Algorithmic Randomness and Complexity
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...
| Main Authors: | , |
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| Format: | eBook |
| Language: | English |
| Published: |
New York, NY
Springer New York
2010, 2010
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| Edition: | 1st ed. 2010 |
| Series: | Theory and Applications of Computability, In cooperation with the association Computability in Europe
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| Subjects: | |
| Online Access: | |
| Collection: | Springer eBooks 2005- - Collection details see MPG.ReNa |
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