Related papers: Robustness of non-computability
We introduce three measures which quantify the degree to which quantum systems possess the robustness exhibited by classical systems when subjected to continuous observation. Using these we show that for a fixed environmental interaction…
Turing machines and spin models share a notion of universality according to which some simulate all others. Is there a theory of universality that captures this notion? We set up a categorical framework for universality which includes as…
Incomputability as a mathematical notion arose from work of Alan Turing and Alonzo Church in the 1930s. Like Turing himself, it attracted less attention than it deserved beyond the confines of mathematics. Today our experiences in computer…
The Turing machine (TM) and the Church thesis have formalized the concept of computable number, this allowed to display non-computable numbers. This paper defines the concept of number "approachable" by a TM and shows that some (if not all)…
Robustness in terms of outliers is an important topic and has been formally studied for a variety of problems in machine learning and computer vision. Generalized median computation is a special instance of consensus learning and a common…
Deep neural networks for computer vision are deployed in increasingly safety-critical and socially-impactful applications, motivating the need to close the gap in model performance under varied, naturally occurring imaging conditions.…
Feedback-based online optimization algorithms have gained traction in recent years because of their simple implementation, their ability to reject disturbances in real time, and their increased robustness to model mismatch. While the…
This work exposes which mechanisms and procesess in the Nature of evolution compute a function not computable by Turing machine. The computer with intelligence that is not higher than one bacteria population could have, but with efficency…
In data-based control, dissipativity can be a powerful tool for attaining stability guarantees for nonlinear systems if that dissipativity can be inferred from data. This work provides a tutorial on several existing methods for data-based…
Optimization problems are a staple of today's scientific and technical landscape. However, at present, solvers of such problems are almost exclusively run on digital hardware. Using Turing machines as a mathematical model for any type of…
Robustness measures are increasingly prominent resource quantifiers that have been introduced for quantum resource theories such as entanglement and coherence. Despite the generality of these measures, their usefulness is hindered by the…
We explore in the framework of Quantum Computation the notion of {\em Computability}, which holds a central position in Mathematics and Theoretical Computer Science. A quantum algorithm for Hilbert's tenth problem, which is equivalent to…
We advance a Bayesian concept of 'intrinsic asymptotic universality' taking to its final conclusions previous conceptual and numerical work based upon a concept of a reprogrammability test and an investigation of the complex qualitative…
Quantum computing provides a powerful framework for tackling computational problems that are classically intractable. The goal of this paper is to explore the use of quantum computers for solving relevant problems in systems and control…
In the first of this pair of papers, it was proven that that no physical computer can correctly carry out all computational tasks that can be posed to it. The generality of this result follows from its use of a novel definition of…
We describe the Turing Machine, list some of its many influences on the theory of computation and complexity of computations, and illustrate its importance.
We investigate the theory of thermodynamic formalism from the perspective of computable analysis, with a special focus on the computability of equilibrium states. Specifically, we develop two complementary general approaches to verify the…
Computational complexity characterizes the usage of spatial and temporal resources by computational processes. In the classical theory of computation, e.g. in the Turing Machine model, computational processes employ only local space and…
This article presents a theoretical investigation of computation beyond the Turing barrier from emergent behavior in distributed systems. In particular, we present an algorithmic network that is a mathematical model of a networked…
Unlike computation or the numerical analysis of differential equations, simulation does not have a well established conceptual and mathematical foundation. Simulation is an arguable unique union of modeling and computation. However,…