This tutorial gives a brief introduction to computable analysis. The objective of this theory is
to study algorithmic aspects of real numbers, real number functions, subsets of real …

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 …

The first edition of the monograph Information and Randomness: An Algorithmic Perspective
by Crist ian Calude was published in 1994. In my Foreword I said:" The research in …

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 …

A Chaitin Omega number is the halting probability of a universal prefix-free Turing machine.
Every Omega number is simultaneously computably enumerable (the limit of a computable …

Solovay showed that there are noncomputable reals α such that H (α∥ n)≤ H (1n)+ O (1),
where H is prefix-free Kolmogorov complexity. Such H-trivial reals are interesting due to the …

We introduce the zeta number, natural halting probability, and natural complexity of a Turing
machine and we relate them to Chaitin's Omega number, halting probability, and program …

We develop a statistical mechanical interpretation of algorithmic information theory by
introducing the notion of thermodynamic quantities, such as free energy, energy, statistical …

We study effectively given positive reals (more specifically, computably enumerable reals)
under a measure of relative randomness introduced by Solovay manuscript, IBM Thomas J …

Abstract Shannon's Information Theory (IT)(1948) definitely established the purely
mathematical nature of entropy and relative entropy, in contrast to the previous identification …