The π-calculus is to concurrent programs as the λ-calculus is to sequential programs (although the choice of π is not as canonical as that of λ).

"We introduce a modular toolkit for constructing probability monads, and show that it can be used for everything from discrete distributions to weighted particle filtering."

Argues that thermodynamic entropy can't be identified with the information-theoretic uncertainty of an (ideal) observer’s subjective distribution over a system’s microstates.

Provides a unified view on Information theory, Bayesian probability theory and machine learning.

An implementation of concepts and constructions from category theory in the functional programming language Standard ML.

Videos and slides on algorithmic complexity, universal induction and learning theory.

Suggests a method to obtain a stable approximation of the Kolmogorov complexity for sequences generated by algorithms which are shorter than typical compiler lengths.

Gives a precise methodology for studying learning from a computational viewpoint. Show that there are both serious limits and important nontrivial classes of concepts that ca be learned.

A superseded, or obsolete, scientific theory is a scientific theory that was once commonly accepted but is no longer considered the most complete description of reality by mainstream science; or a falsifiable theory which has been shown to be false.

The predictions of the theory take the form of probability distributions for the outcome of experiments, which makes it testable.

The major theme of the thesis is to develop a mathematical foundation of Artificial Intelligence and, more specifically, to develop a theory for rational agents acting optimally in any environment.

Soweit fürs maschinelle Lernen relevant. Stichwortartige Beilage zur Vorlesung "Maschinelles Lernen II" (SS 2005).

Deals in an abstract way with mathematical structures and relationships between them. A category consists of a class of objects, a class of morphisms (structure-preserving mappings between structures) and a binary operation (composition of morphisms).

The only postulate in this theory of everything is that all structures that exist mathematically exist also physically.

A formalization of Occam's Razor in which the best hypothesis for a given set of data is the one that leads to the largest compression of the data. Computable!

Great introduction to algorithmic information theory. Explains Kolmogorov complexity, Solomonoff probability, Levins Kt-complexity, "Martin-Loef" randomness, ...

A detailed introduction to the main techniques of algorithmic information theory.

If positive solutions to a yes/no problem can be verified quickly in polynomial time, can the answers also be computed quickly in polynomial time? There is no proof one way or the other yet.

Draft of a textbook on computational complexity theory. Basic complexity classes, lower bounds for concrete computational models and more advanced topics.