Computable Analysis - Weihrauch, Klaus

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Is the exponential function computable? Are union and intersection of closed sets in the real plain computable? Are differentiation and integration computable operators? Is zero finding for complex polynomials computable? Is the Mandelbrot set decidable? And in case of computability, what is the computational complexity? Computable analysis supplies exact definitions for these and many other similar questions and tries to solve them. - Merging fundamental concepts of analysis and recursion theory to a new exciting theory, this book provides a solid basis for studying various aspects of…mehr

Produktbeschreibung
Is the exponential function computable? Are union and intersection of closed sets in the real plain computable? Are differentiation and integration computable operators? Is zero finding for complex polynomials computable? Is the Mandelbrot set decidable? And in case of computability, what is the computational complexity? Computable analysis supplies exact definitions for these and many other similar questions and tries to solve them. - Merging fundamental concepts of analysis and recursion theory to a new exciting theory, this book provides a solid basis for studying various aspects of computability and complexity in analysis. It is the result of an introductory course given for many years and is written in a style suitable for graduate-level and senior students in computer science or mathematics. Many examples illustrate the new concepts while numerous exercises of varying difficulty extend the material and stimulate readers to work actively on the text.
  • Produktdetails
  • Texts in Theoretical Computer Science. An EATCS Series
  • Verlag: Springer, Berlin
  • 2000.
  • Seitenzahl: 304
  • Erscheinungstermin: 14. September 2000
  • Englisch
  • Abmessung: 235mm x 155mm x 24mm
  • Gewicht: 636g
  • ISBN-13: 9783540668176
  • ISBN-10: 3540668179
  • Artikelnr.: 08830190
Autorenporträt
Klaus Weihrauch ist seit 1990 bei der SAP AG und dort im Umfeld der Lösung Produktionsplanung und -steuerung (PP) tätig. Unter anderem erstellte er das Daten- und Prozessmodell für die R/3-Komponente PP und war im Rahmen von AcceleratedSAP für den Bereich der Produktionsplanung verantwortlich. Zurzeit ist Klaus Weihrauch Projektleiter im Bereich Best Practices for mySAP SCM, in dem vorkonfigurierte Lösungen für das Supply Chain Management erstellt werden.
Inhaltsangabe
1. Introduction.- 1.1 The Aim of Computable Analysis.- 1.2 Why a New Introduction?.- 1.3 A Sketch of TTE.- 1.3.1 A Model of Computation.- 1.3.2 A Naming System for Real Numbers.- 1.3.3 Computable Real Numbers and Functions.- 1.3.4 Subsets of Real Numbers.- 1.3.5 The Space C[O;1] of ContinuouS Functions.- 1.3.6 Computational Complexity of Real Functions.- 1.4 Prerequisites aud Notation.- 2. Computability on the Cantor Space.- 2.1 Type-2 Machines and Computable String Functions.- 2.2 Computable String Functions are Continuous.- 2.3 Standard Representations of Sets of Continuous String Functions.- 2.4 Effective Subsets.- 3. Naming Systems.- 3.1 Continuity and Computability Induced by Naming Systems.- 3.2 Admissible Naming Systems.- 3.3 Constructions of New Naming Systems.- 4. Computability on the Real Numbers.- 4.1 Various Representations of the Real Numbers.- 4.2 Computable Real Numbers.- 4.3 Computable Real Functions.- 5. Computability on Closed, Open and Compact Sets.- 5.1 Closed