Algorithmic Randomness and Complexity

• Main Authors: Downey, Rodney G. (Author), Hirschfeldt, Denis R. (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: New York, NY : Springer New York, 2010.
• Edition: 1.
• Series: Theory and Applications of Computability, In cooperation with the association Computability in Europe,
• Subjects: 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...