Last edited by Kazrashura

Thursday, April 30, 2020 | History

6 edition of **Theories of computability** found in the catalog.

- 131 Want to read
- 39 Currently reading

Published
**1997** by Cambridge University Press in Cambridge, U.K, New York, NY, USA .

Written in English

- Machine theory.

**Edition Notes**

Includes bibliographical references (p. 234-242) and indexes.

Statement | Nicholas Pippenger. |

Classifications | |
---|---|

LC Classifications | QA267 .P553 1997 |

The Physical Object | |

Pagination | ix, 251 p. : |

Number of Pages | 251 |

ID Numbers | |

Open Library | OL1004879M |

ISBN 10 | 0521553806 |

LC Control Number | 96044633 |

This area of mathematical logic is known by two distinct names: computability theory, and recursion theory. It is one of the four main branches of mathematical logic, along with model theory, set theory, and proof theory, and is a highly active area of current research, both by . The Association Computability in Europe (ACiE) is an international organization of mathematicians, logicians, computer scientists, philosophers, theoretical physicists and others interested in new developments in computability and in their underlying significance for the real world. CiE aims to widen understanding and appreciation of the importance of the concepts and techniques of Type: INGO.

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Broad in coverage, Theories of computability book sophisticated, and up to date, this book provides an introduction to theories of computability. It treats not only "the" theory of computability (the theory created by Alan Turing and others in the s), but also a variety of other theories (of Boolean functions, automata and formal languages) as theories of by: A better reference is Hartley Rogers' Theory of Recursive Functions and Effective Computability.

Buy this book if you are in the middle. It's a great book if you've seen some decidability results, but not a formal mathematical treatment; and if you intend to follow the book and learn what it decides rather than look up specific by: This book presents classical computability theory from Turing Theories of computability book 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 5/5(2). 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. 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 Edition: 1. The book series Theory and Applications of Computability is published by Springer in cooperation with Theories of computability book Association Computability in Europe.

Books published in this series will be of interest to the research community and graduate students, with a unique focus on issues of computability. This book is a general introduction to computability and complexity theory.

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In Chapter 1 we use a Kleene-style introduction to the class of computable functions, and File Size: KB. Computer scientists, mathematicians, and philosophers discuss the conceptual foundations of the notion of computability as well as recent theoretical developments.

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Print Book & E-Book. Theories of computability bookFrom the Back Cover. This book offers a self-contained exposition of the theory of computability in a higher-order context, where 'computable operations' may themselves be passed as arguments to other computable operations.

The subject originated in the s with the work of Kleene, Kreisel and others, and has since expanded Theories of computability book many different Cited by: 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. This Theories of computability book and expanded edition of Computability and Complexity Theory comprises essential materials that are the core knowledge in the theory of computation.

The book is self-contained, with a preliminary chapter describing key mathematical concepts and notations and subsequent chapters moving from the qualitative aspects of classical computability theory to the quantitative aspects of complexity theory. Summary: This book gives an introduction to theories of computability from a mathematically sophisticated point of view.

It treats not only 'the' theory of computability, but also a variety of other theories. Each topic is taken from the beginning and developed. This book starts at turing machines and recursive functions. Going through the basic results like the halting problem and rapidly moving on to more advanced topics like creative sets, cylinders and hypersimple sets.

Posts problem (with Friedberg's solution) and Cited by: Enumerability, Decidability, Computability An Introduction to the Theory of Recursive Functions. Authors: Hermes, Hans Show next edition Free Preview.

Buy this book eB40 € price for Spain (gross) Buy eBook ISBN ; Digitally watermarked, DRM-free; Included format: PDF Brand: Springer-Verlag Berlin Heidelberg. Purchase Computability Theory - 1st Edition.

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Chapter Computability Figure Incomplete and inconsistent axiomatic systems. Bertrand Russell discovered a problem with Frege’s system, which is now known as Russell’s paradox.

Suppose R is deﬁned as the set containing all sets that do Russell’s paradox not contain themselves as members. For example, the set of all prime. Book Description. Computability theory originated with the seminal work of Gödel, Church, Turing, Kleene and Post in the s.

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. 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 : with related auxiliary material. This includes web chapters on automata and computability theory, detailed teaching plans for courses based on this book, a draft of all the book’s chapters, and links to other online resources covering related topics.

The book is divided into three parts: Part I: Basic complexity classes. Computability theory, also known as recursion theory, is a branch of mathematical logic, of computer science, and of the theory of computation that originated in the s with the study of computable functions and Turing degrees.

The field has since expanded to include the study of generalized computability and definability. The book is divided into five parts: Computability, Grammars and Automata, Logic, Complexity, and Unsolvability.

Computability theory is introduced in a manner that makes maximum use of previous programming experience, including a "universal" program that takes up less than a page. The number of exercises included has more than tripled.

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 : Springer-Verlag Berlin Heidelberg.

Computability theory originated with the seminal work of Gödel, Church, Turing, Kleene and Post in the s. 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 3/5(2). The book is self-contained, with a preliminary chapter describing key mathematical concepts and notations. Subsequent chapters move from the qualitative aspects of classical computability theory to the quantitative aspects of complexity theory.

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The basic topics of computability theory are Turing computability (including the recursion theorem) and Turing reductions; Sipser considers the latter an "advanced topic" and discusses it for one page.

art of computability: a skill to be practiced, but also important an esthetic sense of beauty and taste in mathematics.

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Covering the basics as well as recent research results, this book provides an introduction to the interface of computability and randomness for graduates and researchers in computability theory, theoretical computer science, and measure theory.

( views) Computability and Complexity from a Programming Perspective by Neil D. Jones - The MIT. Finally, Part V offers a short history of computability theory. The author is a leading authority on the topic and he has taught the subject using the book content over decades, honing it according to experience and feedback from students, lecturers, and researchers around the world.

Turing computability is an outer boundary, and as you show, any theory that requires more power than that surely is irrelevant to any useful definition of human rationality. A slightly stricter boundary is posed by computational complexity, especially in its common “worst case” form.

Theory of Recursive Functions and Effective Computability book. Read 3 reviews from the world's largest community for readers. (Reprint of the edition)4/5.

Computability Cutland's Computability: An Introduction to Recursive Function Theory (Cambridge). Cutland, Nigel J. ().Computability: An Introduction to Recursive Function dge University Press.

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