Lecture Notes in Logic, 50

Algorithmic Randomness

Johanna N. Y. Franklin and Christopher P. Porter

The last two decades have seen a wave of exciting new developments in the theory of algorithmic randomness and its applications to other areas of mathematics. This volume surveys much of the recent work that has not been included in published volumes until now. It contains a range of articles on algorithmic randomness and its interactions with closely related topics such as computability theory and computational complexity, as well as wider applications in areas of mathematics including analysis, probability, and ergodic theory. In addition to being an indispensable reference for researchers in algorithmic randomness, the unified view of the theory presented here makes this an excellent entry point for graduate students and other newcomers to the field.

Table of Contents

Preface

1. Key developments in algorithmic randomness

2. Algorithmic randomness in ergodic theory

3. Algorithmic randomness and constructive/computable measure theory

4. Algorithmic randomness and layerwise computability

5. Relativization in randomness

6. Aspects of Chaitin’s Omega

7. Biased algorithmic randomness

8. Higher randomness

9. Resource bounded randomness and its applications

Index