Shannon Information and Kolmogorov Complexity

We compare the elementary theories of Shannon information and Kolmogorov complexity, the extent to which they have a common purpose, and where they are fundamentally different. We discuss and relate the basic notions of both theories: Shannon entropy versus Kolmogorov complexity, the relation of both to universal coding, Shannon mutual information versus Kolmogorov (`algorithmic') mutual information, probabilistic sufficient statistic versus algorithmic sufficient statistic (related to lossy compression in the Shannon theory versus meaningful information in the Kolmogorov theory), and rate distortion theory versus Kolmogorov's structure function. Part of the material has appeared in print before, scattered through various publications, but this is the first comprehensive systematic comparison. The last mentioned relations are new.Comment: Survey, LaTeX 54 pages, 3 figures, Submitted to IEEE Trans Information Theor

An Algorithmic Approach to Information and Meaning

I will survey some matters of relevance to a philosophical discussion of information, taking into account developments in algorithmic information theory (AIT). I will propose that meaning is deep in the sense of Bennett's logical depth, and that algorithmic probability may provide the stability needed for a robust algorithmic definition of meaning, one that takes into consideration the interpretation and the recipient's own knowledge encoded in the story attached to a message.Comment: preprint reviewed version closer to the version accepted by the journa

Facticity as the amount of self-descriptive information in a data set

Using the theory of Kolmogorov complexity the notion of facticity {\phi}(x) of a string is defined as the amount of self-descriptive information it contains. It is proved that (under reasonable assumptions: the existence of an empty machine and the availability of a faithful index) facticity is definite, i.e. random strings have facticity 0 and for compressible strings 0 < {\phi}(x) < 1/2 |x| + O(1). Consequently facticity measures the tension in a data set between structural and ad-hoc information objectively. For binary strings there is a so-called facticity threshold that is dependent on their entropy. Strings with facticty above this threshold have no optimal stochastic model and are essentially computational. The shape of the facticty versus entropy plot coincides with the well-known sawtooth curves observed in complex systems. The notion of factic processes is discussed. This approach overcomes problems with earlier proposals to use two-part code to define the meaningfulness or usefulness of a data set.Comment: 10 pages, 2 figure

Сравнительный анализ строительных проектов и финансовых инструментов, доступных для их реализации

В работе проведен сравнительный анализ строительных проектов и финансовых инструментов, доступных для их реализации для определения соответствия множества свойств финансовых инструментов требованиям проектов. Проведен морфологический анализ структурных сложностей множества строительных проектов, определенного как управляемое множество, и множества финансовых инструментов, определенное как управляющее множество. Выявлена отрицательная разность мощности управляемого множества и мощности управляемого множества. Определены области соответствия элементов управляемого и управляющего множеств. На основе закона необходимого разнообразия сделан вывод о несостоятельной процедуре управления в системе рассматриваемых множеств. Сделаны выводы о перспективности работ в направлении развития множества финансовых инструментов.An article presents results of a competitive analysis of construction projects and financial instruments available to implement them. The results were achieved by a morphological analysis of a structural complexity of the construction projects’ set which was determined as a controlled set and the financial instruments’ set which was determined as a control set. Negative difference between a power of the control set and a power of the controlled set have been shown. Correspondence areas of elements of the control and the controlled sets have been determined. As a result failure of an effective management in a system of the controlled and the control sets have been shown. Findings of a perspective of further works in this field concludes the paper