000 04396nam a22005295i 4500
001 978-0-387-68441-3
003 DE-He213
005 20140220084454.0
007 cr nn 008mamaa
008 101029s2010 xxu| s |||| 0|eng d
020 _a9780387684413
_9978-0-387-68441-3
024 7 _a10.1007/978-0-387-68441-3
_2doi
050 4 _aQA76.9.A43
072 7 _aPBKS
_2bicssc
072 7 _aCOM051300
_2bisacsh
082 0 4 _a518.1
_223
100 1 _aDowney, Rodney G.
_eauthor.
245 1 0 _aAlgorithmic Randomness and Complexity
_h[electronic resource] /
_cby Rodney G. Downey, Denis R. Hirschfeldt.
250 _a1.
264 1 _aNew York, NY :
_bSpringer New York,
_c2010.
300 _aXXVIII, 855p. 8 illus.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aTheory and Applications of Computability, In cooperation with the association Computability in Europe,
_x2190-619X
505 0 _aBackground -- 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 _aIntuitively, 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 _aMathematics.
650 0 _aInformation theory.
650 0 _aComputer science.
650 0 _aComputer software.
650 0 _aAlgorithms.
650 1 4 _aMathematics.
650 2 4 _aAlgorithms.
650 2 4 _aAlgorithm Analysis and Problem Complexity.
650 2 4 _aTheory of Computation.
650 2 4 _aComputation by Abstract Devices.
700 1 _aHirschfeldt, Denis R.
_eauthor.
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9780387955674
830 0 _aTheory and Applications of Computability, In cooperation with the association Computability in Europe,
_x2190-619X
856 4 0 _uhttp://dx.doi.org/10.1007/978-0-387-68441-3
912 _aZDB-2-SMA
999 _c109760
_d109760