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Computability

Computability Author Nigel Cutland
ISBN-10 0521294657
Release 1980-06-19
Pages 251
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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

Computability Theory Author Herbert B. Enderton
ISBN-10 0123849594
Release 2010-12-30
Pages 192
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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



A Recursive Introduction to the Theory of Computation

A Recursive Introduction to the Theory of Computation Author Carl Smith
ISBN-10 9781441985019
Release 2012-12-06
Pages 148
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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.



Enumerability Decidability Computability

Enumerability  Decidability  Computability Author Hans Hermes
ISBN-10 9783662116869
Release 2013-03-14
Pages 245
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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

Reflexive Structures Author Luis E. Sanchis
ISBN-10 9781461238782
Release 2012-12-06
Pages 233
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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.



Recursively Enumerable Sets and Degrees

Recursively Enumerable Sets and Degrees Author Robert I. Soare
ISBN-10 3540152997
Release 1999-11-01
Pages 437
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..."The book, written by one of the main researchers on the field, gives a complete account of the theory of r.e. degrees. .... The definitions, results and proofs are always clearly motivated and explained before the formal presentation; the proofs are described with remarkable clarity and conciseness. The book is highly recommended to everyone interested in logic. It also provides a useful background to computer scientists, in particular to theoretical computer scientists." Acta Scientiarum Mathematicarum, Ungarn 1988 ..."The main purpose of this book is to introduce the reader to the main results and to the intricacies of the current theory for the recurseively enumerable sets and degrees. The author has managed to give a coherent exposition of a rather complex and messy area of logic, and with this book degree-theory is far more accessible to students and logicians in other fields than it used to be." Zentralblatt für Mathematik, 623.1988



Computability Theory

Computability Theory Author Neil D. Jones
ISBN-10 9781483218489
Release 2014-06-20
Pages 168
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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.



Recursive function theory and logic

Recursive function theory and logic Author Ann Yasuhara
ISBN-10 UOM:39015012663020
Release 1971-06
Pages 338
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Recursive function theory and logic has been writing in one form or another for most of life. You can find so many inspiration from Recursive function theory and logic also informative, and entertaining. Click DOWNLOAD or Read Online button to get full Recursive function theory and logic book for free.



The ries t s gl ssas the ries t s math s s

The  ries t  s gl  ssas  the  ries t  s math  s  s Author Jean Piaget
ISBN-10 9608392772
Release 2009
Pages 119
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The ries t s gl ssas the ries t s math s s has been writing in one form or another for most of life. You can find so many inspiration from The ries t s gl ssas the ries t s math s s also informative, and entertaining. Click DOWNLOAD or Read Online button to get full The ries t s gl ssas the ries t s math s s book for free.



Economics of Structural and Technological Change

Economics of Structural and Technological Change Author Cristiano Antonelli
ISBN-10 9781134716623
Release 2002-09-11
Pages 328
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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.



Proceedings of the Fifth International Congress on Mathematical Education

Proceedings of the Fifth International Congress on Mathematical Education Author CARASS
ISBN-10 9781475742381
Release 2013-03-14
Pages 401
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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.



Theory of Computation

Theory of Computation Author Dr. O. G. Kakde
ISBN-10 8131801799
Release 2007-01-01
Pages 221
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Theory of Computation has been writing in one form or another for most of life. You can find so many inspiration from Theory of Computation also informative, and entertaining. Click DOWNLOAD or Read Online button to get full Theory of Computation book for free.



Unconventional Models of Computation

Unconventional Models of Computation Author Cristian Calude
ISBN-10 9783540458333
Release 2003-06-30
Pages 329
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Unconventional Models of Computation has been writing in one form or another for most of life. You can find so many inspiration from Unconventional Models of Computation also informative, and entertaining. Click DOWNLOAD or Read Online button to get full Unconventional Models of Computation book for free.



Theories of Computability

Theories of Computability Author Nicholas Pippenger
ISBN-10 0521553806
Release 1997-05-28
Pages 251
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A mathematically sophisticated introduction to Turing's theory, Boolean functions, automata, and formal languages.



Classical Recursion Theory

Classical Recursion Theory Author P. Odifreddi
ISBN-10 0080886590
Release 1992-02-04
Pages 667
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1988 marked the first centenary of Recursion Theory, since Dedekind's 1888 paper on the nature of number. Now available in paperback, this book is both a comprehensive reference for the subject and a textbook starting from first principles. Among the subjects covered are: various equivalent approaches to effective computability and their relations with computers and programming languages; a discussion of Church's thesis; a modern solution to Post's problem; global properties of Turing degrees; and a complete algebraic characterization of many-one degrees. Included are a number of applications to logic (in particular Gödel's theorems) and to computer science, for which Recursion Theory provides the theoretical foundation.



Recursion Theory

Recursion Theory Author Joseph R. Shoenfield
ISBN-10 9781351419413
Release 2018-04-27
Pages 96
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This volume, which ten years ago appeared as the first in the acclaimed series Lecture Notes in Logic, serves as an introduction to recursion theory. The fundamental concept of recursion makes the idea of computability accessible to a mathematical analysis, thus forming one of the pillars on which modern computer science rests. The clarity and focus of this text have established it as a classic instrument for teaching and self-study that prepares its readers for the study of advanced monographs and the current literature on recursion theory.



Models of Computation

Models of Computation Author Maribel Fernández
ISBN-10 1848824343
Release 2009-04-14
Pages 184
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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.