Theory of Recursive Functions and Effective Computability PDF Download

Author: Hartley Rogers (Jr.)
Publisher:
ISBN:
Category :
Languages : en
Pages : 482

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Author: Nigel Cutland
Publisher: Cambridge University Press
ISBN: 9780521294652
Category : Computers
Languages : en
Pages : 268

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Book Description
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.

Author: Ann Yasuhara
Publisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 370

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Author: Carl Smith
Publisher: Springer Science & Business Media
ISBN: 1441985018
Category : Computers
Languages : en
Pages : 155

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Book Description
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.

Author: Mark Burgin
Publisher: Springer Science & Business Media
ISBN: 0387268065
Category : Mathematics
Languages : en
Pages : 314

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Book Description
* The first exposition on super-recursive algorithms, systematizing all main classes and providing an accessible, focused examination of the theory and its ramifications * Demonstrates how these algorithms are more appropriate as mathematical models for modern computers and how they present a better framework for computing methods * Develops a new practically-oriented perspective on the theory of algorithms, computation, and automata, as a whole

Author: Gerald E. Sacks
Publisher: Cambridge University Press
ISBN: 1107168430
Category : Computers
Languages : en
Pages : 361

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Book Description
This almost self-contained introduction to higher recursion theory is essential reading for all researchers in the field.

Author: Piergiorgio Odifreddi
Publisher:
ISBN: 9780444589439
Category : Recursion theory
Languages : en
Pages : 668

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Author: K. Ko
Publisher: Springer Science & Business Media
ISBN: 1468468022
Category : Computers
Languages : en
Pages : 318

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Book Description
Starting with Cook's pioneering work on NP-completeness in 1970, polynomial complexity theory, the study of polynomial-time com putability, has quickly emerged as the new foundation of algorithms. On the one hand, it bridges the gap between the abstract approach of recursive function theory and the concrete approach of analysis of algorithms. It extends the notions and tools of the theory of computability to provide a solid theoretical foundation for the study of computational complexity of practical problems. In addition, the theoretical studies of the notion of polynomial-time tractability some times also yield interesting new practical algorithms. A typical exam ple is the application of the ellipsoid algorithm to combinatorial op timization problems (see, for example, Lovasz [1986]). On the other hand, it has a strong influence on many different branches of mathe matics, including combinatorial optimization, graph theory, number theory and cryptography. As a consequence, many researchers have begun to re-examine various branches of classical mathematics from the complexity point of view. For a given nonconstructive existence theorem in classical mathematics, one would like to find a construc tive proof which admits a polynomial-time algorithm for the solution. One of the examples is the recent work on algorithmic theory of per mutation groups. In the area of numerical computation, there are also two tradi tionally independent approaches: recursive analysis and numerical analysis.

Author: Martin Davis
Publisher: Academic Press
ISBN: 0122063821
Category : Computers
Languages : en
Pages : 631

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Book Description
This introductory text covers the key areas of computer science, including recursive function theory, formal languages, and automata. Additions to the second edition include: extended exercise sets, which vary in difficulty; expanded section on recursion theory; new chapters on program verification and logic programming; updated references and examples throughout.

Author: Robert I. Soare
Publisher: Springer Science & Business Media
ISBN: 9783540152996
Category : Mathematics
Languages : en
Pages : 460

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Book Description
..."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