34 citations · 54 across the 14 of their papers we have counts for
17 papers
Termination of Real Linear Loops
Eike Neumann, Margret Tembo
We study the problem of deciding universal termination of linear and affine loops over the reals in the bit-model of real computation. We show that both problems are as close to de…
Deciding Robust Instances of an Escape Problem for Dynamical Systems in Euclidean Space
Eike Neumann
We study the problem of deciding whether a point escapes a closed subset of under the iteration of a continuous map in the b…
Computably discrete represented spaces
Eike Neumann, Arno Pauly, Cécilia Pradic +1
In computable topology, a represented space is called computably discrete if its equality predicate is semidecidable. While any such space is classically isomorphic to an initial s…
The equational theory of the Weihrauch lattice with multiplication
Eike Neumann, Arno Pauly, Cécilia Pradic
We study the equational theory of the Weihrauch lattice with multiplication, meaning the collection of equations between terms built from variables, the lattice operations …
On the Complexity of Robust Eventual Inequality Testing for C-Finite Functions
Eike Neumann
We study the computational complexity of a robust version of the problem of testing two univariate C-finite functions for eventual inequality at large times. Specifically, working…
Bounding the Escape Time of a Linear Dynamical System over a Compact Semialgebraic Set
Julian D'Costa, Engel Lefaucheux, Eike Neumann +2
We study the Escape Problem for discrete-time linear dynamical systems over compact semialgebraic sets. We establish a uniform upper bound on the number of iterations it takes for…
On the Complexity of the Escape Problem for Linear Dynamical Systems over Compact Semialgebraic Sets
Julian D'Costa, Engel Lefaucheux, Eike Neumann +2
We study the computational complexity of the Escape Problem for discrete-time linear dynamical systems over compact semialgebraic sets, or equivalently the Termination Problem for…
Uniform Envelopes
Eike Neumann
In the author's PhD thesis (2019) universal envelopes were introduced as a tool for studying the continuously obtainable information on discontinuous functions. To any function $f…
Decision problems for linear recurrences involving arbitrary real numbers
Eike Neumann
We study the decidability of the Skolem Problem, the Positivity Problem, and the Ultimate Positivity Problem for linear recurrences with real number initial values and real number…
Implementing evaluation strategies for continuous real functions
Michal Konečný, Eike Neumann
We give a technical overview of our exact-real implementation of various representations of the space of continuous unary real functions over the unit domain and a family of associ…
Parametrised second-order complexity theory with applications to the study of interval computation
Eike Neumann, Florian Steinberg
We extend the framework for complexity of operators in analysis devised by Kawamura and Cook (2012) to allow for the treatment of a wider class of representations. The main novelty…
On the computability of the Fréchet distance of surfaces in the bit-model of real computation
Eike Neumann
We show that the Fréchet distance of two-dimensional parametrised surfaces in a metric space is computable in the bit-model of real computation. An analogous result in the real RAM…
Representations and evaluation strategies for feasibly approximable functions
Michal Konečný, Eike Neumann
A famous result due to Ko and Friedman (1982) asserts that the problems of integration and maximisation of a univariate real function are computationally hard in a well-defined sen…
Computability in Basic Quantum Mechanics
Eike Neumann, Martin Pape, Thomas Streicher
The basic notions of quantum mechanics are formulated in terms of separable infinite dimensional Hilbert space . In terms of the Hilbert lattice of close…
Semantics, Specification Logic, and Hoare Logic of Exact Real Computation
Sewon Park, Franz Brauße, Pieter Collins +7
We propose a simple imperative programming language, ERC, that features arbitrary real numbers as primitive data type, exactly. Equipped with a denotational semantics, ERC provides…
A topological view on algebraic computation models
Eike Neumann, Arno Pauly
We investigate the topological aspects of some algebraic computation models, in particular the BSS-model. Our results can be seen as bounds on how different BSS-computability and c…
Computational Problems in Metric Fixed Point Theory and their Weihrauch Degrees
Eike Neumann
We study the computational difficulty of the problem of finding fixed points of nonexpansive mappings in uniformly convex Banach spaces. We show that the fixed point sets of comput…