Recursion

Recursion PDF Book Detail Author: David J. Lobina
Publisher: Oxford University Press
ISBN: 0198785151
Category : Language Arts & Disciplines
Languages : en
Pages : 256

Book Description
This book provides a comprehensive account of the role of recursion in language in two distinct but interconnected ways. First, David J. Lobina examines how recursion applies at different levels within a full description of natural language. Specifically, he identifies and evaluates recursion as: a) a central property of the computational system underlying the faculty of language; b) a possible feature of the derivations yielded by this computational system; c) a global characteristic of the structures generated by the language faculty; and d) a probable factor in the parsing operations employed during the processing of recursive structures. Second, the volume orders these different levels into a tripartite explanatory framework. According to this framework, the investigation of any particular cognitive domain must begin by first outlining what sort of mechanical procedure underlies the relevant capacity (including what sort of structures it generates). Only then, the author argues, can we properly investigate its implementation, both at the level of abstract computations typical of competence-level analyses, and at the level of the real-time processing of behaviour.

Recursion Via Pascal

Recursion Via Pascal PDF Book Detail Author: Jeffrey Soden Rohl
Publisher: Cambridge University Press
ISBN: 9780521269346
Category : Computers
Languages : en
Pages : 191

Book Description
This book is devoted to recursion in programming, the technique by which the solution to a problem is expressed partly in terms of the solution to a simpler version of the same problem. Ultimately the solution to the simplest version must be given explicitly. In functional programming, recursion has received its full due since it is quite often the only repetitive construct. However, the programming language used here is Pascal and the examples have been chosen accordingly. It makes an interesting contrast with the use of recursion in functional and logic programming. The early chapters consider simple linear recursion using examples such as finding the highest common factor of a pair of numbers, and processing linked lists. Subsequent chapters move up through binary recursion, with examples which include the Towers of Hanoi problem and symbolic differentiation, to general recursion. The book contains well over 100 examples.

Recursion across Domains

Recursion across Domains PDF Book Detail Author: Luiz Amaral
Publisher: Cambridge University Press
ISBN: 1108314163
Category : Language Arts & Disciplines
Languages : en
Pages : 410

Book Description
Recursion and self-embedding are at the heart of our ability to formulate our thoughts, articulate our imagination and share with other human beings. Nonetheless, controversy exists over the extent to which recursion is shared across all domains of syntax. A collection of 18 studies are presented here on the central linguistic property of recursion, examining a range of constructions in over a dozen languages representing great areal, typological and genetic diversity and spanning wide latitudes. The volume expands the topic to include prepositional phrases, possessives, adjectives, and relative clauses - our many vehicles to express creative thought - to provide a critical perspective on claims about how recursion connects to broader aspects of the mind. Parallel explorations across language families, literate and non-literate societies, children and adults are investigated and constitutes a new step in the generative tradition by simultaneously focusing on formal theory, acquisition and experimentation, and ecologically-sensitive fieldwork, and initiates a new community where these diverse experts collaborate.

Language and Recursion

Language and Recursion PDF Book Detail Author: Francis Lowenthal
Publisher: Springer Science & Business Media
ISBN: 1461494141
Category : Psychology
Languages : en
Pages : 232

Book Description
As humans, our many levels of language use distinguish us from the rest of the animal world. For many scholars, it is the recursive aspect of human speech that makes it truly human. But linguists continue to argue about what recursion actually is, leading to the central dilemma: is full recursion, as defined by mathematicians, really necessary for human language? Language and Recursion defines the elusive construct with the goal of furthering research into language and cognition. An up-to-date literature review surveys extensive findings based on non-verbal communication devices and neuroimaging techniques. Comparing human and non-human primate communication, the book’s contributors examine meaning in chimpanzee calls, and consider the possibility of a specific brain structure for recursion. The implications are then extended to formal grammars associated with artificial intelligence, and to the question of whether recursion is a valid concept at all. Among the topics covered: • The pragmatic origins of recursion. • Recursive cognition as a prelude to language. • Computer simulations of recursive exercises for a non-verbal communication device. • Early rule learning ability and language acquisition. • Computational language related to recursion, incursion, and fractals • Why there may be no recursion in language. Regardless of where one stands in the debate, Language and Recursion has much to offer the science community, particularly cognitive psychologists and researchers in the science of language. By presenting these multiple viewpoints, the book makes a solid case for eventual reconciliation.

