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Zusatztext Review from previous edition A great introduction to the field. It is well written and moves systematically to advanced topics. It can be used both as a reference and as a text book for a one-semester course in advanced algorithmic randomness and computability theory. Informationen zum Autor PhD, Mathematics, Univ. of Heidelberg, Germany, 1992Univ of Wisconsin, Madison 1994Cornell University 1995Univ of Chicago 1995-2001Habilitation, Univ. of Heidelberg, 1998Univ of Auckland 2002-present.60 journal and conference publications.Invited Speaker, International Congress of Mathematicians, Hyderabad 2010 Klappentext 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. randomness of sets of natural numbers. Zusammenfassung A monograph on the interface of computational complexity and randomness of sets of natural numbers. Inhaltsverzeichnis 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
