Algorithmic Randomness and Complexity / Edition 1 available in Hardcover
- Pub. Date:
- Springer New York
Computability and complexity theory are two central areas of research in theoretical computer science. Until recently, most work in these areas concentrated on problems over discrete structures, but there has been enormous growth of computability theory and complexity theory over the real numbers and other continuous structures, especially incorporating concepts of "randomness." One reason for this growth is that more and more computation problems over the real numbers are being dealt with by computer scientistsin computational geometry and in the modeling of dynamical and hybrid systems. Scientists working on these questions come from such diverse fields as theoretical computer science, domain theory, logic, constructive mathematics, computer arithmetic, numerical mathematics, and analysis.
An essential resource for all researchers in theoretical computer science, logic, computability theory and complexity.
Table of Contents
Preface.- Acknowledgments.- Introduction.- I. Background.- Preliminaries.- Computability Theory.- Kolmogorov Complexity of Finite Strings.- Relating Plain and Prefix-Free Complexity.- Effective Reals.- II. Randomness of Sets.- Martin-Löf Randomness.- Other Notions of Effective Randomness.- Algorithmic Randomness and Turing Reducibility.- III. Relative Randomness.- Measures of Relative Randomness.- The Quantity of K- and Other Degrees.- Randomness-Theoretic Weakness.- Lowness for Other Randomness Notions.- Effective Hausdorff Dimension.- IV. Further Topics.- Omega as an Operator.- Complexity of C.E. Sets.- References.- Index.