Overview
Volume II of Classical Recursion Theory describes the universe from a local (bottom-up or synthetical) point of view, and covers the whole spectrum, from the recursive to the arithmetical sets. The first half of the book provides a detailed picture of the computable sets from the perspective of Theoretical Computer Science. Besides giving a detailed description of the theories of abstract Complexity Theory and of Inductive Inference, it contributes a uniform picture of the most basic complexity classes, ranging from small time and space bounds to the elementary functions, with a particular attention to polynomial time and space computability. It also deals with primitive recursive functions and larger classes, which are of interest to the proof theorist. The second half of the book starts with the classical theory of recursively enumerable sets and degrees, which constitutes the core of Recursion or Computability Theory. Unlike other texts, usually confined to the Turing degrees, the book covers a variety of other strong reducibilities, studying both their individual structures and their mutual relationships.The last chapters extend the theory to limit sets and arithmetical sets. The volume ends with the first textbook treatment of the enumeration degrees, which admit a number of applications from algebra to the Lambda Calculus. The book is a valuable source of information for anyone interested in Complexity and Computability Theory. The student will appreciate the detailed but informal account of a wide variety of basic topics, while the specialist will find a wealth of material sketched in exercises and asides. A massive bibliography of more than a thousand titles completes the treatment on the historical side.
Full Product Details
Author: P. Odifreddi (University of Turin, Italy)
Publisher: Elsevier Science & Technology
Imprint: North-Holland
Volume: v.143
Dimensions:
Width: 15.90cm
, Height: 6.40cm
, Length: 24.10cm
Weight: 1.520kg
ISBN: 9780444502056
ISBN 10: 044450205
Pages: 966
Publication Date: 07 September 1999
Audience:
Professional and scholarly
,
Professional & Vocational
Format: Hardback
Publisher's Status: Active
Availability: Out of stock
The supplier is temporarily out of stock of this item. It will be ordered for you on backorder and shipped when it becomes available.
Reviews
Rodney G. DowneyThe scope of the material is amazing. For instance, I can think of no other book with a treatment of w-REA sets inductive reference, and models of lambda calculus! This is especially gratifying in a world of continuing mathematical fragmentation.Mathematical Reviews
Rodney G. Downey The scope of the material is amazing. For instance, I can think of no other book with a treatment of w-REA sets inductive reference, and models of lambda calculus! This is especially gratifying in a world of continuing mathematical fragmentation. Mathematical Reviews
Rodney G. Downey The scope of the material is amazing. For instance, I can think of no other book with a treatment of w-REA sets inductive reference, and models of lambda calculus! This is especially gratifying in a world of continuing mathematical fragmentation. Mathematical Reviews
