Computable Functions
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Computable Functions
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Author : Nikolai Konstantinovich Vereshchagin
language : en
Publisher: American Mathematical Soc.
Release Date : 2003
Computable Functions written by Nikolai Konstantinovich Vereshchagin and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003 with Mathematics categories.
Based on the lectures for undergraduates at Moscow State University, this book presents a lively and concise introduction to the central facts and basic notions of the general theory of computation. It begins with the definition of a computable function and an algorithm, and discusses decidability, enumerability, universal functions, numberings and their properties, the fixed point theorem, arithmetical hierarchy, oracle computations, and degrees.
Computability
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Author : Nigel Cutland
language : en
Publisher: Cambridge University Press
Release Date : 1980-06-19
Computability written by Nigel Cutland and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1980-06-19 with Computers categories.
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.
Computable Structure Theory
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Author : Antonio Montalbán
language : en
Publisher: Cambridge University Press
Release Date : 2021-06-24
Computable Structure Theory written by Antonio Montalbán and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-06-24 with Mathematics categories.
Presents main results and techniques in computable structure theory together in a coherent framework for the first time in 20 years.
Recursively Enumerable Sets And Degrees
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Author : Robert I. Soare
language : en
Publisher: Springer Science & Business Media
Release Date : 1999-11-01
Recursively Enumerable Sets And Degrees written by Robert I. Soare and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999-11-01 with Mathematics categories.
..."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
Computability And Complexity
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Author : Neil D. Jones
language : en
Publisher: MIT Press
Release Date : 1997
Computability And Complexity written by Neil D. Jones and has been published by MIT Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997 with Computers categories.
Computability and complexity theory should be of central concern to practitioners as well as theorists. Unfortunately, however, the field is known for its impenetrability. Neil Jones's goal as an educator and author is to build a bridge between computability and complexity theory and other areas of computer science, especially programming. In a shift away from the Turing machine- and G�del number-oriented classical approaches, Jones uses concepts familiar from programming languages to make computability and complexity more accessible to computer scientists and more applicable to practical programming problems. According to Jones, the fields of computability and complexity theory, as well as programming languages and semantics, have a great deal to offer each other. Computability and complexity theory have a breadth, depth, and generality not often seen in programming languages. The programming language community, meanwhile, has a firm grasp of algorithm design, presentation, and implementation. In addition, programming languages sometimes provide computational models that are more realistic in certain crucial aspects than traditional models. New results in the book include a proof that constant time factors do matter for its programming-oriented model of computation. (In contrast, Turing machines have a counterintuitive "constant speedup" property: that almost any program can be made to run faster, by any amount. Its proof involves techniques irrelevant to practice.) Further results include simple characterizations in programming terms of the central complexity classes PTIME and LOGSPACE, and a new approach to complete problems for NLOGSPACE, PTIME, NPTIME, and PSPACE, uniformly based on Boolean programs. Foundations of Computing series
Computability And Complexity In Analysis
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Author : Jens Blanck
language : en
Publisher: Springer
Release Date : 2003-06-29
Computability And Complexity In Analysis written by Jens Blanck and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-06-29 with Computers categories.
The workshop on Computability and Complexity in Analysis, CCA 2000, was hosted by the Department of Computer Science of the University of Wales Swansea, September 17{19, 2000. It was the fourth workshop in a successful series of workshops: CCA’95 in Hagen, Germany, CCA’96 in Trier, Germany, and CCA’98 in Brno, Czech Republic. About 40 participants from the countries United Kingdom, Germany, Japan, Italy, Russia, France, Denmark, Greece, and Ireland contributed to the success of this meeting. Altogether, 28 talkswere p- sented in Swansea. These proceedings include 23 papers which represent a cro- section through recent research on computability and complexity in analysis. The workshop succeeded in bringing together people interested in computability and complexity aspects of analysis and in exploring connections with nume- cal methods, physics and, of course, computer science. It was rounded o by a number of talks and papers on exact computer arithmetic and by a competition of v e implemented systems. A report on this competition has been included in these proceedings. We would like to thank the authors for their contributions and the referees for their careful work, and we hope for further inspiring and constructive meetings of the same kind. April 2001 Jens Blanck Vasco Brattka Peter Hertling Organization CCA2000was hosted by the Department of Computer Science of the University of Wales Swansea and took place on September 17{19, 2000.
Computability
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Author : Douglas S. Bridges
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Computability written by Douglas S. Bridges and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
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 theorem and the recursion theorem, and provides a systematic account of Blum's complexity theory as well as an introduction to the theory of computable real numbers and functions. The book is intended as a university text, but it may also be used for self-study; appropriate exercises and solutions are included.
Computability And Randomness
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Author : André Nies
language : en
Publisher: OUP Oxford
Release Date : 2012-03-29
Computability And Randomness written by André Nies and has been published by OUP Oxford this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-03-29 with Philosophy categories.
The interplay between computability and randomness has been an active area of research in recent years, reflected by ample funding in the USA, numerous workshops, and publications on the subject. The complexity and the randomness aspect of a set of natural numbers are closely related. Traditionally, computability theory is concerned with the complexity aspect. However, computability theoretic tools can also be used to introduce mathematical counterparts for the intuitive notion of randomness of a set. Recent research shows that, conversely, concepts and methods originating from randomness enrich computability theory. The book covers topics such as lowness and highness properties, Kolmogorov complexity, betting strategies and higher computability. Both the basics and recent research results are desribed, providing a very readable introduction to the exciting interface of computability and randomness for graduates and researchers in computability theory, theoretical computer science, and measure theory.
Fundamentals Of Computation Theory
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Author : Olaf Owe
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-08-09
Fundamentals Of Computation Theory written by Olaf Owe and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-08-09 with Computers categories.
This book constitutes the refereed proceedings of the 18th International Symposium Fundamentals of Computation Theory, FCT 2011, held in Oslo, Norway, in August 2011. The 28 revised full papers presented were carefully reviewed and selected from 78 submissions. FCT 2011 focused on algorithms, formal methods, and emerging fields, such as ad hoc, dynamic and evolving systems; algorithmic game theory; computational biology; foundations of cloud computing and ubiquitous systems; and quantum computation.
Computability Complexity And Languages
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Author : Martin Davis
language : en
Publisher: Academic Press
Release Date : 1994-02-03
Computability Complexity And Languages written by Martin Davis and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994-02-03 with Computers categories.
This introductory text covers the key areas of computer science, including recursive function theory, formal languages, and automata. Additions to the second edition include: extended exercise sets, which vary in difficulty; expanded section on recursion theory; new chapters on program verification and logic programming; updated references and examples throughout.