

We introduce a quantum-like classical computational model, called affine computation, as a generalization of probabilistic computation. After giving the basics of affine computation, we define affine finite automata (AfA) and compare it…

A conformable time-scale fractional calculus of order $\alpha \in ]0,1]$ is introduced. The basic tools for fractional differentiation and fractional integration are then developed. The Hilger time-scale calculus is obtained as a particular…

We study the existence of algorithms generating almost surely nonnegative unbiased estimators. We show that given a nonconstant real-valued function $f$ and a sequence of unbiased estimators of $\lambda\in\mathbb{R}$, there is no algorithm…

We present a novel approach to Bayesian inference and general Bayesian computation that is defined through a sequential decision loop. Our method defines a recursive partitioning of the sample space. It neither relies on gradients nor…

We begin the systematic study of decision problems for finitely generated groups given by a solution to their word problem. We relate this to the study of computable analysis on the space of marked groups. We point out that several distinct…

We study several questions in the reliable agnostic learning framework of Kalai et al. (2009), which captures learning tasks in which one type of error is costlier than others. A positive reliable classifier is one that makes no false…

We show that for a fixed positive integer k one can efficiently decide if a finite algebra A admits a k-ary weak near unanimity operation by looking at the local behavior of the terms of A. We also observe that the problem of deciding if a…

We introduce a nabla, a delta, and a symmetric fractional calculus on arbitrary nonempty closed subsets of the real numbers. These fractional calculi provide a study of differentiation and integration of noninteger order on discrete,…

We introduce a notion of complexity of diagrams (and in particular of objects and morphisms) in an arbitrary category, as well as a notion of complexity of functors between categories equipped with complexity functions. We discuss several…

In this article, we impose a new class of fractional analytic functions in the open unit disk. By considering this class, we define a fractional operator, which is generalized Salagean and Ruscheweyh differential operators. Moreover, by…

We begin to study classical dimension theory from the computable analysis (TTE) point of view. For computable metric spaces, several effectivisations of zero-dimensionality are shown to be equivalent. The part of this characterisation that…