An Introduction to Recursive Function Theory

Author: Nigel Cutland

Publisher: Cambridge University Press

ISBN: 9780521294652

Category: Computers

Page: 251

View: 7490

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: Academic Press

ISBN: 9780123849595

Category: Computers

Page: 192

View: 558

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

Enumerability, Decidability, Computability

An Introduction to the Theory of Recursive Functions

Author: Hans Hermes

Publisher: Springer

ISBN: 3662116863

Category: Mathematics

Page: 245

View: 1806

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.

Reflexive Structures

An Introduction to Computability Theory

Author: Luis E. Sanchis

Publisher: Springer Science & Business Media

ISBN: 1461238781

Category: Mathematics

Page: 233

View: 9784

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.

A Recursive Introduction to the Theory of Computation

Author: Carl Smith

Publisher: Springer Science & Business Media

ISBN: 1441985018

Category: Computers

Page: 148

View: 2795

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.

An Introduction to Functional Programming Through Lambda Calculus

Author: Greg Michaelson

Publisher: Courier Corporation

ISBN: 0486280292

Category: Mathematics

Page: 336

View: 8053

Well-respected text for computer science students provides an accessible introduction to functional programming. Cogent examples illuminate the central ideas, and numerous exercises offer reinforcement. Includes solutions. 1989 edition.

An Introduction to Formal Languages and Machine Computation

Author: Song Y. Yan

Publisher: World Scientific

ISBN: 9789810234225

Category: Computers

Page: 400

View: 6505

This book provides a concise and modern introduction to Formal Languages and Machine Computation, a group of disparate topics in the theory of computation, which includes formal languages, automata theory, turing machines, computability, complexity, number-theoretic computation, public-key cryptography, and some new models of computation, such as quantum and biological computation. As the theory of computation is a subject based on mathematics, a thorough introduction to a number of relevant mathematical topics, including mathematical logic, set theory, graph theory, modern abstract algebra, and particularly number theory, is given in the first chapter of the book. The book can be used either as a textbook for an undergraduate course, for a first-year graduate course, or as a basic reference in the field.

Models of Computation

An Introduction to Computability Theory

Author: Maribel Fernandez

Publisher: Springer Science & Business Media

ISBN: 9781848824348

Category: Computers

Page: 184

View: 8967

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.

Die spezielle Relativitätstheorie

M.I.T. Einführungskurs Physik

Author: Anthony P. French

Publisher: Springer-Verlag

ISBN: 332290122X

Category: Science

Page: 288

View: 4943

Das Education Research Center am M.I. T. (früher: Science Teaching Center) befaßt sich mit Verbesserungen des Lehrplanes, mit dem Lehr- und Lernprozeß sowie mit Unterrichtshilfen, vor allem für die unteren Semester. Das Center wurde im Jahre 1960 vom M.I. T. geschaffen. Sein erster Direktor war der verstorbene Professor Francis L. Friedman. Seit 1961 wurde das Center hauptsächlich von der National Science Foundation unterstützt; großzügige Hilfe wurde auch von den folgenden Fonds gewährt: Kettering Foundation, Shell Companies Foundation, Victoria Foundation, W. T. Grant Foundation und Bing Foundation. Die M.I.T.-Reihe: Einführung ist die Physik (Introductory Physics Series) ist ein direktes Resultat der Arbeit des Centers. Die Reihe wird aus einer Anzahl kurzgefaßter Einführungswerke bestehen, die die wichtigsten Gebiete der Physik behandeln werden. Es soll dabei der wechselseitige Einfluß von Experiment und Intuition bei der Aufstellung physikalischer Theorien betont werden. Die Bücher der Reihe sind als Grundlage für eine Auswahl von Einflihrungskursen gedacht, beginnend mit den Werken, in denen vor allem die klassische Physik behandelt wird, bis zu jenen, dieThemen der Atom- und Quantenphysik behandeln. Die einzelnen Bände sollen in Niveau und Behandlungsweise ihrer Themen zwar ein heitlich sein, sind jedoch nicht als untrennbare Einheit anzusehen; im Gegenteil. Eswurde getrachtet, daß jedes Buch in vernünftigem Maße eine Einheit für sich ist und als individuelle Komponente in den Aufbau eines Kurses einbezogen werden kann .

