Search Results: computability-theory-an-introduction-to-recursion-theory

Computability Theory

An Introduction to Recursion Theory

Author: Herbert B. Enderton

Publisher: Academic Press

ISBN: 9780123849595

Category: Computers

Page: 192

View: 829

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

An Introduction to Recursive Function Theory

Author: Nigel Cutland

Publisher: Cambridge University Press

ISBN: 9780521294652

Category: Computers

Page: 251

View: 4622

This introduction to recursive theory computability begins with a mathematical characterization of computable functions, develops the mathematical theory and includes a full discussion of noncomputability and undecidability. Later chapters move on to more advanced topics such as degrees of unsolvability and Gödel's Incompleteness Theorem.

Computability Theory

An Introduction to Recursion Theory

Author: Herbert B. Enderton

Publisher: N.A

ISBN: 9780123849588

Category: Computers

Page: 174

View: 1536

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

Reflexive Structures

An Introduction to Computability Theory

Author: Luis E. Sanchis

Publisher: Springer Science & Business Media

ISBN: 1461238781

Category: Mathematics

Page: 233

View: 8675

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.

Aufzählbarkeit Entscheidbarkeit Berechenbarkeit

Einführung in die Theorie der rekursiven Funktionen

Author: Hans Hermes

Publisher: Springer-Verlag

ISBN: 3642953271

Category: Mathematics

Page: 260

View: 3769

Enumerability, Decidability, Computability

An Introduction to the Theory of Recursive Functions

Author: Hans Hermes

Publisher: Springer

ISBN: 3662116863

Category: Mathematics

Page: 245

View: 6628

The task of developing algorithms to solve problems has always been considered by mathematicians to be an especially interesting and im portant one. Normally an algorithm is applicable only to a narrowly limited group of problems. Such is for instance the Euclidean algorithm, which determines the greatest common divisor of two numbers, or the well-known procedure which is used to obtain the square root of a natural number in decimal notation. The more important these special algorithms are, all the more desirable it seems to have algorithms of a greater range of applicability at one's disposal. Throughout the centuries, attempts to provide algorithms applicable as widely as possible were rather unsuc cessful. It was only in the second half of the last century that the first appreciable advance took place. Namely, an important group of the inferences of the logic of predicates was given in the form of a calculus. (Here the Boolean algebra played an essential pioneer role. ) One could now perhaps have conjectured that all mathematical problems are solvable by algorithms. However, well-known, yet unsolved problems (problems like the word problem of group theory or Hilbert's tenth problem, which considers the question of solvability of Diophantine equations) were warnings to be careful. Nevertheless, the impulse had been given to search for the essence of algorithms. Leibniz already had inquired into this problem, but without success.

Models of Computation

An Introduction to Computability Theory

Author: Maribel Fernandez

Publisher: Springer Science & Business Media

ISBN: 9781848824348

Category: Computers

Page: 184

View: 8899

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

Author: Neil D. Jones

Publisher: Academic Press

ISBN: 1483218481

Category: Mathematics

Page: 168

View: 6235

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.

A Recursive Introduction to the Theory of Computation

Author: Carl Smith

Publisher: Springer Science & Business Media

ISBN: 1441985018

Category: Computers

Page: 148

View: 9009

The aim of this textbook is to present an account of the theory of computation. After introducing the concept of a model of computation and presenting various examples, the author explores the limitations of effective computation via basic recursion theory. Self-reference and other methods are introduced as fundamental and basic tools for constructing and manipulating algorithms. From there the book considers the complexity of computations and the notion of a complexity measure is introduced. Finally, the book culminates in considering time and space measures and in classifying computable functions as being either feasible or not. The author assumes only a basic familiarity with discrete mathematics and computing, making this textbook ideal for a graduate-level introductory course. It is based on many such courses presented by the author and so numerous exercises are included. In addition, the solutions to most of these exercises are provided.

The Foundations of Computability Theory

Author: Borut Robič

Publisher: Springer

ISBN: 3662448084

Category: Computers

Page: 331

View: 7692

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.

Systems that Learn

An Introduction to Learning Theory

Author: Sanjay Jain, MD, MBA,Sanjay Jain,Daniel Osherson,James S. Royer,Arun Sharma

Publisher: MIT Press

ISBN: 9780262100779

Category: Computers

Page: 317

View: 7310

Formal learning theory is one of several mathematical approaches to the study of intelligent adaptation to the environment. The analysis developed in this book is based on a number theoretical approach to learning and uses the tools of recursive-function theory to understand how learners come to an accurate view of reality. This revised and expanded edition of a successful text provides a comprehensive, self-contained introduction to the concepts and techniques of the theory. Exercises throughout the text provide experience in the use of computational arguments to prove facts about learning.

Computability Theory

Author: S. Barry Cooper

Publisher: CRC Press

ISBN: 1351991965

Category: Mathematics

Page: 420

View: 2312

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.

An introduction to the general theory of algorithms

Author: M. Machtey,Paul Young

Publisher: North Holland

ISBN: N.A

Category: Mathematics

Page: 264

View: 5081

An Introduction to Mathematical Logic

Author: Richard E. Hodel

Publisher: Courier Corporation

ISBN: 0486497852

Category: Mathematics

Page: 491

View: 403

This comprehensive overview ofmathematical logic is designedprimarily for advanced undergraduatesand graduate studentsof mathematics. The treatmentalso contains much of interest toadvanced students in computerscience and philosophy. Topics include propositional logic;first-order languages and logic; incompleteness, undecidability,and indefinability; recursive functions; computability;and Hilbert’s Tenth Problem.Reprint of the PWS Publishing Company, Boston, 1995edition.

Theories of Computability

Author: Nicholas Pippenger

Publisher: Cambridge University Press

ISBN: 9780521553803

Category: Computers

Page: 251

View: 6118

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

Abstract Recursion and Intrinsic Complexity

Author: Yiannis N. Moschovakis

Publisher: Cambridge University Press

ISBN: 110841558X

Category: Computers

Page: 283

View: 482

Presents a new framework for the complexity of algorithms, for all readers interested in the theory of computation.

Real and Abstract Analysis

A modern treatment of the theory of functions of a real variable

Author: Edwin Hewitt,Karl Stromberg

Publisher: Springer-Verlag

ISBN: 3662297949

Category: Mathematics

Page: 476

View: 6457

Der Turing Omnibus

Eine Reise durch die Informatik mit 66 Stationen

Author: A.K. Dewdney

Publisher: Springer-Verlag

ISBN: 3642788726

Category: Computers

Page: 496

View: 5021

Der Turing Omnibus macht in 66 exzellent geschriebenen Beiträgen Station bei den interessantesten Themen aus der Informatik, der Computertechnologie und ihren Anwendungen.

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