The Resource Algorithmic randomness and complexity, Rod Downey, Denis Hirschfeldt
Algorithmic randomness and complexity, Rod Downey, Denis Hirschfeldt
Resource Information
The item Algorithmic randomness and complexity, Rod Downey, Denis Hirschfeldt represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of Missouri Libraries.This item is available to borrow from 1 library branch.
Resource Information
The item Algorithmic randomness and complexity, Rod Downey, Denis Hirschfeldt represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of Missouri Libraries.
This item is available to borrow from 1 library branch.
 Summary
 Intuitively, a sequence such as 101010101010101010... does not seem random, whereas 101101011101010100..., obtained using coin tosses, does. How can we reconcile this intuition with the fact that both are statistically equally likely? What does it mean to say that an individual mathematical object such as a real number is random, or to say that one real is more random than another? And what is the relationship between randomness and computational power. The theory of algorithmic randomness uses tools from computability theory and algorithmic information theory to address questions such as these. Much of this theory can be seen as exploring the relationships between three fundamental concepts: relative computability, as measured by notions such as Turing reducibility; information content, as measured by notions such as Kolmogorov complexity; and randomness of individual objects, as first successfully defined by MartinLöf. Although algorithmic randomness has been studied for several decades, a dramatic upsurge of interest in the area, starting in the late 1990s, has led to significant advances. This is the first comprehensive treatment of this important field, designed to be both a reference tool for experts and a guide for newcomers. It surveys a broad section of work in the area, and presents most of its major results and techniques in depth. Its organization is designed to guide the reader through this large body of work, providing context for its many concepts and theorems, discussing their significance, and highlighting their interactions. It includes a discussion of effective dimension, which allows us to assign concepts like Hausdorff dimension to individual reals, and a focused but detailed introduction to computability theory. It will be of interest to researchers and students in computability theory, algorithmic information theory, and theoretical computer science
 Language
 eng
 Extent
 1 online resource (xxviii, 855 pages)
 Contents

 Background
 Preliminaries
 Computability Theory
 Kolmogorov Complexity of Finite Strings
 Relating Complexities
 Effective Reals
 Notions of Randomness
 MartinLöf Randomness
 Other Notions of Algorithmic Randomness
 Algorithmic Randomness and Turing Reducibility
 Relative Randomness
 Measures of Relative Randomness
 Complexity and Relative Randomness for 1Random Sets
 RandomnessTheoretic Weakness
 Lowness and Triviality for Other Randomness Notions
 Algorithmic Dimension
 Further Topics
 Strong Jump Traceability
 ? as an Operator
 Complexity of Computably Enumerable Sets
 Isbn
 9780387684413
 Label
 Algorithmic randomness and complexity
 Title
 Algorithmic randomness and complexity
 Statement of responsibility
 Rod Downey, Denis Hirschfeldt
 Language
 eng
 Summary
 Intuitively, a sequence such as 101010101010101010... does not seem random, whereas 101101011101010100..., obtained using coin tosses, does. How can we reconcile this intuition with the fact that both are statistically equally likely? What does it mean to say that an individual mathematical object such as a real number is random, or to say that one real is more random than another? And what is the relationship between randomness and computational power. The theory of algorithmic randomness uses tools from computability theory and algorithmic information theory to address questions such as these. Much of this theory can be seen as exploring the relationships between three fundamental concepts: relative computability, as measured by notions such as Turing reducibility; information content, as measured by notions such as Kolmogorov complexity; and randomness of individual objects, as first successfully defined by MartinLöf. Although algorithmic randomness has been studied for several decades, a dramatic upsurge of interest in the area, starting in the late 1990s, has led to significant advances. This is the first comprehensive treatment of this important field, designed to be both a reference tool for experts and a guide for newcomers. It surveys a broad section of work in the area, and presents most of its major results and techniques in depth. Its organization is designed to guide the reader through this large body of work, providing context for its many concepts and theorems, discussing their significance, and highlighting their interactions. It includes a discussion of effective dimension, which allows us to assign concepts like Hausdorff dimension to individual reals, and a focused but detailed introduction to computability theory. It will be of interest to researchers and students in computability theory, algorithmic information theory, and theoretical computer science
 Cataloging source
 GW5XE
 http://library.link/vocab/creatorName
 Downey, R. G.
 Dewey number
 511.3
 Illustrations
 illustrations
 Index
 index present
 LC call number
 QA267.7
 LC item number
 .D69 2008
 Literary form
 non fiction
 Nature of contents

 dictionaries
 bibliography
 http://library.link/vocab/relatedWorkOrContributorName
 Hirschfeldt, Denis Roman
 http://library.link/vocab/subjectName

