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008 | 101029s2010 xxu| s |||| 0|eng d | ||
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_a9780387684413 _9978-0-387-68441-3 |
024 | 8 | 7 |
_a10.1007/978-0-387-68441-3 _2doi |
050 | 8 | 4 | _aLibro electrónico |
072 | 8 | 7 |
_aPBKS _2bicssc |
072 | 8 | 7 |
_aCOM051300 _2bisacsh |
082 |
_a518.1 _223 |
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100 | 8 | 1 |
_aDowney, Rodney G. _eauthor. _922521 |
245 | 9 | 7 |
_aAlgorithmic Randomness and Complexity _h[electronic resource] / _cby Rodney G. Downey, Denis R. Hirschfeldt. |
001 | 000046123 | ||
250 | 6 | 4 | _a1. |
300 | 6 | 4 |
_aXXVIII, 855p. 8 illus. _bonline resource. |
490 | 8 | 1 |
_aTheory and Applications of Computability, In cooperation with the association Computability in Europe, _x2190-619X |
505 | 8 | 0 | _aBackground -- Preliminaries -- Computability Theory -- Kolmogorov Complexity of Finite Strings -- Relating Complexities -- Effective Reals -- Notions of Randomness -- Martin-Lȵf 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 | 6 | 4 | _aIntuitively, a sequence such as 101010101010101010Ǫ does not seem random, whereas 101101011101010100Ǫ, 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-Lȵf. 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 | 8 | 0 |
_aMathematics. _98571 |
650 | 8 | 0 |
_aInformation theory. _922522 |
650 | 8 | 0 |
_aComputer science. _922523 |
650 | 8 | 0 |
_aComputer software. _910118 |
650 | 8 | 0 |
_aAlgorithms. _98598 |
650 |
_aMathematics. _98571 |
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650 |
_aAlgorithms. _98598 |
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650 |
_aAlgorithm Analysis and Problem Complexity. _910120 |
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650 |
_aTheory of Computation. _922524 |
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650 |
_aComputation by Abstract Devices. _99725 |
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700 | 8 | 1 |
_aHirschfeldt, Denis R. _eauthor. _922525 |
710 | 8 | 2 |
_aSpringerLink (Online service) _922526 |
773 | 8 | 0 | _tSpringer eBooks |
776 |
_iPrinted edition: _z9780387955674 |
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830 | 8 | 0 |
_aTheory and Applications of Computability, In cooperation with the association Computability in Europe, _x2190-619X _922527 |
856 |
_uhttp://dx.doi.org/10.1007/978-0-387-68441-3 _zde clik aquí para ver el libro electrónico |
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264 | 8 | 1 |
_aNew York, NY : _bSpringer New York, _c2010. |
336 | 6 | 4 |
_atext _btxt _2rdacontent |
337 | 6 | 4 |
_acomputer _bc _2rdamedia |
338 | 6 | 4 |
_aonline resource _bcr _2rdacarrier |
347 | 6 | 4 |
_atext file _bPDF _2rda |
516 | 6 | 4 | _aZDB-2-SMA |
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