Theory of Recursive Functions and Effective Computability
Author: Hartley Rogers (Jr.)
Publisher:
Published: 1967
Total Pages: 482
ISBN-13:
DOWNLOAD EBOOKRead and Download eBook Full
Author: Hartley Rogers (Jr.)
Publisher:
Published: 1967
Total Pages: 482
ISBN-13:
DOWNLOAD EBOOKAuthor: Hartley Rogers
Publisher:
Published: 1967
Total Pages: 526
ISBN-13:
DOWNLOAD EBOOKAuthor: 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: Douglas Elliott Ashford
Publisher:
Published: 1967
Total Pages:
ISBN-13:
DOWNLOAD EBOOKAuthor: Nigel Cutland
Publisher: Cambridge University Press
Published: 1980-06-19
Total Pages: 268
ISBN-13: 1139935607
DOWNLOAD EBOOKWhat can computers do in principle? What are their inherent theoretical limitations? These are questions to which computer scientists must address themselves. 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: intuitively a function whose values can be calculated in an effective or automatic way. This book is an introduction to computability theory (or recursion theory as it is traditionally known to mathematicians). Dr Cutland begins with a mathematical characterisation of computable functions using a simple idealised computer (a register machine); after some comparison with other characterisations, he develops the mathematical theory, including a full discussion of non-computability and undecidability, and the theory of recursive and recursively enumerable sets. The later chapters provide an introduction to more advanced topics such as Gödel's incompleteness theorem, degrees of unsolvability, the Recursion theorems and the theory of complexity of computation. Computability is thus a branch of mathematics which is of relevance also to computer scientists and philosophers. Mathematics students with no prior knowledge of the subject and computer science students who wish to supplement their practical expertise with some theoretical background will find this book of use and interest.
Author: Peter Smith
Publisher: Cambridge University Press
Published: 2007-07-26
Total Pages: 376
ISBN-13: 1139465937
DOWNLOAD EBOOKIn 1931, the young Kurt Gödel published his First Incompleteness Theorem, which tells us that, for any sufficiently rich theory of arithmetic, there are some arithmetical truths the theory cannot prove. This remarkable result is among the most intriguing (and most misunderstood) in logic. Gödel also outlined an equally significant Second Incompleteness Theorem. How are these Theorems established, and why do they matter? Peter Smith answers these questions by presenting an unusual variety of proofs for the First Theorem, showing how to prove the Second Theorem, and exploring a family of related results (including some not easily available elsewhere). The formal explanations are interwoven with discussions of the wider significance of the two Theorems. This book will be accessible to philosophy students with a limited formal background. It is equally suitable for mathematics students taking a first course in mathematical logic.
Author: Rogers Jr Hartley
Publisher:
Published: 1967
Total Pages: 482
ISBN-13:
DOWNLOAD EBOOKAuthor: Piergiorgio Odifreddi
Publisher:
Published: 1999
Total Pages: 668
ISBN-13: 9780444589439
DOWNLOAD EBOOKAuthor: 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.
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