Related papers: Some Theorems on the Algorithmic Approach to Proba…

Presents a history of the evolution of the author's ideas on program-size complexity and its applications to metamathematics over the course of more than four decades. Includes suggestions for further work.

This paper covers two topics: first an introduction to Algorithmic Complexity Theory: how it defines probability, some of its characteristic properties and past successful applications. Second, we apply it to problems in A.I. - where it…

The paper elaborates an endeavor on applying the algorithmic information-theoretic computational complexity to meta-social-sciences. It is motivated by the effort on seeking the impact of the well-known incompleteness theorem to the…

The original version of the paper was published in Contemporary Mathematics 378 ``Groups, Languages, Algorithms''; 2005, pp. 319-348. This is a modified version with Appendix that holds a corrected formulation of Proposition 4.1.

In this thesis I present a short review of ideas in quantum information theory. The first chapter contains introductory material, sketching the central ideas of probability and information theory. Quantum mechanics is presented at the level…

This dissertation contributes to mathematical and algorithmic problems that arise in the analysis of network and biological data.

The use of algorithmic information theory (Kolmogorov complexity theory) to explain the relation between mathematical probability theory and `real world' is discussed.

Algorithmic information theory roots the concept of information in computation rather than probability. These lecture notes were constructed in conjunction with the graduate course I taught at Universit\`a della Svizzera italiana in the…

The last theme of Kolmogorov's mathematics research was algorithmic theory of information, now often called Kolmogorov complexity theory. There are only two main publications of Kolmogorov (1965 and 1968-1969) on this topic. So Kolmogorov's…

Decision theories offer principled methods for making choices under various types of uncertainty. Algorithms that implement these theories have been successfully applied to a wide range of real-world problems, including materials and drug…

The current state-of-the-art in artificial intelligence is impressive, especially in terms of mastery of language, but not so much in terms of mathematical reasoning. What could be missing? Can we learn something useful about that gap from…

This work proposes an algebraic model for classical information theory. We first give an algebraic model of probability theory. Information theoretic constructs are based on this model. In addition to theoretical insights provided by our…

A didactical survey of the foundations of Algorithmic Information Theory. These notes are short on motivation, history and background but introduce some of the main techniques and concepts of the field. The "manuscript" has been evolving…

This paper has been withdrawn by the author; a revised version is part of the author's phd-thesis "Quasi-logarithmic structures" (Zurich, 2007).

The ideas here are a continuation of a previous article. Some of the applications of the main ideas in the previous article are explained, along with some limitations of the general ideas. There are situations where additional hypotheses…

Algorithmic information theory studies description complexity and randomness and is now a well known field of theoretical computer science and mathematical logic. There are several textbooks and monographs devoted to this theory where one…

Short review article on quantum information processing accepted for Supplement III, Encyclopaedia of Mathematics (publication expected Summer 2001). See also http://www.wkap.nl/series.htm/ENM

This is a position paper written as an introduction to the special volume on quantum algorithms I edited for the journal Mathematical Structures in Computer Science (Volume 20 - Special Issue 06 (Quantum Algorithms), 2010).

Short review article on quantum computation accepted for Supplement III, Encyclopaedia of Mathematics (publication expected Summer 2001). See also http://www.wkap.nl/series.htm/ENM

This habilitation thesis is cumulative and, therefore, is collecting and connecting research that I (together with several co-authors) have conducted over the last few years. Thus, the absolute core of the work is formed by the ten…