Algorithmic Randomness and Complexity

• Κύριοι συγγραφείς: Downey, Rodney G. (Συγγραφέας), Hirschfeldt, Denis R. (Συγγραφέας)
• Συγγραφή απο Οργανισμό/Αρχή: SpringerLink (Online service)
• Μορφή: Ηλεκτρονική πηγή Ηλ. βιβλίο
• Γλώσσα: English
• Έκδοση: New York, NY : Springer New York, 2010.
• Έκδοση: 1.
• Σειρά: Theory and Applications of Computability, In cooperation with the association Computability in Europe,
• Θέματα: Mathematics.; Computers.; Algorithms.; Algorithm Analysis and Problem Complexity.; Theory of Computation.; Computation by Abstract Devices.

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...

Πίνακας περιεχομένων:

• 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.