rdf-syntax-grammar
mods:
  schema location: http://www.loc.gov/mods/v3 http://www.loc.gov/standards/mods/v3/mods-3-2.xsd
  title info:
    title: Algorithmic Randomness and Complexity
  name:
    name part: Downey, Rodney G.
    role:
      role term: creator
    role:
      role term: author.
  name:
    name part: Hirschfeldt, Denis R.
    role:
      role term: author.
  name:
    name part: SpringerLink (Online service)
  type of resource: text
  origin info:
    place:
      place term: xxu
    date issued: 2010
    edition: 1.
    issuance: monographic
  language:
    language term: eng
  physical description:
    form: electronic
    form: electronic resource
    reformatting quality: access
    form: remote
    extent: XXVIII, 855 p. 8 illus. online resource.
  abstract: 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.
  table of contents: 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.
  note: by Rodney G. Downey, Denis R. Hirschfeldt.
  subject:
    topic: Mathematics
  subject:
    topic: Computers
  subject:
    topic: Algorithms
  subject:
    topic: Mathematics
  subject:
    topic: Algorithms
  subject:
    topic: Algorithm Analysis and Problem Complexity
  subject:
    topic: Theory of Computation
  subject:
    topic: Computation by Abstract Devices
  classification: QA76.9.A43
  classification: 518.1
  related item:
    title info:
      title: Springer eBooks
  related item:
    title info:
      title: Theory and Applications of Computability, In cooperation with the association Computability in Europe
  identifier: 9780387684413
  identifier: http://dx.doi.org/10.1007/978-0-387-68441-3
  record info:
    record creation date: 101029
    record change date: 20151111201853.0
    record identifier: 978-0-387-68441-3