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Computability Enumerability Unsolvability


Computability Enumerability Unsolvability
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Computability Enumerability Unsolvability


Computability Enumerability Unsolvability
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Author : S. B. Cooper
language : en
Publisher: Cambridge University Press
Release Date : 1996-01-11

Computability Enumerability Unsolvability written by S. B. Cooper 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 1996-01-11 with Mathematics categories.


The fundamental ideas concerning computation and recursion naturally find their place at the interface between logic and theoretical computer science. The contributions in this book, by leaders in the field, provide a picture of current ideas and methods in the ongoing investigations into the pure mathematical foundations of computability theory. The topics range over computable functions, enumerable sets, degree structures, complexity, subrecursiveness, domains and inductive inference. A number of the articles contain introductory and background material which it is hoped will make this volume an invaluable resource.



Computability Unsolvability


Computability Unsolvability
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Author : Martin Davis
language : en
Publisher: Courier Corporation
Release Date : 1982-01-01

Computability Unsolvability written by Martin Davis and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 1982-01-01 with Mathematics categories.


Classic graduate-level introduction to theory of computability. Discusses general theory of computability, computable functions, operations on computable functions, Turing machines self-applied, unsolvable decision problems, applications of general theory, mathematical logic, Kleene hierarchy, more.



Algebraic Computability And Enumeration Models


Algebraic Computability And Enumeration Models
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Author : Cyrus F. Nourani
language : en
Publisher: CRC Press
Release Date : 2016-02-24

Algebraic Computability And Enumeration Models written by Cyrus F. Nourani and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-02-24 with Mathematics categories.


This book, Algebraic Computability and Enumeration Models: Recursion Theory and Descriptive Complexity, presents new techniques with functorial models to address important areas on pure mathematics and computability theory from the algebraic viewpoint. The reader is first introduced to categories and functorial models, with Kleene algebra examples



The Foundations Of Computability Theory


The Foundations Of Computability Theory
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Author : Borut Robič
language : en
Publisher: Springer
Release Date : 2015-09-14

The Foundations Of Computability Theory written by Borut Robič and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-09-14 with Computers categories.


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 crisis of mathematics in the early twentieth century, and formalism; in Part II he explains classical computability theory, with chapters on the quest for formalization, the Turing Machine, and early successes such as defining incomputable problems, c.e. (computably enumerable) sets, and developing methods for proving incomputability; in Part III he explains relative computability, with chapters on computation with external help, degrees of unsolvability, the Turing hierarchy of unsolvability, the class of degrees of unsolvability, c.e. degrees and the priority method, and the arithmetical hierarchy. This is a gentle introduction from the origins of computability theory up to current research, and it will be of value as a textbook and guide for advanced undergraduate and graduate students and researchers in the domains of computability theory and theoretical computer science.



Business Research Methodology


Business Research Methodology
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Author : TN. Srivastava
language : en
Publisher:
Release Date : 2010

Business Research Methodology written by TN. Srivastava and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010 with categories.




Computability Theory


Computability Theory
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Author : S. Barry Cooper
language : en
Publisher: CRC Press
Release Date : 2017-09-06

Computability Theory written by S. Barry Cooper and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-09-06 with Mathematics categories.


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.



Computability Theory And Its Applications


Computability Theory And Its Applications
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Author : Peter Cholak
language : en
Publisher: American Mathematical Soc.
Release Date : 2000

Computability Theory And Its Applications written by Peter Cholak 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 2000 with Mathematics categories.


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 and Applications, which focused on open problems in computability theory and on some related areas in which the ideas, methods, and/or results of computability theory play a role. Some presentations are narrowly focused; others cover a wider area. Topics included from "pure" computability theory are the computably enumerable degrees (M. Lerman), the computably enumerable sets (P. Cholak, R. Soare), definability issues in the c.e. and Turing degrees (A. Nies, R. Shore) and other degree structures (M. Arslanov, S. Badaev and S. Goncharov, P. Odifreddi, A. Sorbi). The topics involving relations between computability and other areas of logic and mathematics are reverse mathematics and proof theory (D. Cenzer and C. Jockusch, C. Chong and Y. Yang, H. Friedman and S. Simpson), set theory (R. Dougherty and A. Kechris, M. Groszek, T. Slaman) and computable mathematics and model theory (K. Ambos-Spies and A. Kucera, R. Downey and J. Remmel, S. Goncharov and B. Khoussainov, J. Knight, M. Peretyat'kin, A. Shlapentokh).



Handbook Of Computability Theory


Handbook Of Computability Theory
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Author : E.R. Griffor
language : en
Publisher: Elsevier
Release Date : 1999-10-01

Handbook Of Computability Theory written by E.R. Griffor and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999-10-01 with Mathematics categories.


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 little of the elementary theory behind them and aim directly toward an exposition of advanced results. Presentations of the latter sort are in some cases restricted to a short survey of recent results (due to the complexity of the methods and proofs themselves). Hence the variation in level of presentation from chapter to chapter only reflects the conceptual situation itself. One example of this is the collective efforts to develop an acceptable theory of computation on the real numbers. The last two decades has seen at least two new definitions of effective operations on the real numbers.



Theory And Applications Of Models Of Computation


Theory And Applications Of Models Of Computation
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Author : Jin-Yi Cai
language : en
Publisher: Springer
Release Date : 2006-05-05

Theory And Applications Of Models Of Computation written by Jin-Yi Cai and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-05-05 with Computers categories.


This book constitutes the refereed proceedings of the Third International Conference on Theory and Applications of Models of Computation, TAMC 2006, held in Beijing, China, in May 2006. The 75 revised full papers presented together with 7 plenary talks were carefully reviewed and selected from 319 submissions. All major areas in computer science, mathematics (especially logic) and the physical sciences particularly with regard to computation and computability theory are addressed.



Computation And Logic In The Real World


Computation And Logic In The Real World
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Author : S. Barry Cooper
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-06-11

Computation And Logic In The Real World written by S. Barry Cooper 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 2007-06-11 with Computers categories.


This book constitutes the refereed proceedings of the Third International Conference on Computability in Europe, CiE 2007, held in Sienna, Italy, in June 2007. The 50 revised full papers presented together with 36 invited papers were carefully reviewed and selected from 167 submissions.