Algorithmic Randomness and Complexity [recurso electrónico] / by Rodney G. Downey, Denis R. Hirschfeldt.
Tipo de material: TextoSeries Theory and Applications of Computability, In cooperation with the association Computability in EuropeEditor: New York, NY : Springer New York, 2010Edición: 1Descripción: XXVIII, 855p. 8 illus. online resourceTipo de contenido: text Tipo de medio: computer Tipo de portador: online resourceISBN: 9780387684413Tema(s): Mathematics | Information theory | Computer science | Computer software | Algorithms | Mathematics | Algorithms | Algorithm Analysis and Problem Complexity | Theory of Computation | Computation by Abstract DevicesFormatos físicos adicionales: Printed edition:: Sin títuloClasificación CDD: 518.1 Clasificación LoC:QA76.9.A43Recursos en línea: Libro electrónicoTipo de ítem | Biblioteca actual | Colección | Signatura | Copia número | Estado | Fecha de vencimiento | Código de barras |
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Libro Electrónico | Biblioteca Electrónica | Colección de Libros Electrónicos | QA76.9 .A43 (Browse shelf(Abre debajo)) | 1 | No para préstamo | 370202-2001 |
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QA76.9 .A25 IT Security Management | QA76.9 .A25 Advances in intelligence and security informatics | QA76.9 .A25 I58 2013 Intelligent systems for security informatics | QA76.9 .A43 Algorithmic Randomness and Complexity | QA76.9 .A43 Algorithms and Programming | QA76.9 .A43 Euclidean Shortest Paths | QA76.9 .A43 Graphs and Algorithms in Communication Networks |
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.
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.
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