Ming Li Paul Vitányi Fourth Edition Page 1 An Introduction to Kolmogorov Complexity and Its
Applications Ming Li Paul Vitányi Fourth Edition Texts in Computer Science Page 2 Texts in …

This book is concerned with the theory of computability and complexity over the real
numbers. This theory was initiated by Turing, Grzegorczyk, Lacombe, Banach and Mazur …

A constructive version of Hausdorff dimension is developed using constructive supergales,
which are betting strategies that generalize the constructive supermartingales used in the …

Classical fractal dimensions (Hausdorff dimension and packing dimension) have recently
been effectivized by (i) characterizing them in terms of real‐valued functions called gales …

We formulate the conditional Kolmogorov complexity of x given y at precision r, where x and
y are points in Euclidean spaces and r is a natural number. We demonstrate the utility of this …

We use Kolmogorov complexity methods to give a lower bound on the effective Hausdorff
dimension of the point (x, a x+ b), given real numbers a, b, and x. We apply our main …

One of the serious mental disorders where people interpret reality in an abnormal state is
schizophrenia. A combination of extremely disordered thinking, delusion, and hallucination …

We report on some recent work centered on attempts to understand when one set is more
random than another. We look at various methods of calibration by initial segment …

The two most important notions of fractal dimension are Hausdorff dimension, developed by
Hausdorff Math. Ann., 79 (1919), pp. 157–179, and packing dimension, developed …

It is time for a new paper about open questions in the currently very active area of
randomness and computability. Ambos-Spies and Kučera presented such a paper in 1999 …