Computability
Published on 23. November 2011
Book
Paperback/Softback
X, 517 pages
978-3-642-69967-2 (ISBN)
Description
Intends to lay a common basis for the different branches of recursion theory. Leads from the very basic theory to modern concepts of computability. Consists of three consecutive parts: 1. Basic Concepts of Computability. 2. Traditional Recursion Theory. 3. Unified Type 2 theory of constructivity and computability on Baire's space including a general the- ory of representations.
More details
Series
Edition
Softcover reprint of the original 1st ed. 1987
Language
English
Place of publication
Berlin
Germany
Publishing group
Springer Berlin
Target group
Lower undergraduate
Illustrations
X, 517 p.
Dimensions
Height: 244 mm
Width: 170 mm
Thickness: 29 mm
Weight
907 gr
ISBN-13
978-3-642-69967-2 (9783642699672)
DOI
10.1007/978-3-642-69965-8
Schweitzer Classification
Other editions
Additional editions
Content
Prerequisites and Notation.- 1: Basic Concepts of Computability.- 1.1 Flowcharts and Machines.- 1.2 Register Machines and Register Computability.- 1.3 Primitive Recursive and ?-Recursive Functions.- 1.4 WHILE-Programs and WHILE-Computability.- 1.5 Tape Machines.- 1.6 Stack Machines.- 1.7 Comparison of Number and Word Functions, Church's Thesis.- 1.8 Recursive and Recursively Enumerable Sets.- 1.9 The Standard Numbering ? of P(1).- 1.10 Some Unsolvable Problems.- 2: Type 1 Recursion Theory.- 2.1 The Basic Concepts of Computability Theory.- 2.2 Numberings.- 2.3 Recursive and Recursively Enumerable Sets (Continued).- 2.4 Many-one and One-one Reducibility.- 2.5 The Recursion Theorem.- 2.6 Creative, Productive, Complete Sets.- 2.7 Effective Numberings.- 2.8 Ordinal Trees and Computable Ordinals.- 2.9 Some Applications to Logic.- 2.10 Oracle Machines and Relativized Recursion Theory.- 2.11 Turing Reducibility and the Kleene Hierarchy.- 2.12 Computational Complexity.- 3: Type 2 Theory of Constructivity and Computability.- 3.1 Type 2 Computability Models.- 3.2 Recursion Theory on Baire's Space.- 3.3 Representations.- 3.4 Effective Representations.- 3.5 Complete Partial Orders.- 3.6 Type 1 Computability and Type 2 Computability.- 3.7 Solving Domain Equations.- 3.8 Applications to Analysis.- Index of Notations.