Computability And Complexity Of Julia Sets
DOWNLOAD
Download Computability And Complexity Of Julia Sets PDF/ePub or read online books in Mobi eBooks. Click Download or Read Online button to get Computability And Complexity Of Julia Sets book now. This website allows unlimited access to, at the time of writing, more than 1.5 million titles, including hundreds of thousands of titles in various foreign languages. If the content not found or just blank you must refresh this page
Computability Of Julia Sets
DOWNLOAD
Author : Mark Braverman
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-02-08
Computability Of Julia Sets written by Mark Braverman and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-02-08 with Computers categories.
Among all computer-generated mathematical images, Julia sets of rational maps occupy one of the most prominent positions. Their beauty and complexity can be fascinating. They also hold a deep mathematical content. Computational hardness of Julia sets is the main subject of this book. By definition, a computable set in the plane can be visualized on a computer screen with an arbitrarily high magnification. There are countless programs to draw Julia sets. Yet, as the authors have discovered, it is possible to constructively produce examples of quadratic polynomials, whose Julia sets are not computable. This result is striking - it says that while a dynamical system can be described numerically with an arbitrary precision, the picture of the dynamics cannot be visualized. The book summarizes the present knowledge (most of it from the authors' own work) about the computational properties of Julia sets in a self-contained way. It is accessible to experts and students with interest in theoretical computer science or dynamical systems.
Computability And Complexity Of Julia Sets
DOWNLOAD
Author : Mark Braverman
language : en
Publisher:
Release Date : 2008
Computability And Complexity Of Julia Sets written by Mark Braverman and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with Computer science categories.
The field of study in the thesis is Real Computation, and Computability and Complexity in Dynamical Systems. The thesis consists of two parts. The first part is devoted to results on general computation of functions and sets over the reals, while in the second part results about computability and complexity in Complex Dynamics are presented. Studying computability and complexity over the reals is important for understanding the relationship between nature and computing, and for providing theoretical backing to fundamental problems in Numerical Analysis. In the first part of the thesis results unifying two most commonly used models of computation are presented. One is the model of Computable Analysis that is based on rational approximations of continuous objects, such as real functions and sets [Grz55, Ko91, Wei00]. The other is the Blum-Shub-Smale (BSS) model that is based on precise algebraic operations [BCSS98]. Insights obtained through this connection are then used to extend the computational complexity notion to some discontinuous functions. In the second part of the thesis, results on the computability and complexity of Julia sets are presented. Julia sets arise in one-dimensional complex dynamics. They have been intensely studied in the past 100 years, and since the 1980s numerous programs have been written to produce images of the sets, both for research and for their aesthetic value. We have studied computational properties of Julia sets, obtaining a virtually complete classification of the computational properties of Julia sets as well as complexity results, that complement the previous empirical work on producing their images.
Handbook Of Computability And Complexity In Analysis
DOWNLOAD
Author : Vasco Brattka
language : en
Publisher: Springer Nature
Release Date : 2021-06-04
Handbook Of Computability And Complexity In Analysis written by Vasco Brattka and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-06-04 with Computers categories.
Computable analysis is the modern theory of computability and complexity in analysis that arose out of Turing's seminal work in the 1930s. This was motivated by questions such as: which real numbers and real number functions are computable, and which mathematical tasks in analysis can be solved by algorithmic means? Nowadays this theory has many different facets that embrace topics from computability theory, algorithmic randomness, computational complexity, dynamical systems, fractals, and analog computers, up to logic, descriptive set theory, constructivism, and reverse mathematics. In recent decades computable analysis has invaded many branches of analysis, and researchers have studied computability and complexity questions arising from real and complex analysis, functional analysis, and the theory of differential equations, up to (geometric) measure theory and topology. This handbook represents the first coherent cross-section through most active research topics on the more theoretical side of the field. It contains 11 chapters grouped into parts on computability in analysis; complexity, dynamics, and randomness; and constructivity, logic, and descriptive complexity. All chapters are written by leading experts working at the cutting edge of the respective topic. Researchers and graduate students in the areas of theoretical computer science and mathematical logic will find systematic introductions into many branches of computable analysis, and a wealth of information and references that will help them to navigate the modern research literature in this field.
Computability And Complexity Of Julia Sets
DOWNLOAD
Author : Kota Hiratsuka
language : en
Publisher:
Release Date : 2013
Computability And Complexity Of Julia Sets written by Kota Hiratsuka and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013 with categories.
Computability And Complexity Of Julia Sets
DOWNLOAD
Author : Kota Hiratsuka
language : en
Publisher:
Release Date : 2014
Computability And Complexity Of Julia Sets written by Kota Hiratsuka and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014 with categories.
