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and monographs devoted to this theory where one can find the detailed exposition of many difficult results as well as historical references.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

Is Antitrust Too Complicated for Generalist Judges? The Impact of Economic Complexity and Judicial Training on Appeals

Modern antitrust litigation sometimes involves complex expert economic and econometric analysis. While this boom in the demand for economic analysis and expert testimony has clearly improved the welfare of economists—and schools offering basic economic training to judges—little is known about the empirical effects of economic complexity or judges' economic training on decision-making in antitrust litigation. We use a unique data set on antitrust litigation in district courts during 1996—2006 to examine whether economic complexity impacts decisions in antitrust cases, and thereby provide a novel test of the frequently asserted hypothesis that antitrust analysis has become too complex for generalist judges. We also examine the impact of one institutional response to economic complexity - basic economic training by judges. We find that decisions involving the evaluation of complex economic evidence are significantly more likely to be appealed, and decisions of judges trained in basic economics are significantly less likely to be appealed than are decisions by their untrained counterparts. Our results are robust to a variety of controls, including the type of case, circuit, and the political party of the judge. Our tentative conclusion, based on a revealed preference argument that views a party’s appeal decision as an indication that the district court got the economics wrong, is that there is support for the hypothesis that some antitrust cases are too complicated for generalist judges.antitrust, Daubert, complexity, economic training, expert witness

Systematic formulation of non-functional characteristics of software

This paper presents NoFun, a notation aimed at dealing with non-functional aspects of software systems at the product level in the component programming framework. NoFun can be used to define hierarchies of non-functional attributes, which can be bound to individual software components, libraries of components or (sets of) software systems. Non-functional attributes can be defined in several ways, being possible to choose a particular definition in a concrete context. Also, NoFun allows to state the values of the attributes in component implementations, and to formulate non-functional requirements over component implementations. The notation is complemented with an algorithm able to select the best implementation of components (with respect to their non-functional characteristics) in their context of use.Peer ReviewedPostprint (published version