Jack H. Lutz

TL;DR: It is proved that almost every problem decidable in exponential space has essentially maximum circuit-size and space-bounded Kolmogorov complexity almost everywhere, and it is shown that infinite pseudorandom sequences have high nonuniform complexityalmost everywhere.

TL;DR: A constructive version of Hausdorff dimension is developed using constructive supergales, which are betting strategies that generalize the constructive supermartingales used in the theory of individual random sequences and the Kolmogorov complexity of a string is proven to be the product of its length and its dimension.

TL;DR: In this paper, a constructive version of Hausdorff dimension is developed using constructive supergales, which are betting strategies that generalize the constructive supermartingales used in the theory of individual random sequences.

TL;DR: A theory of resource-bounded dimension is developed using gales, which are natural generalizations of martingales, and when the resource bound $\Delta$ (a parameter of the theory) is unrestricted, the resulting dimension is precisely the classical Hausdorff dimension.

TL;DR: The measure structure of these classes is seen to interact in informative ways with bi-immunity, complexity cores, /sub