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- Author : S. Barry Cooper
- Publsiher : CRC Press
- Release : 06 September 2017
- ISBN : 1351991965
- Pages : 420 pages
- Rating : 4/5 from 21 reviews

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Read or download book entitled Computability Theory written by S. Barry Cooper which was release on 06 September 2017, this book published by CRC Press. Available in PDF, EPUB and Kindle Format. Book excerpt: Computability 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 : S. Barry Cooper
- Publisher : CRC Press
- Release Date : 2017-09-06
- Total pages : 420
- ISBN : 1351991965

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**Summary :** Computability 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 ...

- Author : E.R. Griffor
- Publisher : Elsevier
- Release Date : 1999-10-01
- Total pages : 724
- ISBN : 1351991965

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**Summary :** The chapters of this volume all have their own level of presentation. The topics have been chosen based on the active research interest associated with them. Since the interest in some topics is older than that in others, some presentations contain fundamental definitions and basic results while others relate very ...

- Author : Robert I. Soare
- Publisher : Springer
- Release Date : 2016-06-20
- Total pages : 263
- ISBN : 1351991965

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**Summary :** 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 ...

- Author : Herbert B. Enderton
- Publisher : Academic Press
- Release Date : 2010-12-30
- Total pages : 192
- ISBN : 1351991965

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**Summary :** Computability 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 ...

- Author : Borut Robič
- Publisher : Springer
- Release Date : 2015-09-14
- Total pages : 331
- ISBN : 1351991965

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**Summary :** This book offers an original and informative view of the development of fundamental concepts of computability theory. The treatment is put into historical context, emphasizing the motivation for ideas as well as their logical and formal development. In Part I the author introduces computability theory, with chapters on the foundational ...

- Author : Maribel Fernandez
- Publisher : Springer Science & Business Media
- Release Date : 2009-04-14
- Total pages : 184
- ISBN : 1351991965

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**Summary :** A Concise Introduction to Computation Models and Computability Theory provides an introduction to the essential concepts in computability, using several models of computation, from the standard Turing Machines and Recursive Functions, to the modern computation models inspired by quantum physics. An in-depth analysis of the basic concepts underlying each model ...

- Author : Nigel Cutland
- Publisher : Cambridge University Press
- Release Date : 1980-06-19
- Total pages : 251
- ISBN : 1351991965

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**Summary :** 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 : Neil D. Jones
- Publisher : Academic Press
- Release Date : 2014-06-20
- Total pages : 168
- ISBN : 1351991965

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**Summary :** Computability 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 ...

- Author : Steven Homer,Alan L. Selman
- Publisher : Springer Science & Business Media
- Release Date : 2013-03-09
- Total pages : 195
- ISBN : 1351991965

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**Summary :** Intended for use in an introductory graduate course in theoretical computer science, this text contains material that should be core knowledge in the theory of computation for all graduates in computer science. It is self-contained and is best suited for a one semester course. The text starts with classical computability ...

- Author : Paul E. Dunne
- Publisher : Prentice Hall
- Release Date : 1991
- Total pages : 150
- ISBN : 1351991965

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**Summary :** A review of computability theory which determines problems that cannot be solved by existing computer programs. The book concentrates on the presentation of basic concepts as opposed to the formal mathematical aspects....

- Author : Rebecca Weber
- Publisher : American Mathematical Soc.
- Release Date : 2012
- Total pages : 203
- ISBN : 1351991965

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**Summary :** What can we compute--even with unlimited resources? Is everything within reach? Or are computations necessarily drastically limited, not just in practice, but theoretically? These questions are at the heart of computability theory. The goal of this book is to give the reader a firm grounding in the fundamentals of computability ...

- Author : Nicholas Pippenger
- Publisher : Cambridge University Press
- Release Date : 1997-05-28
- Total pages : 251
- ISBN : 1351991965

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**Summary :** A mathematically sophisticated introduction to Turing's theory, Boolean functions, automata, and formal languages....

- Author : Luis E. Sanchis
- Publisher : Springer Science & Business Media
- Release Date : 2012-12-06
- Total pages : 233
- ISBN : 1351991965

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**Summary :** Reflexive Structures: An Introduction to Computability Theory is concerned with the foundations of the theory of recursive functions. The approach taken presents the fundamental structures in a fairly general setting, but avoiding the introduction of abstract axiomatic domains. Natural numbers and numerical functions are considered exclusively, which results in a ...

- Author : Douglas S. Bridges
- Publisher : Springer Science & Business Media
- Release Date : 2012-12-06
- Total pages : 180
- ISBN : 1351991965

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**Summary :** Aimed at mathematicians and computer scientists who will only be exposed to one course in this area, Computability: A Mathematical Sketchbook provides a brief but rigorous introduction to the abstract theory of computation, sometimes also referred to as recursion theory. It develops major themes in computability theory, such as Rice's ...

- Author : Peter Cholak
- Publisher : American Mathematical Soc.
- Release Date : 2000-01-01
- Total pages : 320
- ISBN : 1351991965

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**Summary :** This collection of articles presents a snapshot of the status of computability theory at the end of the millennium and a list of fruitful directions for future research. The papers represent the works of experts in the field who were invited speakers at the AMS-IMS-SIAM 1999 Summer Conference on Computability Theory ...