Recursion and Human Language

Recursion and Human Language PDF Book Detail Author: Harry van der Hulst
Publisher: Walter de Gruyter
ISBN: 3110219255
Category : Language Arts & Disciplines
Languages : en
Pages : 469

Book Description
The present volume is an edited collection of original contributions which all deal with the issue of recursion in human language(s). All contributions originate as papers that were presented at a conference on the topic of recursion in human language organized by Dan Everett in March 22, 2007. For the purpose of this collection all articles underwent a double-blind peer-review process. The present chapters were written in the course of 2008. Although the ‘recursive’ nature of linguistic expressions, i.e. the apparent possibility of producing an infinite number of expressions with finite means, has been noted for a long time, no general agreement seems to exist concerning the empirical status as well as mathematical formalization of this ‘characteristic’ of human languages or of the grammars that lie behind these utterances that make up these languages. Renewed interest in this subject was sparked by recent claims that ‘recursion’ is perhaps the sole uniquely human and as such universal trait of human language (cf. Chomsky, Hauser and Fitch 2000). In this volume, the issue of recursion is tackled from a variety of angles. Some articles cover formal issues regarding the proper characterization or definition of recursion, while others focus on empirical issues by examining the kinds of structure in languages that suggest recursive mechanism in the grammar. Most articles discuss syntactic phenomena, but several involve morphology, the lexicon and phonology. In addition, we find discussions that involve evolutionary notions and language disorders, and the broader cognitive context of recursion.

The Recursive Book of Recursion

The Recursive Book of Recursion PDF Book Detail Author: Al Sweigart
Publisher: No Starch Press
ISBN: 1718502028
Category : Computers
Languages : en
Pages : 330

Book Description
An accessible yet rigorous crash course on recursive programming using Python and JavaScript examples. Recursion has an intimidating reputation: it’s considered to be an advanced computer science topic frequently brought up in coding interviews. But there’s nothing magical about recursion. The Recursive Book of Recursion uses Python and JavaScript examples to teach the basics of recursion, exposing the ways that it’s often poorly taught and clarifying the fundamental principles of all recursive algorithms. You’ll learn when to use recursive functions (and, most importantly, when not to use them), how to implement the classic recursive algorithms often brought up in job interviews, and how recursive techniques can help solve countless problems involving tree traversal, combinatorics, and other tricky topics. This project-based guide contains complete, runnable programs to help you learn: How recursive functions make use of the call stack, a critical data structure almost never discussed in lessons on recursion How the head-tail and “leap of faith” techniques can simplify writing recursive functions How to use recursion to write custom search scripts for your filesystem, draw fractal art, create mazes, and more How optimization and memoization make recursive algorithms more efficient Al Sweigart has built a career explaining programming concepts in a fun, approachable manner. If you’ve shied away from learning recursion but want to add this technique to your programming toolkit, or if you’re racing to prepare for your next job interview, this book is for you.

Recursion Theoretic Hierarchies

Recursion Theoretic Hierarchies PDF Book Detail Author: Peter G. Hinman
Publisher: Cambridge University Press
ISBN: 1107168244
Category : Mathematics
Languages : en
Pages : 492

Book Description
The theory set out in this book results from the meeting of descriptive set theory and recursion theory.

Recursion Theory

Recursion Theory PDF Book Detail Author: Chi Tat Chong
Publisher: Walter de Gruyter GmbH & Co KG
ISBN: 3110275643
Category : Mathematics
Languages : en
Pages : 320

Book Description
This monograph presents recursion theory from a generalized point of view centered on the computational aspects of definability. A major theme is the study of the structures of degrees arising from two key notions of reducibility, the Turing degrees and the hyperdegrees, using techniques and ideas from recursion theory, hyperarithmetic theory, and descriptive set theory. The emphasis is on the interplay between recursion theory and set theory, anchored on the notion of definability. The monograph covers a number of fundamental results in hyperarithmetic theory as well as some recent results on the structure theory of Turing and hyperdegrees. It also features a chapter on the applications of these investigations to higher randomness.

Abstract Recursion and Intrinsic Complexity

Abstract Recursion and Intrinsic Complexity PDF Book Detail Author: Yiannis N. Moschovakis
Publisher: Cambridge University Press
ISBN: 1108246494
Category : Mathematics
Languages : en
Pages :

Book Description
This book presents and applies a framework for studying the complexity of algorithms. It is aimed at logicians, computer scientists, mathematicians and philosophers interested in the theory of computation and its foundations, and it is written at a level suitable for non-specialists. Part I provides an accessible introduction to abstract recursion theory and its connection with computability and complexity. This part is suitable for use as a textbook for an advanced undergraduate or graduate course: all the necessary elementary facts from logic, recursion theory, arithmetic and algebra are included. Part II develops and applies an extension of the homomorphism method due jointly to the author and Lou van den Dries for deriving lower complexity bounds for problems in number theory and algebra which (provably or plausibly) restrict all elementary algorithms from specified primitives. The book includes over 250 problems, from simple checks of the reader's understanding, to current open problems.

