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007 cr nn 008mamaa
008 101029s2010 xxu| s |||| 0|eng d
020 6 4 _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
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
650 _aAlgorithms.
_98598
650 _aAlgorithm Analysis and Problem Complexity.
_910120
650 _aTheory of Computation.
_922524
650 _aComputation by Abstract Devices.
_99725
700 8 1 _aHirschfeldt, Denis R.
_eauthor.
_922525
710 8 2 _aSpringerLink (Online service)
_922526
773 8 0 _tSpringer eBooks
776 _iPrinted edition:
_z9780387955674
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
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
999 _c45852
_d45852
942 _c05