Theory Of Recursive Functions And Effective Computability

Author : Hartley Rogers
Publisher : National Geographic Books
ISBN 13 : 0262680521
Total Pages : 0 pages
Book Rating : 4.23/5 ( download)

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Download or read book Theory of Recursive Functions and Effective Computability written by Hartley Rogers and published by National Geographic Books. This book was released on 1987-04-22 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: (Reprint of the 1967 edition)

Author : Hartley Rogers (Jr.)
Publisher :
ISBN 13 :
Total Pages : 482 pages
Book Rating : 4.64/5 ( download)

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Download or read book Theory of Recursive Functions and Effective Computability written by Hartley Rogers (Jr.) and published by . This book was released on 1967 with total page 482 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : Hartley Rogers
Publisher :
ISBN 13 :
Total Pages : 526 pages
Book Rating : 4.39/5 ( download)

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Download or read book Theory of Recursive Functions and Effective Computability written by Hartley Rogers and published by . This book was released on 1967 with total page 526 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : Nigel Cutland
Publisher : Cambridge University Press
ISBN 13 : 9780521294652
Total Pages : 268 pages
Book Rating : 4.57/5 ( download)

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Download or read book Computability written by Nigel Cutland and published by Cambridge University Press. This book was released on 1980-06-19 with total page 268 pages. Available in PDF, EPUB and Kindle. Book excerpt: What 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 : Robert I. Soare
Publisher : Springer Science & Business Media
ISBN 13 : 9783540152996
Total Pages : 460 pages
Book Rating : 4.97/5 ( download)

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Download or read book Recursively Enumerable Sets and Degrees written by Robert I. Soare and published by Springer Science & Business Media. This book was released on 1999-11-01 with total page 460 pages. Available in PDF, EPUB and Kindle. Book excerpt: ..."The book, written by one of the main researchers on the field, gives a complete account of the theory of r.e. degrees. .... The definitions, results and proofs are always clearly motivated and explained before the formal presentation; the proofs are described with remarkable clarity and conciseness. The book is highly recommended to everyone interested in logic. It also provides a useful background to computer scientists, in particular to theoretical computer scientists." Acta Scientiarum Mathematicarum, Ungarn 1988 ..."The main purpose of this book is to introduce the reader to the main results and to the intricacies of the current theory for the recurseively enumerable sets and degrees. The author has managed to give a coherent exposition of a rather complex and messy area of logic, and with this book degree-theory is far more accessible to students and logicians in other fields than it used to be." Zentralblatt für Mathematik, 623.1988

Author : Nigel Cutland
Publisher : Cambridge University Press
ISBN 13 : 1139935607
Total Pages : 314 pages
Book Rating : 4.09/5 ( download)

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Download or read book Computability written by Nigel Cutland and published by Cambridge University Press. This book was released on 1980-06-19 with total page 314 pages. Available in PDF, EPUB and Kindle. Book excerpt: What 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
ISBN 13 : 0521857848
Total Pages : 376 pages
Book Rating : 4.40/5 ( download)

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Download or read book An Introduction to Gödel's Theorems written by Peter Smith and published by Cambridge University Press. This book was released on 2007-07-26 with total page 376 pages. Available in PDF, EPUB and Kindle. Book excerpt: Peter Smith examines Gödel's Theorems, how they were established and why they matter.

Author : Carl Smith
Publisher : Springer Science & Business Media
ISBN 13 : 1441985018
Total Pages : 155 pages
Book Rating : 4.19/5 ( download)

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Download or read book A Recursive Introduction to the Theory of Computation written by Carl Smith and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 155 pages. Available in PDF, EPUB and Kindle. Book excerpt: The aim of this textbook is to present an account of the theory of computation. After introducing the concept of a model of computation and presenting various examples, the author explores the limitations of effective computation via basic recursion theory. Self-reference and other methods are introduced as fundamental and basic tools for constructing and manipulating algorithms. From there the book considers the complexity of computations and the notion of a complexity measure is introduced. Finally, the book culminates in considering time and space measures and in classifying computable functions as being either feasible or not. The author assumes only a basic familiarity with discrete mathematics and computing, making this textbook ideal for a graduate-level introductory course. It is based on many such courses presented by the author and so numerous exercises are included. In addition, the solutions to most of these exercises are provided.

Author : Piergiorgio Odifreddi
Publisher :
ISBN 13 : 9780444589439
Total Pages : 668 pages
Book Rating : 4.30/5 ( download)

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Download or read book Classical recursion theory : the theory of functions and sets of natural numbers written by Piergiorgio Odifreddi and published by . This book was released on 1999 with total page 668 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : Robert I. Soare
Publisher : Springer
ISBN 13 : 3642319335
Total Pages : 263 pages
Book Rating : 4.34/5 ( download)

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Download or read book Turing Computability written by Robert I. Soare and published by Springer. This book was released on 2016-06-20 with total page 263 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.