Algorithmic Randomness and Complexity PDF Download
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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: 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: André Nies
Publisher: OUP Oxford
ISBN: 0191627887
Category : Mathematics
Languages : en
Pages : 450
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Book Description
The interplay between computability and randomness has been an active area of research in recent years, reflected by ample funding in the USA, numerous workshops, and publications on the subject. The complexity and the randomness aspect of a set of natural numbers are closely related. Traditionally, computability theory is concerned with the complexity aspect. However, computability theoretic tools can also be used to introduce mathematical counterparts for the intuitive notion of randomness of a set. Recent research shows that, conversely, concepts and methods originating from randomness enrich computability theory. The book covers topics such as lowness and highness properties, Kolmogorov complexity, betting strategies and higher computability. Both the basics and recent research results are desribed, providing a very readable introduction to the exciting interface of computability and randomness for graduates and researchers in computability theory, theoretical computer science, and measure theory.
Author: Frédérique Bassino
Publisher: Walter de Gruyter GmbH & Co KG
ISBN: 3110667029
Category : Mathematics
Languages : en
Pages : 386
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Book Description
Detailed Description
Author: Cristian Calude
Publisher: World Scientific
ISBN: 9812770828
Category : Science
Languages : en
Pages : 466
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Book Description
The book is a collection of papers written by a selection of eminent authors from around the world in honour of Gregory Chaitin's 60th birthday. This is a unique volume including technical contributions, philosophical papers and essays.
Author: Andrea Sorbi
Publisher: CRC Press
ISBN: 1482269759
Category : Mathematics
Languages : en
Pages : 380
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Book Description
"Integrates two classical approaches to computability. Offers detailed coverage of recent research at the interface of logic, computability theory, nd theoretical computer science. Presents new, never-before-published results and provides informtion not easily accessible in the literature."
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: Jan Krajicek
Publisher: Cambridge University Press
ISBN: 0521452058
Category : Computers
Languages : en
Pages : 361
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Book Description
Discusses the deep connections between logic and complexity theory, and lists a number of intriguing open problems.
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: Sanjeev Arora
Publisher: Cambridge University Press
ISBN: 0521424267
Category : Computers
Languages : en
Pages : 609
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Book Description
New and classical results in computational complexity, including interactive proofs, PCP, derandomization, and quantum computation. Ideal for graduate students.
Author: Jan Krajíček
Publisher: Cambridge University Press
ISBN: 1139493922
Category : Mathematics
Languages : en
Pages : 265
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Book Description
This book introduces a new approach to building models of bounded arithmetic, with techniques drawn from recent results in computational complexity. Propositional proof systems and bounded arithmetics are closely related. In particular, proving lower bounds on the lengths of proofs in propositional proof systems is equivalent to constructing certain extensions of models of bounded arithmetic. This offers a clean and coherent framework for thinking about lower bounds for proof lengths, and it has proved quite successful in the past. This book outlines a brand new method for constructing models of bounded arithmetic, thus for proving independence results and establishing lower bounds for proof lengths. The models are built from random variables defined on a sample space which is a non-standard finite set and sampled by functions of some restricted computational complexity. It will appeal to anyone interested in logical approaches to fundamental problems in complexity theory.
