Recursion

'Recursion takes mind-twisting premises and embeds them in a deeply emotional story about time and loss and grief and most of all, the glory of the human heart' - Gregg Hurwitz, international bestselling author of Orphan X A breathtaking ...

Author: Blake Crouch

Publisher: Pan Macmillan

ISBN: 1509866698

Category: Fiction

Page:

View: 101

'Recursion takes mind-twisting premises and embeds them in a deeply emotional story about time and loss and grief and most of all, the glory of the human heart' - Gregg Hurwitz, international bestselling author of Orphan X A breathtaking exploration of memory and what it means to be human, Recursion is the follow-up novel to the smash-hit thriller, Dark Matter, by Blake Crouch. At first, it looks like a disease. An epidemic that spreads through no known means, driving its victims mad with memories of a life they never lived. But the force that’s sweeping the world is no pathogen. It’s just the first shockwave, unleashed by a stunning discovery – and what’s in jeopardy is not just our minds. In New York City, Detective Barry Sutton is closing in on the truth – and in a remote laboratory, neuroscientist Helena Smith is unaware that she alone holds the key to this mystery . . . and the tools for fighting back. Together, Barry and Helena will have to confront their enemy – before they, and the world, are trapped in a loop of ever-growing chaos. 'A fantastic read' Andy Weir, Number one New York Times bestselling author of The Martian

Recursion Complexity in Cognition

This volume focuses on recursion and reveals a host of new theoretical arguments, philosophical perspectives, formal representations and empirical evidence from parsing, acquisition and computer models, highlighting its central role in ...

Author: Tom Roeper

Publisher: Springer

ISBN: 3319050869

Category: Language Arts & Disciplines

Page: 271

View: 813

This volume focuses on recursion and reveals a host of new theoretical arguments, philosophical perspectives, formal representations and empirical evidence from parsing, acquisition and computer models, highlighting its central role in modern science. Noam Chomsky, whose work introduced recursion to linguistics and cognitive science and other leading researchers in the fields of philosophy, semantics, computer science and psycholinguistics in showing the profound reach of this concept into modern science. Recursion has been at the heart of generative grammar from the outset. Recent work in minimalism has put it at center-stage with a wide range of consequences across the intellectual landscape. The contributor to this volume both advance the field and provide a cross-sectional view of the place that recursion takes in modern science.

Classical Recursion Theory

But this is immediate, since f(i,0) = (f(i,0)) f(£, y + 1) o o o Thus f(£, y + 1) only uses
the last previous value f(i, j), and f is primitive recursive because so are coding
and concatenation. [] Exercise I.7.2 Simultaneous primitive recursion. The class ...

Author: P. Odifreddi

Publisher: Elsevier

ISBN: 9780080886596

Category: Computers

Page: 667

View: 450

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

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.

Author: Joseph R. Shoenfield

Publisher: CRC Press

ISBN: 1351419412

Category: Mathematics

Page: 96

View: 500

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.

Recursion Sequences

The concept of a recursion sequence is a broad generalization of the concept of
an arithmetic or geometric progression . Its particular cases also include the
sequences of squares or cubes of natural numbers , the sequences of digits of a
 ...

Author: Alekseĭ Ivanovich Markushevich

Publisher:

ISBN:

Category: Sequences (Mathematics).

Page: 48

View: 820


The Recursion Method and Its Applications

In these , we are really dealing with the Lanczos Method , which uses the same
algorithm to find individual eigenvalues as does the recursion method to
generate smooth spectra . The scale of the computational problems are
considerably ...

Author: D.G. Pettifor

Publisher: Springer

ISBN: 9783540151739

Category: Science

Page: 184

View: 736

This volume reviews recent advances in the development and application of the recursion method in computational solid state physics and elsewhere. It comprises the invited papers which were presented at a two-day conference at Imperial College, London during September 1984. The recursion method is based on the Lanczos algorithm for the tridiago nalisation of matrices, but it is much more than a straightforward numerical technique. It is widely regarded as the most elegant framework for a variety of calculations into which one may incorporate physical insights and a num ber of technical devices. The standard reference is Volume 35 of Solid State Physics, which contains all the early ideas of Heine, Haydock and others, upon which the method was established. The present volume provides the first review of subsequent developments. It also indicates where problems remain, or opinions differ, in the interpretation of the mathematical details or choice of practical techniques in applications. The field is still very li vely and much remains to be done, as the summary chapter clearly demonstra tes. We are grateful to the S. E. R. C. 's Collaborative Computational Project No. 9 on the electronic structure of solids and the Institute of Physics's Solid State Sub-committee for their sponsorship of the conference. We thank Angus MacKinnon for his help in conference organisation and Jacyntha Crawley for secretarial assistance. December 1984 David G. Pettifor Denis L. Weaire v Contents Part I Introduction Why Recur? By V.

Generalized Recursion Theory

266 he applies the boundedness lemma to a function ¢(¢(a) 2 (H(a))0, so that for
a G OF, Hf is recursive in Jgw) to obtain a d E OS such that each Hf is recursive in
Jg. The function H is defined by the recursion theorem over OF and thus ¢ is ...

Author: Symposium on Generalized Recursion Theory

Publisher:

ISBN:

Category: Mathematics

Page: 417

View: 879


Logic Sets and Recursion

3.1.3 Definition by Recursion We now have the Induction Principle ( IP ) , which is
the basis for mathematical induction proofs . For example , IP plays a vital role in
the earlier proof about the sum function , but we still have not justified the ...

Author: Robert L. Causey

Publisher: Jones & Bartlett Learning

ISBN: 9780763737849

Category: Computers

Page: 512

View: 634

The new Second Edition incorporates a wealth of exercise sets, allowing students to test themselves and review important topics discussed throughout the text."--Jacket.

