Skip to main content

Computability Theory

In Order to Read Online or Download Computability Theory Full eBooks in PDF, EPUB, Tuebl and Mobi you need to create a Free account. Get any books you like and read everywhere you want. Fast Download Speed ~ Commercial & Ad Free. We cannot guarantee that every book is in the library!

Computability Theory

Computability Theory Book
Author : Rebecca Weber
Publisher : American Mathematical Soc.
Release : 2012
ISBN : 082187392X
Language : En, Es, Fr & De

GET BOOK

Book Description :

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

Computability Theory Book
Author : S. Barry Cooper
Publisher : CRC Press
Release : 2017-09-06
ISBN : 1351991965
Language : En, Es, Fr & De

GET BOOK

Book Description :

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

Computability Theory Book
Author : Herbert B. Enderton
Publisher : Academic Press
Release : 2010-12-30
ISBN : 9780123849595
Language : En, Es, Fr & De

GET BOOK

Book Description :

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

Turing Computability

Turing Computability Book
Author : Robert I. Soare
Publisher : Springer
Release : 2016-06-20
ISBN : 3642319335
Language : En, Es, Fr & De

GET BOOK

Book Description :

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.

The Foundations of Computability Theory

The Foundations of Computability Theory Book
Author : Borut Robič
Publisher : Springer
Release : 2015-09-14
ISBN : 3662448084
Language : En, Es, Fr & De

GET BOOK

Book Description :

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

Computability Book
Author : Nigel Cutland
Publisher : Cambridge University Press
Release : 1980-06-19
ISBN : 9780521294652
Language : En, Es, Fr & De

GET BOOK

Book Description :

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.

Computability Theory

Computability Theory Book
Author : Neil D. Jones
Publisher : Academic Press
Release : 2014-06-20
ISBN : 1483218481
Language : En, Es, Fr & De

GET BOOK

Book Description :

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

Models of Computation Book
Author : Maribel Fernandez
Publisher : Springer Science & Business Media
Release : 2009-04-14
ISBN : 9781848824348
Language : En, Es, Fr & De

GET BOOK

Book Description :

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

Handbook of Computability Theory Book
Author : E.R. Griffor
Publisher : Elsevier
Release : 1999-10-01
ISBN : 9780080533049
Language : En, Es, Fr & De

GET BOOK

Book Description :

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.

Computability and Complexity Theory

Computability and Complexity Theory Book
Author : Steven Homer,Alan L. Selman
Publisher : Springer Science & Business Media
Release : 2013-03-09
ISBN : 1475735448
Language : En, Es, Fr & De

GET BOOK

Book Description :

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.

Reflexive Structures

Reflexive Structures Book
Author : Luis E. Sanchis
Publisher : Springer Science & Business Media
Release : 2012-12-06
ISBN : 1461238781
Language : En, Es, Fr & De

GET BOOK

Book Description :

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

Computability Theory Book
Author : Paul E. Dunne
Publisher : Prentice Hall
Release : 1991
ISBN : 0987650XXX
Language : En, Es, Fr & De

GET BOOK

Book Description :

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 Theory and Its Applications

Computability Theory and Its Applications Book
Author : Peter Cholak,Steffen Lempp,Manuel Lerman,Richard A. Shore
Publisher : American Mathematical Soc.
Release : 2000
ISBN : 0821819224
Language : En, Es, Fr & De

GET BOOK

Book Description :

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

Theories of Computability Book
Author : Nicholas Pippenger
Publisher : Cambridge University Press
Release : 1997-05-28
ISBN : 9780521553803
Language : En, Es, Fr & De

GET BOOK

Book Description :

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

Computability Theory Semantics and Logic Programming

Computability Theory  Semantics  and Logic Programming Book
Author : Melvin Fitting,Department of Mathematics and Computer Science Lehman College Melvin Fitting
Publisher : Oxford University Press, USA
Release : 1987
ISBN : 0987650XXX
Language : En, Es, Fr & De

GET BOOK

Book Description :

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 Theory

Computability Theory Book
Author : Anonim
Publisher : Unknown
Release : 2010
ISBN : 0987650XXX
Language : En, Es, Fr & De

GET BOOK

Book Description :

Download Computability Theory book written by , available in PDF, EPUB, and Kindle, or read full book online anywhere and anytime. Compatible with any devices.

Computability Enumerability Unsolvability

Computability  Enumerability  Unsolvability Book
Author : S. B. Cooper,T. A. Slaman,S. S. Wainer
Publisher : Cambridge University Press
Release : 1996-01-11
ISBN : 9780521557368
Language : En, Es, Fr & De

GET BOOK

Book Description :

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

Handbook of Computability and Complexity in Analysis

Handbook of Computability and Complexity in Analysis Book
Author : Vasco Brattka,Peter Hertling
Publisher : Springer Nature
Release : 2021-06-04
ISBN : 3030592340
Language : En, Es, Fr & De

GET BOOK

Book Description :

Computable analysis is the modern theory of computability and complexity in analysis that arose out of Turing's seminal work in the 1930s. This was motivated by questions such as: which real numbers and real number functions are computable, and which mathematical tasks in analysis can be solved by algorithmic means? Nowadays this theory has many different facets that embrace topics from computability theory, algorithmic randomness, computational complexity, dynamical systems, fractals, and analog computers, up to logic, descriptive set theory, constructivism, and reverse mathematics. In recent decades computable analysis has invaded many branches of analysis, and researchers have studied computability and complexity questions arising from real and complex analysis, functional analysis, and the theory of differential equations, up to (geometric) measure theory and topology. This handbook represents the first coherent cross-section through most active research topics on the more theoretical side of the field. It contains 11 chapters grouped into parts on computability in analysis; complexity, dynamics, and randomness; and constructivity, logic, and descriptive complexity. All chapters are written by leading experts working at the cutting edge of the respective topic. Researchers and graduate students in the areas of theoretical computer science and mathematical logic will find systematic introductions into many branches of computable analysis, and a wealth of information and references that will help them to navigate the modern research literature in this field.

Logic Foundations of Mathematics and Computability Theory

Logic  Foundations of Mathematics  and Computability Theory Book
Author : Robert E. Butts,Jaakko Hintikka
Publisher : Springer Science & Business Media
Release : 2012-12-06
ISBN : 9401011389
Language : En, Es, Fr & De

GET BOOK

Book Description :

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.

The University of Western Ontario Series in Philosophy of Science

The University of Western Ontario Series in Philosophy of Science Book
Author : Anonim
Publisher : Unknown
Release : 1995
ISBN : 0987650XXX
Language : En, Es, Fr & De

GET BOOK

Book Description :

Download The University of Western Ontario Series in Philosophy of Science book written by , available in PDF, EPUB, and Kindle, or read full book online anywhere and anytime. Compatible with any devices.