# Computable Analysis: An Introduction

@article{Weihrauch2014ComputableAA, title={Computable Analysis: An Introduction}, author={Klaus Weihrauch}, journal={Computable Analysis}, year={2014} }

Merging fundamental concepts of analysis and recursion theory to a new exciting theory, this book provides a solid fundament for studying various aspects of computability and complexity in analysis. It is the result of an introductory course given for several years and is written in a style suitable for graduate-level and senior students in computer science and mathematics. Many examples illustrate the new concepts while numerous exercises of varying difficulty extend the material and stimulate…

## 1,284 Citations

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We establish a new connection between the two most common traditions in the theory of real computation, the Blum-Shub-Smale model and the computable analysis approach. We then use the connection to…

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An extended survey of the different strands of research on higher type computability to date is given, bringing together material from recursion theory, constructive logic and computer science.

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This PhD thesis presents progress in the search for a mathematical rigorous framework for efficient numerics of partial differential equations based on a realistic machine model and explores the general restrictions of bounded-time computations on metric spaces within the framework of second-order representations.

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A survey of work over the last four decades on generalizations of computability theory to many-sorted algebras and generalized Church-Turing theses is presented.

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### Quantitative continuity and computable analysis in Coq

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A number of formal proofs of theorems from the field of computable analysis are given that the algebraic operations and the efficient limit operator on the reals are computable, and that certain countably infinite products are isomorphic to spaces of functions.

### Theoretical Computer Science: Computability, Decidability and Logic

- Education
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This chapter deals with a question in the very core of IA: what can be computed by a machine? An agreement has been reached on the answer brought by Alan Turing in 1936. Indeed, all other proposed…

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This tutorial will introduce listeners to many questions that can be asked about computable processes on fields, and will present the answers that are known, sometimes with proofs. This is not…

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