7 edition of Computability Theory (Chapman Hall/Crc Mathematics Series) found in the catalog.
November 17, 2003
by Chapman & Hall/CRC
Written in English
|The Physical Object|
|Number of Pages||424|
Computability theory originated with the seminal work of Gödel, Church, Turing, Kleene and Post in the s. This theory includes a wide spectrum of topics, such as the theory of reducibilities and their degree structures, computably enumerable sets and their Brand: CRC Press. Book Abstract: In the s a series of seminal works published by Alan Turing, Kurt Gödel, Alonzo Church, and others established the theoretical basis for computability. This work, advancing precise characterizations of effective, algorithmic computability, was the culmination of intensive investigations into the foundations of mathematics.
What is needed is only some elementary number theory and rudimentary logic. In this book, the authors present the complete proof along with the romantic history that goes with it. Along the way, the reader is introduced to Cantor's transfinite numbers, axiomatic set theory, Turing machines, and Gödel's incompleteness theorems. The book fits perfectly as a textbook, covering standard material for one- or two-semester courses in computability or recursion theory. It is also an excellent study guide and reference for students and researchers in related :
I'm reviewing the books on the MIRI course list. After putting down Model Theory partway through I picked up a book on logic. Computability and Logic, specifically. COMPUTABILITY AND LOGIC This book is not on the MIRI course list. It was recommended to me by Luke along with a number of other books as a potential way to learn provability logic. Computability and Logic is a wonderful book. It's. 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 : Elsevier Science.
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This book is an introduction to computability theory (or recursion theory as it is traditionally known to mathematicians). Dr Cutland begins with a mathematical characterisation of computable functions using a simple idealised computer (a register machine); after some comparison with other characterisations, he develops the mathematical theory Cited by: The book is divided into roughly three parts: an introduction to computability theory, followed by a more advanced introduction to the theory of degrees of unsolvability and decidable theories, and finally some newer material on computation and structure/5(4).
Book Description. Computability theory originated with the seminal work of Gödel, Church, Turing, Kleene and Post in the s. 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.
The book fits perfectly as a textbook, covering standard material for one- or two-semester courses in computability or recursion theory. It is also an excellent study guide and reference for students and researchers in related areas.
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 Computability Theory book and basic subject brought alive in such an approachable way.
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 Edition: 1.
Computability theory originated with the seminal work of Gödel, Church, Turing, Kleene and Post in the s. This theory includes a wide spectrum of topics, such as the theory of reducibilities and their Computability Theory book structures, computably enumerable sets and their automorphisms, and subrecursive hierarchy classifications.
Recent work in computability theory has focused on Turing 3/5(2). Computability, Complexity, and Languages is an introductory text that covers the key areas of computer science, including recursive function theory, formal languages, and automata.
It assumes a minimal background in formal mathematics. The book is divided into five parts: Computability, Grammars and Automata, Logic, Complexity, and Unsolvability. The book series Theory and Applications of Computability is published by Springer in cooperation with the Association Computability in Europe.
Books published in this series will be of interest to the research community and graduate students, with a unique focus on issues of computability. Computability theory deals primarily with the question of the extent to which a problem is solvable on a computer.
The statement that the halting problem cannot be solved by a Turing machine is one of the most important results in computability theory, as it is an example of a concrete problem that is both easy to formulate and impossible to solve using a Turing machine.
This book is a general introduction to computability and complexity theory. It should be of interest to beginning programming language researchers who are interested in com-putability and complexity theory, or vice versa. The view from Olympus Unlike most ﬁelds within computer science, computability and complexity theory dealsFile Size: 1MB.
Turing's famous 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. Covering the basics as well as recent research results, this book provides an introduction to the interface of computability and randomness for graduates and researchers in computability theory, theoretical computer science, and measure theory.
( views) Computability and Complexity from a Programming Perspective by Neil D. Jones - The MIT. 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. Computability theory originated with the seminal work of G del, Church, Turing, Kleene and Post in the s. This theory includes a wide spectrum of topics, such as the theory of reducibilities and their degree structures, computably enumerable sets and their /5.
The book is an excellent book for its intended audience, but it is not really a book in computability theory. $\endgroup$ – Carl Mummert Oct 7 '14 at $\begingroup$ I am one more vote for Sipser.
Not the best introductory text in my opinion. An Introduction to Computability Theory provides an introduction to the essential concepts in computability, using several models of computation, from Turing machines to the modern computation models inspired by quantum physics.
“It is a pleasure to see a book which takes a different approach to computer theory. This short book can be Brand: Springer-Verlag London. The book is suitable for advanced undergraduate and graduate students in computer science and mathematics and researchers engaged with computability and mathematical logic.
Keywords Alan Turing Computability theory Computably enumerable (C.E.) sets Turing reducibility Finite injury method Oracle constructions Tree method Minimal degrees Games. Classical Computability Theory The foundation, Turing’s analysis In Leary  (the text book used locally for the introductory course on logic) the recursive functions are de ned as those that can be represented in elementary number theory.
f: Nk!N is recursive if there is a formula ˚(x 1;;x k;y) such that for all n 1;;n k;mwe. 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. the current book has a quite minimal coverage of computability and no coverage of automata theory, but we provide web-only chapters with more coverage of these topics on the book’s web site.
The prerequisite mathematical background would be some comfort with mathematical.University of Chicago.Computer scientists, mathematicians, and philosophers discuss the conceptual foundations of the notion of computability as well as recent theoretical developments.
In the s a series of seminal works published by Alan Turing, Kurt Gödel, Alonzo Church, and others established the theoretical basis for computability. This work, advancing precise characterizations of effective, algorithmic.