Handbook of Computability Theory

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.

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  • Author : E.R. Griffor
  • Publisher : Elsevier
  • Pages : 724 pages
  • ISBN : 9780080533049
  • Rating : 4/5 from 21 reviews
CLICK HERE TO GET THIS BOOKHandbook of Computability Theory

Handbook of Computability Theory

Handbook of Computability Theory
  • Author : E.R. Griffor
  • Publisher : Elsevier
  • Release : 01 October 1999
GET THIS BOOKHandbook of Computability Theory

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

Computability Theory

Computability Theory
  • Author : S. Barry Cooper
  • Publisher : CRC Press
  • Release : 06 September 2017
GET THIS BOOKComputability Theory

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

Computability Theory

Computability Theory
  • Author : Herbert B. Enderton
  • Publisher : Unknown Publisher
  • Release : 29 May 2022
GET THIS BOOKComputability Theory

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

Turing Computability

Turing Computability
  • Author : Robert I. Soare
  • Publisher : Springer
  • Release : 20 June 2016
GET THIS BOOKTuring Computability

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

The Foundations of Computability Theory

The Foundations of Computability Theory
  • Author : Borut Robič
  • Publisher : Springer Nature
  • Release : 13 November 2020
GET THIS BOOKThe Foundations of Computability Theory

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

Computability Theory

Computability Theory
  • Author : Rebecca Weber
  • Publisher : American Mathematical Soc.
  • Release : 29 May 2022
GET THIS BOOKComputability Theory

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

Computability Theory

Computability Theory
  • Author : Herbert B. Enderton
  • Publisher : Academic Press
  • Release : 30 December 2010
GET THIS BOOKComputability Theory

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

Computability Theory

Computability Theory
  • Author : Neil D. Jones
  • Publisher : Academic Press
  • Release : 20 June 2014
GET THIS BOOKComputability Theory

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

Computability Theory and Its Applications

Computability Theory and Its Applications
  • Author : Peter Cholak,Steffen Lempp,Manuel Lerman,Richard A. Shore
  • Publisher : American Mathematical Soc.
  • Release : 29 May 2022
GET THIS BOOKComputability Theory and Its Applications

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/

Logic, Foundations of Mathematics, and Computability Theory

Logic, Foundations of Mathematics, and Computability Theory
  • Author : Robert E. Butts,Jaakko Hintikka
  • Publisher : Springer Science & Business Media
  • Release : 06 December 2012
GET THIS BOOKLogic, Foundations of Mathematics, and Computability Theory

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,

Computability

Computability
  • Author : Nigel Cutland
  • Publisher : Cambridge University Press
  • Release : 19 June 1980
GET THIS BOOKComputability

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.

Models of Computation

Models of Computation
  • Author : Maribel Fernandez
  • Publisher : Springer Science & Business Media
  • Release : 14 April 2009
GET THIS BOOKModels of Computation

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

Computability and Complexity Theory

Computability and Complexity Theory
  • Author : Steven Homer,Alan L. Selman
  • Publisher : Springer Science & Business Media
  • Release : 09 December 2011
GET THIS BOOKComputability and Complexity Theory

This revised and extensively expanded edition of Computability and Complexity Theory comprises essential materials that are core knowledge in the theory of computation. The book is self-contained, with a preliminary chapter describing key mathematical concepts and notations. Subsequent chapters move from the qualitative aspects of classical computability theory to the quantitative aspects of complexity theory. Dedicated chapters on undecidability, NP-completeness, and relative computability focus on the limitations of computability and the distinctions between feasible and intractable. Substantial new content in