Algorithmic Randomness and Complexity

Authors:

ISBN: 978-0-387-95567-4 (Print) 978-0-387-68441-3 (Online)

Table of contents (16 chapters)

  1. Front Matter

    Pages i-xxviii

  2. Background

    1. Front Matter

      Pages 1-1

    2. No Access

      Book Chapter

      Pages 2-6

      Preliminaries

    3. No Access

      Book Chapter

      Pages 7-109

      Computability Theory

    4. No Access

      Book Chapter

      Pages 110-153

      Kolmogorov Complexity of Finite Strings

    5. No Access

      Book Chapter

      Pages 154-196

      Relating Complexities

    6. No Access

      Book Chapter

      Pages 197-224

      Effective Reals

  3. Notions of Randomness

    1. Front Matter

      Pages 225-225

    2. No Access

      Book Chapter

      Pages 226-268

      Martin-Löf Randomness

    3. No Access

      Book Chapter

      Pages 269-322

      Other Notions of Algorithmic Randomness

    4. No Access

      Book Chapter

      Pages 323-401

      Algorithmic Randomness and Turing Reducibility

  4. Relative Randomness

    1. Front Matter

      Pages 403-403

    2. No Access

      Book Chapter

      Pages 404-463

      Measures of Relative Randomness

    3. No Access

      Book Chapter

      Pages 464-499

      Complexity and Relative Randomness for 1-Random Sets

    4. No Access

      Book Chapter

      Pages 500-553

      Randomness-Theoretic Weakness

    5. No Access

      Book Chapter

      Pages 554-591

      Lowness and Triviality for Other Randomness Notions

    6. No Access

      Book Chapter

      Pages 592-666

      Algorithmic Dimension

  5. Further Topics

    1. Front Matter

      Pages 667-667

    2. No Access

      Book Chapter

      Pages 668-704

      Strong Jump Traceability

    3. No Access

      Book Chapter

      Pages 705-727

      Ω as an Operator

    4. No Access

      Book Chapter

      Pages 728-766

      Complexity of Computably Enumerable Sets

  6. Back Matter

    Pages 767-855