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.
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.
PhD, Mathematics, Univ. of Heidelberg, Germany, 1992 Univ of Wisconsin, Madison 1994 Cornell University 1995 Univ of Chicago 1995-2001 Habilitation, Univ. of Heidelberg, 1998 Univ of Auckland 2002-present. 60 journal and conference publications. Invited Speaker, International Congress of Mathematicians, Hyderabad 2010
Inhaltsangabe
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
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
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