An Early History of Recursive Functions and Computability

From Gödel to Turing

Author: Rod Adams

Publisher: Docent Press

ISBN: 0983700400

Category: Computable functions

Page: 297

View: 8711

Traces the development of recursive functions from their origins in the late nineteenth century to the mid-1930s, with particular emphasis on the work and influence of Kurt Gödel.

Philosophy and Computing

An Introduction

Author: Luciano Floridi

Publisher: Routledge

ISBN: 1134679599

Category: Philosophy

Page: 256

View: 7331

Philosophy and Computing explores each of the following areas of technology: the digital revolution; the computer; the Internet and the Web; CD-ROMs and Mulitmedia; databases, textbases, and hypertexts; Artificial Intelligence; the future of computing. Luciano Floridi shows us how the relationship between philosophy and computing provokes a wide range of philosophical questions: is there a philosophy of information? What can be achieved by a classic computer? How can we define complexity? What are the limits of quantam computers? Is the Internet an intellectual space or a polluted environment? What is the paradox in the Strong Artificial Intlligence program? Philosophy and Computing is essential reading for anyone wishing to fully understand both the development and history of information and communication technology as well as the philosophical issues it ultimately raises.

Mathematische Logik

Author: Martin Ziegler

Publisher: Springer-Verlag

ISBN: 3034606524

Category: Mathematics

Page: 116

View: 4187

Dieses Buch bietet eine Einführung in die verschiedenen Aspekte der mathematischen Logik. Nach dem Praedikatenkalkül und seinen Anwendungen auf die Anfänge der künstlichen Intelligenz stellt der Autor die Mengenlehre axiomatisch dar. Im dritten und vierten Teil führt er die Grundbegriffe der Berechenbarkeitstheorie und die Hierarchie der Teilmengen ein, um schließlich die Gödelschen Unvollständigkeitssätze zu beweisen. Dieser Band zeichnet sich durch einen klaren Schreibstil aus und enthält zahlreiche Übungsaufgaben.

An Introduction to Gödel's Theorems

Author: Peter Smith

Publisher: Cambridge University Press

ISBN: 1107022843

Category: Mathematics

Page: 406

View: 2350

A clear and accessible treatment of Gödel's famous, intriguing, but much misunderstood incompleteness theorems, extensively revised in a second edition.

Proceedings of the Fifth International Congress on Mathematical Education

Author: CARASS

Publisher: Springer Science & Business Media

ISBN: 147574238X

Category: Juvenile Nonfiction

Page: 401

View: 3223

International Congresses on Mathematical Education (ICMEs), under the auspices of the International Commission on Mathematical Instruction, are held every four years. Previous Congresses have been held in France (Lyons), England (Exeter), the Federal Republic of Germany (Karlsruhe), and the United States of America (Berkeley). The Fifth International Congress on Mathematical Education (lCME 5) was held in Adelaide, Australia, from August 24-30, 1984. More than 1800 participants from over 70 countries participated in the Congress, while some additional 200 people attended social functions and excursions. The program for ICME 5 was planned and structured by an International Program Committee, and implemented by the National Program Committee in Australia. For the main body of the program, Chief Organisers, assisted by Australian Coordinators, were invited to plan and prepare the individual components of the program which addressed a wide range of topics and interest areas. Each of these teams involved many individuals from around the world in the detailed planning and preparation of the working sessions for their area of program responsibility. For the actual working sessions at the Congress, the smallest group had some 60 members, while the largest had well over 300. In addition to the working sessions, there were three major plenary addresses, several specially invited presentations, and over 420 individual papers in the form of short communications, either as posters or brief talks.

Economics of Structural and Technological Change

Author: Cristiano Antonelli,Nicola De Liso

Publisher: Routledge

ISBN: 1134716621

Category: Business & Economics

Page: 328

View: 7496

Technology has long been seen as a path to economic growth. However there is considerable debate about the exact nature of this relationship. Economics of Structural and Technological Change employs a wide range of theoretical and applied approaches to explore the concept of technological change. The book begins with a series of in-depth discussions of the economic analysis of technological change. The second section contains a discussion of theoretical models of technological change, focusing on issues such as time and innovation. The third section brings together a number of applied analyses of technological change and examines the effect of factors such as human resource constraints, patenting and science and technology indicators.

Theories of Computability

Author: Nicholas Pippenger

Publisher: Cambridge University Press

ISBN: 9780521553803

Category: Computers

Page: 251

View: 4985

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