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Author: Jens E. Fenstad
Publisher: Cambridge University Press
Published: 2017-03-02
Total Pages: 238
ISBN-13: 1107168163
DOWNLOAD EBOOKThis volume presents a unified and coherent account of the many and various parts of general recursion theory.
Author: Chi Tat Chong
Publisher: Walter de Gruyter GmbH & Co KG
Published: 2015-08-17
Total Pages: 409
ISBN-13: 311038129X
DOWNLOAD EBOOKThis monograph presents recursion theory from a generalized point of view centered on the computational aspects of definability. A major theme is the study of the structures of degrees arising from two key notions of reducibility, the Turing degrees and the hyperdegrees, using techniques and ideas from recursion theory, hyperarithmetic theory, and descriptive set theory. The emphasis is on the interplay between recursion theory and set theory, anchored on the notion of definability. The monograph covers a number of fundamental results in hyperarithmetic theory as well as some recent results on the structure theory of Turing and hyperdegrees. It also features a chapter on the applications of these investigations to higher randomness.
Author: Herbert B. Enderton
Publisher: Academic Press
Published: 2010-12-30
Total Pages: 193
ISBN-13: 0123849594
DOWNLOAD EBOOKComputability Theory: An Introduction to Recursion Theory provides a concise, comprehensive, and authoritative introduction to contemporary computability theory, techniques, and results. The basic concepts and techniques of computability theory are placed in their historical, philosophical and logical context. This presentation is characterized by an unusual breadth of coverage and the inclusion of advanced topics not to be found elsewhere in the literature at this level. The text includes both the standard material for a first course in computability and more advanced looks at degree structures, forcing, priority methods, and determinacy. The final chapter explores a variety of computability applications to mathematics and science. Computability Theory is an invaluable text, reference, and guide to the direction of current research in the field. Nowhere else will you find the techniques and results of this beautiful and basic subject brought alive in such an approachable way. - Frequent historical information presented throughout - More extensive motivation for each of the topics than other texts currently available - Connects with topics not included in other textbooks, such as complexity theory
Author: Piergiorgio Odifreddi
Publisher:
Published: 1999
Total Pages: 668
ISBN-13: 9780444589439
DOWNLOAD EBOOKAuthor: Gerald E. Sacks
Publisher: Cambridge University Press
Published: 2017-03-02
Total Pages: 361
ISBN-13: 1107168430
DOWNLOAD EBOOKThis almost self-contained introduction to higher recursion theory is essential reading for all researchers in the field.
Author: Nigel Cutland
Publisher: Cambridge University Press
Published: 1980-06-19
Total Pages: 268
ISBN-13: 9780521294652
DOWNLOAD EBOOKWhat can computers do in principle? What are their inherent theoretical limitations? The theoretical framework which enables such questions to be answered has been developed over the last fifty years from the idea of a computable function - a function whose values can be calculated in an automatic way.
Author: Luis E Sanchis
Publisher:
Published: 1988-09-01
Total Pages: 248
ISBN-13: 9781461238799
DOWNLOAD EBOOKAuthor: S. Barry Cooper
Publisher: CRC Press
Published: 2017-09-06
Total Pages: 420
ISBN-13: 1420057561
DOWNLOAD EBOOKComputability theory originated with the seminal work of Gödel, Church, Turing, Kleene and Post in the 1930s. This theory includes a wide spectrum of topics, such as the theory of reducibilities and their degree structures, computably enumerable sets and their automorphisms, and subrecursive hierarchy classifications. Recent work in computability theory has focused on Turing definability and promises to have far-reaching mathematical, scientific, and philosophical consequences. Written by a leading researcher, Computability Theory provides a concise, comprehensive, and authoritative introduction to contemporary computability theory, techniques, and results. The basic concepts and techniques of computability theory are placed in their historical, philosophical and logical context. This presentation is characterized by an unusual breadth of coverage and the inclusion of advanced topics not to be found elsewhere in the literature at this level. The book includes both the standard material for a first course in computability and more advanced looks at degree structures, forcing, priority methods, and determinacy. The final chapter explores a variety of computability applications to mathematics and science. Computability Theory is an invaluable text, reference, and guide to the direction of current research in the field. Nowhere else will you find the techniques and results of this beautiful and basic subject brought alive in such an approachable and lively way.
Author: Neil D. Jones
Publisher: Academic Press
Published: 2014-06-20
Total Pages: 169
ISBN-13: 1483218481
DOWNLOAD EBOOKComputability Theory: An Introduction provides information pertinent to the major concepts, constructions, and theorems of the elementary theory of computability of recursive functions. This book provides mathematical evidence for the validity of the Church–Turing thesis. Organized into six chapters, this book begins with an overview of the concept of effective process so that a clear understanding of the effective computability of partial and total functions is obtained. This text then introduces a formal development of the equivalence of Turing machine computability, enumerability, and decidability with other formulations. Other chapters consider the formulas of the predicate calculus, systems of recursion equations, and Post's production systems. This book discusses as well the fundamental properties of the partial recursive functions and the recursively enumerable sets. The final chapter deals with different formulations of the basic ideas of computability that are equivalent to Turing-computability. This book is a valuable resource for undergraduate or graduate students.
Author: Robert I. Soare
Publisher: Springer
Published: 2016-06-20
Total Pages: 289
ISBN-13: 3642319335
DOWNLOAD EBOOKTuring'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.
