Information Theoretic Incompleteness

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Information Theoretic Incompleteness

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Author : Gregory J. Chaitin
language : en
Publisher: World Scientific
Release Date : 1992

Information Theoretic Incompleteness written by Gregory J. Chaitin and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992 with Computers categories.

In this mathematical autobiography, Gregory Chaitin presents a technical survey of his work and a nontechnical discussion of its significance. The volume is an essential companion to the earlier collection of Chaitin's papers Information, Randomness and Incompleteness, also published by World Scientific.The technical survey contains many new results, including a detailed discussion of LISP program size and new versions of Chaitin's most fundamental information-theoretic incompleteness theorems. The nontechnical part includes the lecture given by Chaitin in G?del's classroom at the University of Vienna, a transcript of a BBC TV interview, and articles from New Scientist, La Recherche, and the Mathematical Intelligencer.

Information Randomness Incompleteness

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Author : Gregory J. Chaitin
language : en
Publisher: World Scientific
Release Date : 1990-01-01

Information Randomness Incompleteness written by Gregory J. Chaitin and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1990-01-01 with Mathematics categories.

This book contains in easily accessible form all the main ideas of the creator and principal architect of algorithmic information theory. This expanded second edition has added thirteen abstracts, a 1988 Scientific American Article, a transcript of a EUROPALIA 89 lecture, an essay on biology, and an extensive bibliography. Its new larger format makes it easier to read. Chaitin's ideas are a fundamental extension of those of G”del and Turning and have exploded some basic assumptions of mathematics and thrown new light on the scientific method, epistemology, probability theory, and of course computer science and information theory.

Thinking About G Del And Turing

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Author : Gregory J. Chaitin
language : en
Publisher: World Scientific
Release Date : 2007

Thinking About G Del And Turing written by Gregory J. Chaitin and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007 with Mathematics categories.

Dr Gregory Chaitin, one of the world's leading mathematicians, is best known for his discovery of the remarkable ê number, a concrete example of irreducible complexity in pure mathematics which shows that mathematics is infinitely complex. In this volume, Chaitin discusses the evolution of these ideas, tracing them back to Leibniz and Borel as well as G”del and Turing.This book contains 23 non-technical papers by Chaitin, his favorite tutorial and survey papers, including Chaitin's three Scientific American articles. These essays summarize a lifetime effort to use the notion of program-size complexity or algorithmic information content in order to shed further light on the fundamental work of G”del and Turing on the limits of mathematical methods, both in logic and in computation. Chaitin argues here that his information-theoretic approach to metamathematics suggests a quasi-empirical view of mathematics that emphasizes the similarities rather than the differences between mathematics and physics. He also develops his own brand of digital philosophy, which views the entire universe as a giant computation, and speculates that perhaps everything is discrete software, everything is 0's and 1's.Chaitin's fundamental mathematical work will be of interest to philosophers concerned with the limits of knowledge and to physicists interested in the nature of complexity.

Information Randomness Incompleteness

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Author : Gregory J. Chaitin
language : en
Publisher: World Scientific
Release Date : 1987

Information Randomness Incompleteness written by Gregory J. Chaitin and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1987 with Computers categories.

The papers gathered in this book were published over a period of more than twenty years in widely scattered journals. They led to the discovery of randomness in arithmetic which was presented in the recently published monograph on ?Algorithmic Information Theory? by the author. There the strongest possible version of G”del's incompleteness theorem, using an information-theoretic approach based on the size of computer programs, was discussed. The present book is intended as a companion volume to the monograph and it will serve as a stimulus for work on complexity, randomness and unpredictability, in physics and biology as well as in metamathematics.

Logic Foundations The P Vs Np Problem And Information Theoretic Perspectives

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Author : Lucien Sina
language : en
Publisher: BoD – Books on Demand
Release Date : 2025-07-17

Logic Foundations The P Vs Np Problem And Information Theoretic Perspectives written by Lucien Sina and has been published by BoD – Books on Demand this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-07-17 with Mathematics categories.

