Algorithmic Randomness and Complexity (Record no. 109760)
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| 000 -LEADER | |
|---|---|
| fixed length control field | 04396nam a22005295i 4500 |
| 001 - CONTROL NUMBER | |
| control field | 978-0-387-68441-3 |
| 003 - CONTROL NUMBER IDENTIFIER | |
| control field | DE-He213 |
| 005 - DATE AND TIME OF LATEST TRANSACTION | |
| control field | 20140220084454.0 |
| 007 - PHYSICAL DESCRIPTION FIXED FIELD--GENERAL INFORMATION | |
| fixed length control field | cr nn 008mamaa |
| 008 - FIXED-LENGTH DATA ELEMENTS--GENERAL INFORMATION | |
| fixed length control field | 101029s2010 xxu| s |||| 0|eng d |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER | |
| International Standard Book Number | 9780387684413 |
| -- | 978-0-387-68441-3 |
| 024 7# - OTHER STANDARD IDENTIFIER | |
| Standard number or code | 10.1007/978-0-387-68441-3 |
| Source of number or code | doi |
| 050 #4 - LIBRARY OF CONGRESS CALL NUMBER | |
| Classification number | QA76.9.A43 |
| 072 #7 - SUBJECT CATEGORY CODE | |
| Subject category code | PBKS |
| Source | bicssc |
| 072 #7 - SUBJECT CATEGORY CODE | |
| Subject category code | COM051300 |
| Source | bisacsh |
| 082 04 - DEWEY DECIMAL CLASSIFICATION NUMBER | |
| Classification number | 518.1 |
| Edition number | 23 |
| 100 1# - MAIN ENTRY--PERSONAL NAME | |
| Personal name | Downey, Rodney G. |
| Relator term | author. |
| 245 10 - TITLE STATEMENT | |
| Title | Algorithmic Randomness and Complexity |
| Medium | [electronic resource] / |
| Statement of responsibility, etc | by Rodney G. Downey, Denis R. Hirschfeldt. |
| 250 ## - EDITION STATEMENT | |
| Edition statement | 1. |
| 264 #1 - | |
| -- | New York, NY : |
| -- | Springer New York, |
| -- | 2010. |
| 300 ## - PHYSICAL DESCRIPTION | |
| Extent | XXVIII, 855p. 8 illus. |
| Other physical details | online resource. |
| 336 ## - | |
| -- | text |
| -- | txt |
| -- | rdacontent |
| 337 ## - | |
| -- | computer |
| -- | c |
| -- | rdamedia |
| 338 ## - | |
| -- | online resource |
| -- | cr |
| -- | rdacarrier |
| 347 ## - | |
| -- | text file |
| -- | |
| -- | rda |
| 490 1# - SERIES STATEMENT | |
| Series statement | Theory and Applications of Computability, In cooperation with the association Computability in Europe, |
| International Standard Serial Number | 2190-619X |
| 505 0# - FORMATTED CONTENTS NOTE | |
| Formatted contents note | Background -- Preliminaries -- Computability Theory -- Kolmogorov Complexity of Finite Strings -- Relating Complexities -- Effective Reals -- Notions of Randomness -- Martin-Löf Randomness -- Other Notions of Algorithmic Randomness -- Algorithmic Randomness and Turing Reducibility -- Relative Randomness -- Measures of Relative Randomness -- Complexity and Relative Randomness for 1-Random Sets -- Randomness-Theoretic Weakness -- Lowness and Triviality for Other Randomness Notions -- Algorithmic Dimension -- Further Topics -- Strong Jump Traceability -- ? as an Operator -- Complexity of Computably Enumerable Sets. |
| 520 ## - SUMMARY, ETC. | |
| Summary, etc | 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 Martin-Löf. 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. |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name as entry element | Mathematics. |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name as entry element | Information theory. |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name as entry element | Computer science. |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name as entry element | Computer software. |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name as entry element | Algorithms. |
| 650 14 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name as entry element | Mathematics. |
| 650 24 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name as entry element | Algorithms. |
| 650 24 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name as entry element | Algorithm Analysis and Problem Complexity. |
| 650 24 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name as entry element | Theory of Computation. |
| 650 24 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name as entry element | Computation by Abstract Devices. |
| 700 1# - ADDED ENTRY--PERSONAL NAME | |
| Personal name | Hirschfeldt, Denis R. |
| Relator term | author. |
| 710 2# - ADDED ENTRY--CORPORATE NAME | |
| Corporate name or jurisdiction name as entry element | SpringerLink (Online service) |
| 773 0# - HOST ITEM ENTRY | |
| Title | Springer eBooks |
| 776 08 - ADDITIONAL PHYSICAL FORM ENTRY | |
| Display text | Printed edition: |
| International Standard Book Number | 9780387955674 |
| 830 #0 - SERIES ADDED ENTRY--UNIFORM TITLE | |
| Uniform title | Theory and Applications of Computability, In cooperation with the association Computability in Europe, |
| -- | 2190-619X |
| 856 40 - ELECTRONIC LOCATION AND ACCESS | |
| Uniform Resource Identifier | http://dx.doi.org/10.1007/978-0-387-68441-3 |
| 912 ## - | |
| -- | ZDB-2-SMA |
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