000			04382nam a22005055i 4500
001			978-0-387-68441-3
003			DE-He213
005			20250710084006.0
007			cr nn 008mamaa
008			101029s2010 xxu| s |||| 0|eng d
020			_a9780387684413 _a99780387684413
024	7		_a10.1007/978-0-387-68441-3 _2doi
082	0	4	_a518.1 _223
100	1		_aDowney, Rodney G. _eauthor.
245	1	0	_aAlgorithmic Randomness and Complexity _h[recurso electrónico] / _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			_arecurso en línea _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 _zVer el texto completo en las instalaciones del CICY
912			_aZDB-2-SMA
942			_2ddc _cER
999			_c57971 _d57971