Around Kolmogorov complexity: basic notions and results

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and monographs devoted to this theory where one can find the detailed exposition of many difficult results as well as historical references. However, it seems that a short survey of its basic notions and main results relating these notions to each other, is missing. This report attempts to fill this gap and covers the basic notions of algorithmic information theory: Kolmogorov complexity (plain, conditional, prefix), Solomonoff universal a priori probability, notions of randomness (Martin-L\"of randomness, Mises--Church randomness), effective Hausdorff dimension. We prove their basic properties (symmetry of information, connection between a priori probability and prefix complexity, criterion of randomness in terms of complexity, complexity characterization for effective dimension) and show some applications (incompressibility method in computational complexity theory, incompleteness theorems). It is based on the lecture notes of a course at Uppsala University given by the author

Basic notions of information structure

This article takes stock of the basic notions of Information Structure (IS). It first provides a general characterization of IS — following Chafe (1976) — within a communicative model of Common Ground(CG), which distinguishes between CG content and CG management. IS is concerned with those features of language that concern the local CG. Second, this paper defines and discusses the notions of Focus (as indicating alternatives) and its various uses, Givenness (as indicating that a denotation is already present in the CG), and Topic (as specifying what a statement is about). It also proposes a new notion, Delimitation, which comprises contrastive topics and frame setters, and indicates that the current conversational move does not entirely satisfy the local communicative needs. It also points out that rhetorical structuring partly belongs to IS.Peer Reviewe