Higher Recursion Theory

Higher Recursion Theory PDF Book Detail Author: Gerald E. Sacks
Publisher: Cambridge University Press
ISBN: 1316739465
Category : Mathematics
Languages : en
Pages :

Book Description
Since their inception, the Perspectives in Logic and Lecture Notes in Logic series have published seminal works by leading logicians. Many of the original books in the series have been unavailable for years, but they are now in print once again. This volume, the second publication in the Perspectives in Logic series, is an almost self-contained introduction to higher recursion theory, in which the reader is only assumed to know the basics of classical recursion theory. The book is divided into four parts: hyperarithmetic sets, metarecursion, α-recursion, and E-recursion. This text is essential reading for all researchers in the field.

Classical Recursion Theory

Classical Recursion Theory PDF Book Detail Author: P. Odifreddi
Publisher: Elsevier
ISBN: 9780080886596
Category : Computers
Languages : en
Pages : 667

Book Description
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 for Metamathematics

Recursion Theory for Metamathematics PDF Book Detail Author: Raymond M. Smullyan
Publisher: Oxford University Press on Demand
ISBN: 019508232X
Category : Social Science
Languages : en
Pages : 180

Book Description
This work is a sequel to the author's G�del's Incompleteness Theorems, though it can be read independently by anyone familiar with G�del's incompleteness theorem for Peano arithmetic. The book deals mainly with those aspects of recursion theory that have applications to the metamathematics of incompleteness, undecidability, and related topics. It is both an introduction to the theory and a presentation of new results in the field.

Computing with Maple

Computing with Maple PDF Book Detail Author: Francis Wright
Publisher: CRC Press
ISBN: 9781584882367
Category : Mathematics
Languages : en
Pages : 558

Book Description
Powerful, flexible, easy to use-small wonder that the use of MAPLE® continues to increase, particularly since the latest releases of MAPLE. The built-in nature of its numerical and graphical facilities gives MAPLE a distinct advantage over traditional programming languages, yet to date, no textbook has used that advantage to introduce programming concepts. Moreover, few books based on MAPLE's latest versions even exist. Computing with MAPLE presents general programming principles using MAPLE as a concrete example of a programming language. The author first addresses the basic MAPLE functions accessible for interactive use then moves to actual programming, discussing all of the programming facilities that MAPLE provides, including control structures, data types, graphics, spreadsheets, text processing, and object oriented programming. Reflecting MAPLE's primary function as a computational tool, the book's emphasis is on mathematical examples, and it includes a full chapter devoted to algebraic programming. Classroom tested since 1995, the material in Computing with MAPLE is particularly appropriate for an intermediate-level introductory course in programming for both mathematics and computing students. It includes numerous exercises and test questions, with MAPLE worksheets, contact information, and supplementary material available on the Internet.

Data Structures and Algorithms in Java

Data Structures and Algorithms in Java PDF Book Detail Author: Michael T. Goodrich
Publisher: John Wiley & Sons
ISBN: 1118771338
Category : Computers
Languages : en
Pages : 736

Book Description
The design and analysis of efficient data structures has long been recognized as a key component of the Computer Science curriculum. Goodrich, Tomassia and Goldwasser's approach to this classic topic is based on the object-oriented paradigm as the framework of choice for the design of data structures. For each ADT presented in the text, the authors provide an associated Java interface. Concrete data structures realizing the ADTs are provided as Java classes implementing the interfaces. The Java code implementing fundamental data structures in this book is organized in a single Java package, net.datastructures. This package forms a coherent library of data structures and algorithms in Java specifically designed for educational purposes in a way that is complimentary with the Java Collections Framework.

C Programming From Problem Analysis to Program Design

C   Programming  From Problem Analysis to Program Design PDF Book Detail Author: D. S. Malik
Publisher: Cengage Learning
ISBN: 1285225570
Category : Computers
Languages : en
Pages : 1392

Book Description
C++ PROGRAMMING: FROM PROBLEM ANALYSIS TO PROGRAM DESIGN, Sixth Edition remains the definitive text for a first programming language course. D.S. Malik's time-tested, student-centered methodology uses a strong focus on problem-solving and full-code examples to vividly demonstrate the how and why of applying programming concepts and utilizing C++ to work through a problem. This new edition includes updated end-of-chapter exercises, new debugging exercises, an earlier introduction to variables and a streamlined discussion of user-discussion of user-defined functions to best meet the needs of the modern CS1 course. An optional CourseMate brings C++ PROGRAMMING: FROM PROBLEM ANALYSIS TO PROGRAM DESIGN to life with interactive study tools including videos, quizzing, flashcards, and games. The CourseMate's digital Lab Manual offers additional hands-on exercises, allowing students to reinforce critical thinking through practice. Important Notice: Media content referenced within the product description or the product text may not be available in the ebook version.