This groundbreaking textbook presents a new approach to the study of logic by combining classical foundations with modern information-theoretic perspectives. Following a detailed introduction, it offers an information-theoretic formalization of logic. Subsequently, well-known but still unsolved problems, such as the P versus NP problem, are addressed using the provided tools. An optimization algorithm for the target requirements of logical problem-solving-regarding computability, expressiveness, and consistency-is presented, and finally, a few applications in other fields are showcased. The book offers students and researchers a comprehensive journey through the fundamental principles of logic while introducing innovative concepts at the intersection of logic, information theory, and computational complexity. Key features include: -Solid foundations in classical logic, including propositional and predicate logic, validity, and formal inference. -Novel integration of Shannon's information theory with traditional logical concepts. -Exploration of new approaches to axiomatization and formalization in light of Gödel's incompleteness results. -In-depth analysis of the P versus NP problem with information-theoretic and optimization approaches. -Clear explanations and examples suitable for beginners and beyond. -Applications in mathematics, computer science, and related fields.

Information Theory Evolution And The Origin Of Life

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Author : Hubert P. Yockey
language : en
Publisher: Cambridge University Press
Release Date : 2005-04-18

Information Theory Evolution And The Origin Of Life written by Hubert P. Yockey and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-04-18 with Computers categories.

Publisher Description

Information Theoretic Incompleteness

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Author : G. J. Chaitin
language : en
Publisher:
Release Date : 1992

Information Theoretic Incompleteness written by G. J. Chaitin and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992 with categories.

An Introduction To Kolmogorov Complexity And Its Applications

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Author : Ming Li
language : en
Publisher: Springer
Release Date : 2019-06-11

An Introduction To Kolmogorov Complexity And Its Applications written by Ming Li and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-06-11 with Mathematics categories.

This must-read textbook presents an essential introduction to Kolmogorov complexity (KC), a central theory and powerful tool in information science that deals with the quantity of information in individual objects. The text covers both the fundamental concepts and the most important practical applications, supported by a wealth of didactic features. This thoroughly revised and enhanced fourth edition includes new and updated material on, amongst other topics, the Miller-Yu theorem, the Gács-Kučera theorem, the Day-Gács theorem, increasing randomness, short lists computable from an input string containing the incomputable Kolmogorov complexity of the input, the Lovász local lemma, sorting, the algorithmic full Slepian-Wolf theorem for individual strings, multiset normalized information distance and normalized web distance, and conditional universal distribution. Topics and features: describes the mathematical theory of KC, including the theories of algorithmic complexity and algorithmic probability; presents a general theory of inductive reasoning and its applications, and reviews the utility of the incompressibility method; covers the practical application of KC in great detail, including the normalized information distance (the similarity metric) and information diameter of multisets in phylogeny, language trees, music, heterogeneous files, and clustering; discusses the many applications of resource-bounded KC, and examines different physical theories from a KC point of view; includes numerous examples that elaborate the theory, and a range of exercises of varying difficulty (with solutions); offers explanatory asides on technical issues, and extensive historical sections; suggests structures for several one-semester courses in the preface. As the definitive textbook on Kolmogorov complexity, this comprehensive and self-contained work is an invaluable resource for advanced undergraduate students, graduate students, and researchers in all fields of science.

Handbook Of Ecosystem Theories And Management

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Author : Felix Muller
language : en
Publisher: CRC Press
Release Date : 2000-02-10

Handbook Of Ecosystem Theories And Management written by Felix Muller and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000-02-10 with Science categories.

As part of the Environmental and Ecological Modeling Handbooks series, the Handbook of Ecosystem Theories and Management provides a comprehensive overview of ecosystem theory and the tools - ecological engineering, ecological modeling, ecotoxicology and ecological economics -to manage these systems. The book is laid out to provide a summary or

Information And Randomness

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Author : Cristian Calude
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09

Information And Randomness written by Cristian Calude 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 2013-03-09 with Computers categories.

"Algorithmic information theory (AIT) is the result of putting Shannon's information theory and Turing's computability theory into a cocktail shaker and shaking vigorously", says G.J. Chaitin, one of the fathers of this theory of complexity and randomness, which is also known as Kolmogorov complexity. It is relevant for logic (new light is shed on Gödel's incompleteness results), physics (chaotic motion), biology (how likely is life to appear and evolve?), and metaphysics (how ordered is the universe?). This book, benefiting from the author's research and teaching experience in Algorithmic Information Theory (AIT), should help to make the detailed mathematical techniques of AIT accessible to a much wider audience.