DEFINITION OF MARKOV NETWORKS FROM THE POSITION OF THE THEORIES OF CATEGORIES AND N-CATEGORIES

Abstract

The study develops new provisions of the theory of Markov algorithms. The area of use of the N-scheme of the Markov algorithm, developed to replace its wellknown y-scheme, is being expanded. The study solves the scientific problem of developing the Markov algorithm in the direction of processing not only words, but also morphisms. Such a problem has not been posed or solved before in the theory of Markov algorithms. Morphisms that differ from each other by types, where some are numeric and others are categorical, are proposed to be processed together. In the study of methods for processing morphisms in the Markov algorithm, it is proposed to use the wellknown in science and practice idea of weighing numerical morphisms. The very idea of weighting morphisms is considered more broadly as a task for the synthesis of a Markov network from separate components, such as an N-schema Markov algorithm for a single data source and a Markov system for many sources of big data. Markov networks are introduced into scientific circulation using the methodology adopted for artificial neural networks. This approach allows us to reduce the time for comprehending the main theoretical provisions of Markov networks, in comparison with artificial neural networks. The same technique is used to classify diagrams of Markov occurrences of words in each other, which are the basis for the synthesis of Markov networks. Approaches to weighting the values of morphisms in Markov networks do not fundamentally differ from those used in artificial neural networks. Diagrams of Markov occurrences are considered from category-theoretic positions, where words are assumed to be associated categories, otherwise, n-categories. For Markov networks, theoretical considerations are given on the activation of their elements by a secret morphism. The use of category-theoretic positions in Markov networks allows us to say that these networks are also activated by all associators used in the N-scheme of the Markov algorithm, as well as by the control channel, which is also an associator. At the same time, associators are considered as n-category objects, which distinguishes Markov networks from artificial neural networks. An N-scheme of the Markov algorithm and a Markov system with weight coefficients and thresholds for weighting the values of morphisms are synthesized. It is concluded that Markov networks provide joint processing of words and morphisms, and it is in the network that additional methods of processing morphisms are implemented that were not previously taken into account in the theory of Markov algorithms.