Theories Of Computability
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Theories Of Computability
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Author : Nicholas Pippenger
language : en
Publisher: Cambridge University Press
Release Date : 1997-05-28
Theories Of Computability written by Nicholas Pippenger 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 1997-05-28 with Computers categories.
A mathematically sophisticated introduction to Turing's theory, Boolean functions, automata, and formal languages.
Turing Computability
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Author : Robert I. Soare
language : en
Publisher: Springer
Release Date : 2016-06-20
Turing Computability written by Robert I. Soare and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-06-20 with Computers categories.
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.
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 And Complexity Theory
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Author : Steven Homer
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09
Computability And Complexity Theory written by Steven Homer 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 2013-03-09 with Computers categories.
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 theory which forms the basis for complexity theory. This has the pedagogical advantage that students learn a qualitative subject before advancing to a quantitative one. Since this is a graduate course, students should have some knowledge of such topics as automata theory, formal languages, computability theory, or complexity theory.
Computability Complexity And Languages
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Author : Martin D. Davis
language : en
Publisher: Academic Press
Release Date : 2014-05-10
Computability Complexity And Languages written by Martin D. 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 2014-05-10 with Reference categories.
Computability, Complexity, and Languages: Fundamentals of Theoretical Computer Science provides an introduction to the various aspects of theoretical computer science. Theoretical computer science is the mathematical study of models of computation. This text is composed of five parts encompassing 17 chapters, and begins with an introduction to the use of proofs in mathematics and the development of computability theory in the context of an extremely simple abstract programming language. The succeeding parts demonstrate the performance of abstract programming language using a macro expansion technique, along with presentations of the regular and context-free languages. Other parts deal with the aspects of logic that are important for computer science and the important theory of computational complexity, as well as the theory of NP-completeness. The closing part introduces the advanced recursion and polynomial-time computability theories, including the priority constructions for recursively enumerable Turing degrees. This book is intended primarily for undergraduate and graduate mathematics students.
Models Of Computation
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Author : Maribel Fernandez
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-04-14
Models Of Computation written by Maribel Fernandez 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 2009-04-14 with Computers categories.
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 of computation is provided. Divided into two parts, the first highlights the traditional computation models used in the first studies on computability: - Automata and Turing Machines; - Recursive functions and the Lambda-Calculus; - Logic-based computation models. and the second part covers object-oriented and interaction-based models. There is also a chapter on concurrency, and a final chapter on emergent computation models inspired by quantum mechanics. At the end of each chapter there is a discussion on the use of computation models in the design of programming languages.
Computability Theory An Introduction
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Author : Neil D. Jones
language : en
Publisher:
Release Date : 1973
Computability Theory An Introduction written by Neil D. Jones and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1973 with Mathematics categories.
The Foundations Of Computability Theory
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Author : Borut Robič
language : en
Publisher: Springer Nature
Release Date : 2020-11-13
The Foundations Of Computability Theory written by Borut Robič and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-11-13 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. Finally, in the new Part IV the author revisits the computability (Church-Turing) thesis in greater detail. He offers a systematic and detailed account of its origins, evolution, and meaning, he describes more powerful, modern versions of the thesis, and he discusses recent speculative proposals for new computing paradigms such as hypercomputing. 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. This new edition is completely revised, with almost one hundred pages of new material. In particular the author applied more up-to-date, more consistent terminology, and he addressed some notational redundancies and minor errors. He developed a glossary relating to computability theory, expanded the bibliographic references with new entries, and added the new part described above and other new sections.
Computability Theory
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Author : Paul E. Dunne
language : en
Publisher: Prentice Hall
Release Date : 1991
Computability Theory written by Paul E. Dunne and has been published by Prentice Hall this book supported file pdf, txt, epub, kindle and other format this book has been release on 1991 with Computers categories.
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.
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.