Recursion Sequences

Recursion Sequences
Author: Alekseĭ Ivanovich Markushevich
Publisher:
Total Pages: 52
Release: 1975
Genre: Sequences (Mathematics).
ISBN:

A Recursive Introduction to the Theory of Computation

A Recursive Introduction to the Theory of Computation
Author: Carl Smith
Publisher: Springer Science & Business Media
Total Pages: 155
Release: 2012-12-06
Genre: Computers
ISBN: 1441985018

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.

Classical Recursion Theory

Classical Recursion Theory
Author: P. Odifreddi
Publisher: Elsevier
Total Pages: 667
Release: 1992-02-04
Genre: Computers
ISBN: 9780080886596

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.

Introduction to Recursive Programming

Introduction to Recursive Programming
Author: Manuel Rubio-Sanchez
Publisher: CRC Press
Total Pages: 451
Release: 2017-10-05
Genre: Computers
ISBN: 1498735304

Recursion is one of the most fundamental concepts in computer science and a key programming technique that allows computations to be carried out repeatedly. Despite the importance of recursion for algorithm design, most programming books do not cover the topic in detail, despite the fact that numerous computer programming professors and researchers in the field of computer science education agree that recursion is difficult for novice students. Introduction to Recursive Programming provides a detailed and comprehensive introduction to recursion. This text will serve as a useful guide for anyone who wants to learn how to think and program recursively, by analyzing a wide variety of computational problems of diverse difficulty. It contains specific chapters on the most common types of recursion (linear, tail, and multiple), as well as on algorithm design paradigms in which recursion is prevalent (divide and conquer, and backtracking). Therefore, it can be used in introductory programming courses, and in more advanced classes on algorithm design. The book also covers lower-level topics related to iteration and program execution, and includes a rich chapter on the theoretical analysis of the computational cost of recursive programs, offering readers the possibility to learn some basic mathematics along the way. It also incorporates several elements aimed at helping students master the material. First, it contains a larger collection of simple problems in order to provide a solid foundation of the core concepts, before diving into more complex material. In addition, one of the book's main assets is the use of a step-by-step methodology, together with specially designed diagrams, for guiding and illustrating the process of developing recursive algorithms. Furthermore, the book covers combinatorial problems and mutual recursion. These topics can broaden students' understanding of recursion by forcing them to apply the learned concepts differently, or in a more sophisticated manner. The code examples have been written in Python 3, but should be straightforward to understand for students with experience in other programming languages. Finally, worked out solutions to over 120 end-of-chapter exercises are available for instructors.

Discrete Mathematics

Discrete Mathematics
Author: Oscar Levin
Publisher: Createspace Independent Publishing Platform
Total Pages: 342
Release: 2016-08-16
Genre:
ISBN: 9781534970748

This gentle introduction to discrete mathematics is written for first and second year math majors, especially those who intend to teach. The text began as a set of lecture notes for the discrete mathematics course at the University of Northern Colorado. This course serves both as an introduction to topics in discrete math and as the "introduction to proof" course for math majors. The course is usually taught with a large amount of student inquiry, and this text is written to help facilitate this. Four main topics are covered: counting, sequences, logic, and graph theory. Along the way proofs are introduced, including proofs by contradiction, proofs by induction, and combinatorial proofs. The book contains over 360 exercises, including 230 with solutions and 130 more involved problems suitable for homework. There are also Investigate! activities throughout the text to support active, inquiry based learning. While there are many fine discrete math textbooks available, this text has the following advantages: It is written to be used in an inquiry rich course. It is written to be used in a course for future math teachers. It is open source, with low cost print editions and free electronic editions.

Recursively Enumerable Sets and Degrees

Recursively Enumerable Sets and Degrees
Author: Robert I. Soare
Publisher: Springer Science & Business Media
Total Pages: 460
Release: 1999-11-01
Genre: Mathematics
ISBN: 9783540152996

..."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

Instruction Sequences for Computer Science

Instruction Sequences for Computer Science
Author: Jan A Bergstra
Publisher: Springer Science & Business Media
Total Pages: 241
Release: 2012-06-12
Genre: Computers
ISBN: 9491216651

This book demonstrates that the concept of an instruction sequence offers a novel and useful viewpoint on issues relating to diverse subjects in computer science. Selected issues relating to well-known subjects from the theory of computation and the area of computer architecture are rigorously investigated in this book thinking in terms of instruction sequences. The subjects from the theory of computation, to wit the halting problem and non-uniform computational complexity, are usually investigated thinking in terms of a common model of computation such as Turing machines and Boolean circuits. The subjects from the area of computer architecture, to wit instruction sequence performance, instruction set architectures and remote instruction processing, are usually not investigated in a rigorous way at all.

The Recursive Mind

The Recursive Mind
Author: Michael C. Corballis
Publisher: Princeton University Press
Total Pages: 309
Release: 2014-04-27
Genre: Psychology
ISBN: 1400851491

A groundbreaking theory of what makes the human mind unique The Recursive Mind challenges the commonly held notion that language is what makes us uniquely human. In this compelling book, Michael Corballis argues that what distinguishes us in the animal kingdom is our capacity for recursion: the ability to embed our thoughts within other thoughts. "I think, therefore I am," is an example of recursive thought, because the thinker has inserted himself into his thought. Recursion enables us to conceive of our own minds and the minds of others. It also gives us the power of mental "time travel"—the ability to insert past experiences, or imagined future ones, into present consciousness. Drawing on neuroscience, psychology, animal behavior, anthropology, and archaeology, Corballis demonstrates how these recursive structures led to the emergence of language and speech, which ultimately enabled us to share our thoughts, plan with others, and reshape our environment to better reflect our creative imaginations. He shows how the recursive mind was critical to survival in the harsh conditions of the Pleistocene epoch, and how it evolved to foster social cohesion. He traces how language itself adapted to recursive thinking, first through manual gestures, then later, with the emergence of Homo sapiens, vocally. Toolmaking and manufacture arose, and the application of recursive principles to these activities in turn led to the complexities of human civilization, the extinction of fellow large-brained hominins like the Neandertals, and our species' supremacy over the physical world.

Complexity, Logic, and Recursion Theory

Complexity, Logic, and Recursion Theory
Author: Andrea Sorbi
Publisher: CRC Press
Total Pages: 384
Release: 2019-05-07
Genre: Mathematics
ISBN: 0429529953

"Integrates two classical approaches to computability. Offers detailed coverage of recent research at the interface of logic, computability theory, nd theoretical computer science. Presents new, never-before-published results and provides informtion not easily accessible in the literature."