# Computability Theory

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## Computability Theory

Author | : S. Barry Cooper |

Publsiher | : CRC Press |

Total Pages | : 420 |

Release | : 2017-09-06 |

ISBN 10 | : 1351991965 |

ISBN 13 | : 9781351991964 |

Language | : EN, FR, DE, ES & NL |

**Computability Theory Book Review:**

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

Author | : Rebecca Weber |

Publsiher | : American Mathematical Soc. |

Total Pages | : 203 |

Release | : 2012 |

ISBN 10 | : 082187392X |

ISBN 13 | : 9780821873922 |

Language | : EN, FR, DE, ES & NL |

**Computability Theory Book Review:**

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 theory and an overview of currently active areas of research, such as reverse mathematics and algorithmic randomness. Turing machines and partial recursive functions are explored in detail, and vital tools and concepts including coding, uniformity, and diagonalization are described explicitly. From there the material continues with universal machines, the halting problem, parametrization and the recursion theorem, and thence to computability for sets, enumerability, and Turing reduction and degrees. A few more advanced topics round out the book before the chapter on areas of research. The text is designed to be self-contained, with an entire chapter of preliminary material including relations, recursion, induction, and logical and set notation and operators. That background, along with ample explanation, examples, exercises, and suggestions for further reading, make this book ideal for independent study or courses with few prerequisites.

## Computability Theory

Author | : Herbert B. Enderton |

Publsiher | : Academic Press |

Total Pages | : 192 |

Release | : 2010-12-30 |

ISBN 10 | : 9780123849595 |

ISBN 13 | : 0123849594 |

Language | : EN, FR, DE, ES & NL |

**Computability Theory Book Review:**

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 inclusion of advanced topics not to be found elsewhere in the literature at this level. The text 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 way. Frequent historical information presented throughout More extensive motivation for each of the topics than other texts currently available Connects with topics not included in other textbooks, such as complexity theory

## The Foundations of Computability Theory

Author | : Borut Robič |

Publsiher | : Springer |

Total Pages | : 331 |

Release | : 2015-09-14 |

ISBN 10 | : 3662448084 |

ISBN 13 | : 9783662448083 |

Language | : EN, FR, DE, ES & NL |

**The Foundations of Computability Theory Book Review:**

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.

## Computability

Author | : Nigel Cutland |

Publsiher | : Cambridge University Press |

Total Pages | : 251 |

Release | : 1980-06-19 |

ISBN 10 | : 9780521294652 |

ISBN 13 | : 0521294657 |

Language | : EN, FR, DE, ES & NL |

**Computability Book Review:**

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.

## Turing Computability

Author | : Robert I. Soare |

Publsiher | : Springer |

Total Pages | : 263 |

Release | : 2016-06-20 |

ISBN 10 | : 3642319335 |

ISBN 13 | : 9783642319334 |

Language | : EN, FR, DE, ES & NL |

**Turing Computability Book Review:**

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

Author | : Neil D. Jones |

Publsiher | : Academic Press |

Total Pages | : 168 |

Release | : 2014-06-20 |

ISBN 10 | : 1483218481 |

ISBN 13 | : 9781483218489 |

Language | : EN, FR, DE, ES & NL |

**Computability Theory Book Review:**

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 effective process so that a clear understanding of the effective computability of partial and total functions is obtained. This text then introduces a formal development of the equivalence of Turing machine computability, enumerability, and decidability with other formulations. Other chapters consider the formulas of the predicate calculus, systems of recursion equations, and Post's production systems. This book discusses as well the fundamental properties of the partial recursive functions and the recursively enumerable sets. The final chapter deals with different formulations of the basic ideas of computability that are equivalent to Turing-computability. This book is a valuable resource for undergraduate or graduate students.

## Models of Computation

Author | : Maribel Fernandez |

Publsiher | : Springer Science & Business Media |

Total Pages | : 184 |

Release | : 2009-04-14 |

ISBN 10 | : 9781848824348 |

ISBN 13 | : 1848824343 |

Language | : EN, FR, DE, ES & NL |

**Models of Computation Book Review:**

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.

## Handbook of Computability Theory

Author | : E.R. Griffor |

Publsiher | : Elsevier |

Total Pages | : 724 |

Release | : 1999-10-01 |

ISBN 10 | : 9780080533049 |

ISBN 13 | : 0080533043 |

Language | : EN, FR, DE, ES & NL |

**Handbook of Computability Theory Book Review:**

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.

## Reflexive Structures

Author | : Luis E. Sanchis |

Publsiher | : Springer Science & Business Media |

Total Pages | : 233 |

Release | : 2012-12-06 |

ISBN 10 | : 1461238781 |

ISBN 13 | : 9781461238782 |

Language | : EN, FR, DE, ES & NL |

**Reflexive Structures Book Review:**

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 concrete theory conceptually organized around Church's thesis. The book develops the important structures in recursive function theory: closure properties, reflexivity, enumeration, and hyperenumeration. Of particular interest is the treatment of recursion, which is considered from two different points of view: via the minimal fixed point theory of continuous transformations, and via the well known stack algorithm. Reflexive Structures is intended as an introduction to the general theory of computability. It can be used as a text or reference in senior undergraduate and first year graduate level classes in computer science or mathematics.