 Computational complexity
 Computable functions
 Computational complexity
 Computable functions
 Computable functions
 Computational complexity
 Label
 Algorithmic randomness and complexity, Rod Downey, Denis Hirschfeldt
 Bibliography note
 Includes bibliographical references (pages 767795) and index
 Carrier category
 online resource
 Carrier category code

 cr
 Carrier MARC source
 rdacarrier
 Color
 multicolored
 Content category
 text
 Content type code

 txt
 Content type MARC source
 rdacontent
 Contents
 Background  Preliminaries  Computability Theory  Kolmogorov Complexity of Finite Strings  Relating Complexities  Effective Reals  Notions of Randomness  MartinLöf Randomness  Other Notions of Algorithmic Randomness  Algorithmic Randomness and Turing Reducibility  Relative Randomness  Measures of Relative Randomness  Complexity and Relative Randomness for 1Random Sets  RandomnessTheoretic Weakness  Lowness and Triviality for Other Randomness Notions  Algorithmic Dimension  Further Topics  Strong Jump Traceability  ? as an Operator  Complexity of Computably Enumerable Sets
 Control code
 681900553
 Dimensions
 unknown
 Extent
 1 online resource (xxviii, 855 pages)
 Form of item
 online
 Isbn
 9780387684413
 Media category
 computer
 Media MARC source
 rdamedia
 Media type code

 c
 Other physical details
 illustrations
 http://library.link/vocab/ext/overdrive/overdriveId
 9780387955674
 Specific material designation
 remote
 System control number
 (OCoLC)681900553
 Label
 Algorithmic randomness and complexity, Rod Downey, Denis Hirschfeldt
 Bibliography note
 Includes bibliographical references (pages 767795) and index
 Carrier category
 online resource
 Carrier category code

 cr
 Carrier MARC source
 rdacarrier
 Color
 multicolored
 Content category
 text
 Content type code

 txt
 Content type MARC source
 rdacontent
 Contents
 Background  Preliminaries  Computability Theory  Kolmogorov Complexity of Finite Strings  Relating Complexities  Effective Reals  Notions of Randomness  MartinLöf Randomness  Other Notions of Algorithmic Randomness  Algorithmic Randomness and Turing Reducibility  Relative Randomness  Measures of Relative Randomness  Complexity and Relative Randomness for 1Random Sets  RandomnessTheoretic Weakness  Lowness and Triviality for Other Randomness Notions  Algorithmic Dimension  Further Topics  Strong Jump Traceability  ? as an Operator  Complexity of Computably Enumerable Sets
 Control code
 681900553
 Dimensions
 unknown
 Extent
 1 online resource (xxviii, 855 pages)
 Form of item
 online
 Isbn
 9780387684413
 Media category
 computer
 Media MARC source
 rdamedia
 Media type code

 c
 Other physical details
 illustrations
 http://library.link/vocab/ext/overdrive/overdriveId
 9780387955674
 Specific material designation
 remote
 System control number
 (OCoLC)681900553
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<div class="citation" vocab="http://schema.org/"><i class="fa faexternallinksquare fafw"></i> Data from <span resource="http://link.library.missouri.edu/portal/AlgorithmicrandomnessandcomplexityRod/ziD2p4x9Smc/" typeof="Book http://bibfra.me/vocab/lite/Item"><span property="name http://bibfra.me/vocab/lite/label"><a href="http://link.library.missouri.edu/portal/AlgorithmicrandomnessandcomplexityRod/ziD2p4x9Smc/">Algorithmic randomness and complexity, Rod Downey, Denis Hirschfeldt</a></span>  <span property="potentialAction" typeOf="OrganizeAction"><span property="agent" typeof="LibrarySystem http://library.link/vocab/LibrarySystem" resource="http://link.library.missouri.edu/"><span property="name http://bibfra.me/vocab/lite/label"><a property="url" href="http://link.library.missouri.edu/">University of Missouri Libraries</a></span></span></span></span></div>