Buch, Englisch, Band 51, 452 Seiten, Format (B × H): 155 mm x 231 mm, Gewicht: 739 g
Reihe: Oxford Logic Guides
Buch, Englisch, Band 51, 452 Seiten, Format (B × H): 155 mm x 231 mm, Gewicht: 739 g
Reihe: Oxford Logic Guides
ISBN: 978-0-19-965260-0
Verlag: Oxford University Press
The interplay between computability and randomness has been an active area of research in recent years, reflected by ample funding in the USA, numerous workshops, and publications on the subject. The complexity and the randomness aspect of a set of natural numbers are closely related. Traditionally, computability theory is concerned with the complexity aspect. However, computability theoretic tools can also be used to introduce mathematical counterparts for the
intuitive notion of randomness of a set. Recent research shows that, conversely, concepts and methods originating from randomness enrich computability theory.
The book covers topics such as lowness and highness properties, Kolmogorov complexity, betting strategies and higher computability. Both the basics and recent research results are desribed, providing a very readable introduction to the exciting interface of computability and randomness for graduates and researchers in computability theory, theoretical computer science, and measure theory.
Zielgruppe
Graduates and researchers in computability theory, computer science and measure theory.
Autoren/Hrsg.
Fachgebiete
Weitere Infos & Material
Preface
1: The complexity of sets
2: The descriptive complexity of strings
3: Martin-Löf randomness and its variants
4: Diagonally noncomputable functions
5: Lowness Properties and K-triviality
6: Some advanced computability theory
7: Randomness and betting strategies
8: Classes of computational complexity
9: Higher computability and randomness
Solutions to exercises
References
Index
