Turing Computability: Theory and Applications

ISBN-10: 3642319335
ISBN-13: 9783642319334
Category: Computers
Pages: 263
Language: English
Published: 2016-06-20
Publisher: Springer
Author: Robert I. Soare

Description

Turing's famous 1936 paper introduced a formal definition of a computing machine, a Turing machine. This model led to both the development of actual computers and to computability theory, the study of what machines can and cannot compute. This book presents classical computability theory from Turing and Post to current results and methods, and their use in studying the information content of algebraic structures, models, and their relation to Peano arithmetic. The author presents the subject as an art to be practiced, and an art in the aesthetic sense of inherent beauty which all mathematicians recognize in their subject. Part I gives a thorough development of the foundations of computability, from the definition of Turing machines up to finite injury priority arguments. Key topics include relative computability, and computably enumerable sets, those which can be effectively listed but not necessarily effectively decided, such as the theorems of Peano arithmetic. Part II includes the study of computably open and closed sets of reals and basis and nonbasis theorems for effectively closed sets. Part III covers minimal Turing degrees. Part IV is an introduction to games and their use in proving theorems. Finally, Part V offers a short history of computability theory. The author has honed the content over decades according to feedback from students, lecturers, and researchers around the world. Most chapters include exercises, and the material is carefully structured according to importance and difficulty. The book is suitable for advanced undergraduate and graduate students in computer science and mathematics and researchers engaged with computability and mathematical logic.

Get the book

Similar books

Family History Digital Libraries
By William Sims Bainbridge
One named Sara and Timberlake had 11 male workers, 1 female worker, and 4 children workers, so it might have employed the Minor family.
Foundation Dreamweaver MX
By Craig Grannell, Jerome Turner, Matt Stephens
So here's what we need to do to arrive at our layout: s Create the main table to hold all the page elements. s Deal with the navigation area which is ...
Cisco CCNA Certification, 2 Volume Set: Exam 200-301
By Todd Lammle
This inclusive, two-book set provides what you need to know to succeed on the new CCNA exam. The set includes Understanding Cisco Networking Technologies: Volume 1 and the CCNA Certification Study Guide: Volume 2.
CompTIA Network+ Study Guide: Exam N10-006
By Todd Lammle
... you can use: –a –A –c –n –r –R –S –s All nbtstat switches are case sensitive. Generally speaking, lowercase switches deal with NetBIOS names of hosts, ...
CompTIA Network+ Study Guide with Online Labs: N10-007 Exam
By Todd Lammle, Jon Buhagiar
... you can use: –a –A –c –n –r –R –S –s All nbtstat switches are case sensitive. Generally speaking, lowercase switches deal with NetBIOS names of hosts, ...
CCNA: Cisco Certified Network Associate FastPass
By Todd Lammle
S The S reference point defines the point between the customer router and an ... with the letter E deal with using ISDN on the existing telephone network.
Stranger in the Chat Room
By Todd Hafer, Jedd Hafer
A sequel to In the Chat Room With God finds a group of teens contacted by a mysterious and increasingly malevolent character who claims to know about their encounters with the Almighty and challenges their beliefs. Original.
Error Correction Coding: Mathematical Methods and Algorithms
By Todd K. Moon
M M−1∑ k=0 −∞ ∞ k=0 The average energy per signal E s ∫ can be related to the ... we will deal primarily with additive white Gaussian noise (AWGN), ...
Security+ Training Guide
By Todd King
... to deal with most , but unfortunately not all , of these potential threats . ... The S / MIME standard implements encryption for message content using ...
CCDA: Cisco Certified Design Associate Study Guide: Exam 640-861
By Todd Lammle, Andy Barkl
S reference point The S reference point defines the reference point between ... with the letter E deal with using ISDN on the existing telephone network.