Computability And Complexity
DOWNLOAD
Author : Neil D. Jones
language : en
Publisher: MIT Press
Release Date : 1997
Computability And Complexity written by Neil D. Jones and has been published by MIT Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997 with Computers categories.
Computability and complexity theory should be of central concern to practitioners as well as theorists. Unfortunately, however, the field is known for its impenetrability. Neil Jones's goal as an educator and author is to build a bridge between computability and complexity theory and other areas of computer science, especially programming. In a shift away from the Turing machine- and G�del number-oriented classical approaches, Jones uses concepts familiar from programming languages to make computability and complexity more accessible to computer scientists and more applicable to practical programming problems. According to Jones, the fields of computability and complexity theory, as well as programming languages and semantics, have a great deal to offer each other. Computability and complexity theory have a breadth, depth, and generality not often seen in programming languages. The programming language community, meanwhile, has a firm grasp of algorithm design, presentation, and implementation. In addition, programming languages sometimes provide computational models that are more realistic in certain crucial aspects than traditional models. New results in the book include a proof that constant time factors do matter for its programming-oriented model of computation. (In contrast, Turing machines have a counterintuitive "constant speedup" property: that almost any program can be made to run faster, by any amount. Its proof involves techniques irrelevant to practice.) Further results include simple characterizations in programming terms of the central complexity classes PTIME and LOGSPACE, and a new approach to complete problems for NLOGSPACE, PTIME, NPTIME, and PSPACE, uniformly based on Boolean programs. Foundations of Computing series
Crossroads Of Computability And Logic Insights Inspirations And Innovations
DOWNLOAD
Author : Arnold Beckmann
language : en
Publisher: Springer Nature
Release Date : 2025-06-19
Crossroads Of Computability And Logic Insights Inspirations And Innovations written by Arnold Beckmann and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-06-19 with Computers categories.
This book constitutes the refereed proceedings of the 21st Conference on Computability and Logic, CiE 2025, held in Lisbon, Portugal, during July 14–18, 2025. The 27 full papers included in this book were carefully reviewed and selected from 49 submissions. They focus on computability-related science, ranging over mathematics, computer science and applications in various natural and engineering sciences, such as physics and biology, as well as related fields, such as philosophy and history of computing. CiE 2025 had as its motto Crossroads of Computability and Logic: Insights, Inspirations, and Innovations, drawing on the numerous interconnections between computability research and broader logical methodologies, considering both well-established perspectives as well as recent innovations.
Computable Analysis
DOWNLOAD
Author : Klaus Weihrauch
language : en
Publisher: Springer Science & Business Media
Release Date : 2000-09-14
Computable Analysis written by Klaus Weihrauch and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000-09-14 with Computers categories.
Merging fundamental concepts of analysis and recursion theory to a new exciting theory, this book provides a solid fundament for studying various aspects of computability and complexity in analysis. It is the result of an introductory course given for several years and is written in a style suitable for graduate-level and senior students in computer science and mathematics. Many examples illustrate the new concepts while numerous exercises of varying difficulty extend the material and stimulate readers to work actively on the text.
Proceedings Of The 7th 8th Asian Logic Conferences
DOWNLOAD
Author : Rod Downey
language : en
Publisher: World Scientific
Release Date : 2003
Proceedings Of The 7th 8th Asian Logic Conferences written by Rod Downey and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003 with Computers categories.
The 7th and the 8th Asian Logic Conferences belong to the series of logic conferences inaugurated in Singapore in 1981. This meeting is held once every three years and rotates among countries in the Asia-Pacific region, with interests in the broad area of logic, including theoretical computer science. It is now considered a major conference in this field and is regularly sponsored by the Association for Symbolic Logic.This book contains papers ? many of them surveys by leading experts ? of both the 7th meeting (in Hsi-Tou, Taiwan) and the 8th (in Chongqing, China). The volume planned for the 7th meeting was interrupted by the earthquake in Taiwan and the decision was made to combine the two proceedings. The 8th conference is also the ICM2002 Satellite Conference on Mathematical Logic.
New Computational Paradigms
DOWNLOAD
Author : S.B. Cooper
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-11-28
New Computational Paradigms written by S.B. Cooper and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-11-28 with Computers categories.
This superb exposition of a complex subject examines new developments in the theory and practice of computation from a mathematical perspective, with topics ranging from classical computability to complexity, from biocomputing to quantum computing. This book is suitable for researchers and graduate students in mathematics, philosophy, and computer science with a special interest in logic and foundational issues. Most useful to graduate students are the survey papers on computable analysis and biological computing. Logicians and theoretical physicists will also benefit from this book.