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Author: Gregory. J. Chaitin
Publisher: Cambridge University Press
ISBN: 9780521616041
Category : Computers
Languages : en
Pages : 192
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Book Description
Chaitin, the inventor of algorithmic information theory, presents in this book the strongest possible version of Gödel's incompleteness theorem, using an information theoretic approach based on the size of computer programs. One half of the book is concerned with studying the halting probability of a universal computer if its program is chosen by tossing a coin. The other half is concerned with encoding the halting probability as an algebraic equation in integers, a so-called exponential diophantine equation.
Author: Gregory. J. Chaitin
Publisher: Cambridge University Press
ISBN: 9780521616041
Category : Computers
Languages : en
Pages : 192
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Book Description
Chaitin, the inventor of algorithmic information theory, presents in this book the strongest possible version of Gödel's incompleteness theorem, using an information theoretic approach based on the size of computer programs. One half of the book is concerned with studying the halting probability of a universal computer if its program is chosen by tossing a coin. The other half is concerned with encoding the halting probability as an algebraic equation in integers, a so-called exponential diophantine equation.
Author: Rodney G. Downey
Publisher: Springer Science & Business Media
ISBN: 0387684417
Category : Computers
Languages : en
Pages : 883
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Book Description
Computability and complexity theory are two central areas of research in theoretical computer science. This book provides a systematic, technical development of "algorithmic randomness" and complexity for scientists from diverse fields.
Author: Sean D Devine
Publisher:
ISBN: 9780750326414
Category :
Languages : en
Pages : 238
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Book Description
Algorithmic information theory (AIT), or Kolmogorov complexity as it is known to mathematicians, can provide a useful tool for scientists to look at natural systems, however, some critical conceptual issues need to be understood and the advances already made collated and put in a form accessible to scientists. This book has been written in the hope that readers will be able to absorb the key ideas behind AIT so that they are in a better position to access the mathematical developments and to apply the ideas to their own areas of interest. The theoretical underpinning of AIT is outlined in the earlier chapters, while later chapters focus on the applications, drawing attention to the thermodynamic commonality between ordered physical systems such as the alignment of magnetic spins, the maintenance of a laser distant from equilibrium, and ordered living systems such as bacterial systems, an ecology, and an economy. Key Features Presents a mathematically complex subject in language accessible to scientists Provides rich insights into modelling far-from-equilibrium systems Emphasises applications across range of fields, including physics, biology and econophysics Empowers scientists to apply these mathematical tools to their own research
Author: Peter Seibt
Publisher: Springer Science & Business Media
ISBN: 3540332197
Category : Computers
Languages : en
Pages : 446
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Book Description
Algorithmic Information Theory treats the mathematics of many important areas in digital information processing. It has been written as a read-and-learn book on concrete mathematics, for teachers, students and practitioners in electronic engineering, computer science and mathematics. The presentation is dense, and the examples and exercises are numerous. It is based on lectures on information technology (Data Compaction, Cryptography, Polynomial Coding) for engineers.
Author: Ming Li
Publisher: Springer Science & Business Media
ISBN: 1475726066
Category : Mathematics
Languages : en
Pages : 655
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Book Description
Briefly, we review the basic elements of computability theory and prob ability theory that are required. Finally, in order to place the subject in the appropriate historical and conceptual context we trace the main roots of Kolmogorov complexity. This way the stage is set for Chapters 2 and 3, where we introduce the notion of optimal effective descriptions of objects. The length of such a description (or the number of bits of information in it) is its Kolmogorov complexity. We treat all aspects of the elementary mathematical theory of Kolmogorov complexity. This body of knowledge may be called algo rithmic complexity theory. The theory of Martin-Lof tests for random ness of finite objects and infinite sequences is inextricably intertwined with the theory of Kolmogorov complexity and is completely treated. We also investigate the statistical properties of finite strings with high Kolmogorov complexity. Both of these topics are eminently useful in the applications part of the book. We also investigate the recursion theoretic properties of Kolmogorov complexity (relations with Godel's incompleteness result), and the Kolmogorov complexity version of infor mation theory, which we may call "algorithmic information theory" or "absolute information theory. " The treatment of algorithmic probability theory in Chapter 4 presup poses Sections 1. 6, 1. 11. 2, and Chapter 3 (at least Sections 3. 1 through 3. 4).
Author: Marcus Hutter
Publisher: Springer Science & Business Media
ISBN: 3540268774
Category : Computers
Languages : en
Pages : 294
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Book Description
Personal motivation. The dream of creating artificial devices that reach or outperform human inteUigence is an old one. It is also one of the dreams of my youth, which have never left me. What makes this challenge so interesting? A solution would have enormous implications on our society, and there are reasons to believe that the AI problem can be solved in my expected lifetime. So, it's worth sticking to it for a lifetime, even if it takes 30 years or so to reap the benefits. The AI problem. The science of artificial intelligence (AI) may be defined as the construction of intelligent systems and their analysis. A natural definition of a system is anything that has an input and an output stream. Intelligence is more complicated. It can have many faces like creativity, solving prob lems, pattern recognition, classification, learning, induction, deduction, build ing analogies, optimization, surviving in an environment, language processing, and knowledge. A formal definition incorporating every aspect of intelligence, however, seems difficult. Most, if not all known facets of intelligence can be formulated as goal driven or, more precisely, as maximizing some utility func tion. It is, therefore, sufficient to study goal-driven AI; e. g. the (biological) goal of animals and humans is to survive and spread. The goal of AI systems should be to be useful to humans.
Author: Cristian Calude
Publisher: Springer Science & Business Media
ISBN: 3662030497
Category : Mathematics
Languages : en
Pages : 252
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Book Description
"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.
Author:
Publisher: Elsevier
ISBN: 0080930840
Category : Mathematics
Languages : en
Pages : 823
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Book Description
Information is a recognized fundamental notion across the sciences and humanities, which is crucial to understanding physical computation, communication, and human cognition. The Philosophy of Information brings together the most important perspectives on information. It includes major technical approaches, while also setting out the historical backgrounds of information as well as its contemporary role in many academic fields. Also, special unifying topics are high-lighted that play across many fields, while we also aim at identifying relevant themes for philosophical reflection. There is no established area yet of Philosophy of Information, and this Handbook can help shape one, making sure it is well grounded in scientific expertise. As a side benefit, a book like this can facilitate contacts and collaboration among diverse academic milieus sharing a common interest in information.• First overview of the formal and technical issues involved in the philosophy of information• Integrated presentation of major mathematical approaches to information, form computer science, information theory, and logic• Interdisciplinary themes across the traditional boundaries of natural sciences, social sciences, and humanities.
Author: Emmanuel Desurvire
Publisher: Cambridge University Press
ISBN: 0521881714
Category : Computers
Languages : en
Pages : 714
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Book Description
This complete overview of classical and quantum information theory employs an informal yet accurate approach, for students, researchers and practitioners.
Author: Frank Emmert-Streib
Publisher: Springer Science & Business Media
ISBN: 0387848150
Category : Computers
Languages : en
Pages : 443
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Book Description
This interdisciplinary text offers theoretical and practical results of information theoretic methods used in statistical learning. It presents a comprehensive overview of the many different methods that have been developed in numerous contexts.