Trace Constructions in recursion Theory

INTRODUCTION a - recursion theory is the study of operations and structures
analogous to those of ordinary recursion theory in the framework of the
admissible levels of the constructible hierarchy , the so - called Lao While being
as broad as ...

Author: David Alan Odell

Publisher:

ISBN:

Category: Recursion theory

Page: 220

View: 633


Development of a Recursion RNG based Turbulence Model

Now , it will be demonstrated that the use of the proposed recursive RNG - based
model can yield a more significant improvement in the results . The computed
streamlines for the flow field shown in figure 5 ( a ) have a mean reattachment ...

Author: Institute for Computer Applications in Science and Engineering

Publisher:

ISBN:

Category:

Page: 31

View: 235

Reynolds stress closure models based on the recursion renormalization group theory are developed for the prediction of turbulent separated flows. The proposed model uses a finite wavenumber truncation scheme to account for the spectral distribution of energy. In particular, the model incorporates effects of both local and nonlocal interactions. The nonlocal interactions are shown to yield a contribution identical to that from the Epsilon-RNG, while the local interactions introduce higher order dispersive effects. A formal analysis of the model is presented and its ability to accurately predict separated flows is analyzed from a combined theoretical and computational stand point. Turbulent flow past a backward facing step is chosen as a test case and the results obtained based on detailed computations demonstrate that the proposed recursion -RNG model with finite cut-off wavenumber can yield very good predictions for the backstep problem. Reynolds stress model, Renormalization group, Turbulent separated flows.

Topics in Recursion Theory

A recursive function F ( x , y ) will be called doubly productive for a pair of sets ( a
, b ) if , whenever We sa and wg 5 B , then F ( 1,3 ) can B - ( wg ungle Theorem 1.
There is a recursive function p of 4 variables such that 1f 4g np are partial ...

Author: Louis (Schmir) Hay

Publisher:

ISBN:

Category: Recursive functions

Page: 170

View: 918


Recursion Theory Week

{Vx}xeo c SU(2) follows from Lemma 0(b), (c) and Lemmas 1,3. d Directly from
Lemma 4 we conclude that S has an OON. D. References Friedberg, R.M. [Frí8]
Three theorems on recursive enumeration. I. Decomposition II. Maximal set III.

Author: Klaus Ambos-Spies

Publisher: Springer

ISBN: 9783540527725

Category: Mathematics

Page: 400

View: 459

These proceedings contain research and survey papers from many subfields of recursion theory, with emphasis on degree theory, in particular the development of frameworks for current techniques in this field. Other topics covered include computational complexity theory, generalized recursion theory, proof theoretic questions in recursion theory, and recursive mathematics.

Recursion Theory on Countable Abelian Groups

RECURSION THEORY ON COUNTABLE ABELIAN GROUPS Charlotte Rose Lin
, Ph.D. Cornell University 1977 We use recursion theory to determine the
effective content * { Y } } * of ( countable abelian group ) theory . Each G is
presented as ...

Author: Charlotte Rose Lin

Publisher:

ISBN:

Category: Abelian groups

Page: 72

View: 767


Induction Recursion and Programming

8 PROVING RECURSIVE PROGRAMS CORRECT In this section we shall prove
the correctness of programs in the language of expressions . As usual , our
proofs will be by induction . Theorem 3 . 8 . 1 . Let 8 F = if empty ? ( xi ) then
empty ...

Author: Mitchell Wand

Publisher: Elsevier Science Limited

ISBN:

Category: Computers

Page: 202

View: 828


Transfinite Induction and Hierarchies Generated by Transfinite Recursion Within Peano Arithmetic

This allows us to classify the TI ( wwa , IIn ) -provably recursive functions . 4.7.3
Classifying the TI ( a , II . ) - Provably Recursive Functions We now show a
correspondence between the 140 + ( F , 1 ) -provably recursive functions and
functions ...

Author: Richard D. Sommer

Publisher:

ISBN:

Category:

Page: 318

View: 660


Axiomatic Analysis and Relativizations of Recursion Theory

Robert Steven Winternitz. ) \ i : i < i 4.4 Theorem. Given a recursion theory
satisfying consistent selection, there : \

Author: Robert Steven Winternitz

Publisher:

ISBN:

Category: Recursion theory

Page: 194

View: 948


Matroid Algorithms Recursion and the Subgraph Homeomorphism Problem

Author: Paul August Kaschube

Publisher:

ISBN:

Category: Algorithms

Page: 224

View: 466


Construction of Recursion Operators for Scalar Evolution Equations

Author: Ayse Humeyra Bilge

Publisher:

ISBN:

Category:

Page: 132

View: 339


Syntax and Semantics in Higher type Recursion Theory

Author: David Philip Kierstead

Publisher:

ISBN:

Category: Recursive functions

Page: 166

View: 231


The Recursion Method

6 RECURSION METHOD ILLUSTRATED The goal of this Chapter is to introduce
the non-expert reader to the practicalities of the recursion method and to
demonstrate its elegance and aesthetic appeal. All model systems considered in
this ...

Author: V.S. Viswanath

Publisher: Springer Science & Business Media

ISBN: 354058319X

Category: Science

Page: 259

View: 149

In this monograph the recursion method is presented as a method for the analysis of dynamical properties of quantum and classical many-body systems in thermal equilibrium. Such properties are probed by many different experimental techniques used in materials science. Several representations and formulations of the recursion method are described in detail and documented with numerous examples, ranging from elementary illustrations for tutorial purposes to realistic models of interest in current research in the areas of spin dynamics and low-dimensional magnetism. The performance of the recursion method is calibrated by exact results in a number of benchmark tests and compared with the performance of other calculational techniques. The book addresses graduate students and researchers.