## Computability Theory

Author | : Herbert B. Enderton |

Publsiher | : Unknown |

Total Pages | : 174 |

Release | : 2011 |

ISBN 10 | : 9780123849588 |

ISBN 13 | : 0123849586 |

Language | : EN, FR, DE, ES & NL |

**Computability Theory Book Review:**

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 inclusion of advanced topics not to be found elsewhere in the literature at this level. The text 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 way. Frequent historical information presented throughout More extensive motivation for each of the topics than other texts currently available Connects with topics not included in other textbooks, such as complexity theory

## Computability and Complexity Theory

Author | : Steven Homer,Alan L. Selman |

Publsiher | : Springer Science & Business Media |

Total Pages | : 195 |

Release | : 2013-03-09 |

ISBN 10 | : 1475735448 |

ISBN 13 | : 9781475735444 |

Language | : EN, FR, DE, ES & NL |

**Computability and Complexity Theory Book Review:**

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 Theory and Its Applications

Author | : Peter Cholak,Steffen Lempp,Manuel Lerman,Richard A. Shore |

Publsiher | : American Mathematical Soc. |

Total Pages | : 320 |

Release | : 2000 |

ISBN 10 | : 0821819224 |

ISBN 13 | : 9780821819227 |

Language | : EN, FR, DE, ES & NL |

**Computability Theory and Its Applications Book Review:**

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 Joint Summer Conference on Computability Theory and Applications held at the University of Colorado (Boulder). The conference 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).

## Theories of Computability

Author | : Nicholas Pippenger |

Publsiher | : Cambridge University Press |

Total Pages | : 251 |

Release | : 1997-05-28 |

ISBN 10 | : 9780521553803 |

ISBN 13 | : 0521553806 |

Language | : EN, FR, DE, ES & NL |

**Theories of Computability Book Review:**

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

## Computability Theory

Author | : Paul E. Dunne |

Publsiher | : Prentice Hall |

Total Pages | : 150 |

Release | : 1991 |

ISBN 10 | : |

ISBN 13 | : UOM:39015021884823 |

Language | : EN, FR, DE, ES & NL |

**Computability Theory Book Review:**

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.

## Computability Complexity and Languages

Author | : Martin Davis,Ron Sigal,Elaine J. Weyuker |

Publsiher | : Academic Press |

Total Pages | : 609 |

Release | : 1994 |

ISBN 10 | : 0122063821 |

ISBN 13 | : 9780122063824 |

Language | : EN, FR, DE, ES & NL |

**Computability Complexity and Languages Book Review:**

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.

## Logic Foundations of Mathematics and Computability Theory

Author | : Robert E. Butts,Jaakko Hintikka |

Publsiher | : Springer Science & Business Media |

Total Pages | : 416 |

Release | : 2012-12-06 |

ISBN 10 | : 9401011389 |

ISBN 13 | : 9789401011389 |

Language | : EN, FR, DE, ES & NL |

**Logic Foundations of Mathematics and Computability Theory Book Review:**

The Fifth International Congress of Logic, Methodology and Philosophy of Science was held at the University of Western Ontario, London, Canada, 27 August to 2 September 1975. The Congress was held under the auspices of the International Union of History and Philosophy of Science, Division of Logic, Methodology and Philosophy of Science, and was sponsored by the National Research Council of Canada and the University of Western Ontario. As those associated closely with the work of the Division over the years know well, the work undertaken by its members varies greatly and spans a number of fields not always obviously related. In addition, the volume of work done by first rate scholars and scientists in the various fields of the Division has risen enormously. For these and related reasons it seemed to the editors chosen by the Divisional officers that the usual format of publishing the proceedings of the Congress be abandoned in favour of a somewhat more flexible, and hopefully acceptable, method of pre sentation. Accordingly, the work of the invited participants to the Congress has been divided into four volumes appearing in the University of Western Ontario Series in Philosophy of Science. The volumes are entitled, Logic, Foundations of Mathematics and Computability Theory, Foun dational Problems in the Special Sciences, Basic Problems in Methodol ogy and Linguistics, and Historical and Philosophical Dimensions of Logic, Methodology and Philosophy of Science.

## Computability Theory

Author | : Anonim |

Publsiher | : Unknown |

Total Pages | : 329 |

Release | : 2010 |

ISBN 10 | : |

ISBN 13 | : OCLC:733447333 |

Language | : EN, FR, DE, ES & NL |

**Computability Theory Book Review:**

## Computability Theory Semantics and Logic Programming

Author | : Melvin Fitting,Department of Mathematics and Computer Science Lehman College Melvin Fitting |

Publsiher | : Oxford University Press, USA |

Total Pages | : 198 |

Release | : 1987 |

ISBN 10 | : |

ISBN 13 | : UOM:39015011743922 |

Language | : EN, FR, DE, ES & NL |

**Computability Theory Semantics and Logic Programming Book Review:**

This book describes computability theory and provides an extensive treatment of data structures and program correctness. It makes accessible some of the author's work on generalized recursion theory, particularly the material on the logic programming language PROLOG, which is currently of great interest. Fitting considers the relation of PROLOG logic programming to the LISP type of language.

## Computability Enumerability Unsolvability

Author | : S. B. Cooper,T. A. Slaman,S. S. Wainer |

Publsiher | : Cambridge University Press |

Total Pages | : 347 |

Release | : 1996-01-11 |

ISBN 10 | : 9780521557368 |

ISBN 13 | : 0521557364 |

Language | : EN, FR, DE, ES & NL |

**Computability Enumerability Unsolvability Book Review:**

Provides a picture of current ideas and methods in the ongoing investigations into the pure mathematical foundations of computability theory.