LOGICAL ASSOCIATORS IN MARKOV NETWORKS

In the theory of algorithms, A.A. Markov defined (introduced) his own logic, but it is not the only one that can be applied to his theory and algorithm. Markov networks and work in them using logical methods are studied. The categorical cNnet-scheme of the Markov algorithm is refined. An additional category-theoretic and n-category approach to the association of words and morphisms in Markov occurrence diagrams is used. Logical n-category associators of words and their morphisms in this scheme are synthesized. A Markov network is considered as a mathematical composition consisting of cNnet-algorithm circuits. This scheme was introduced into scientific circulation in addition to the well-known γ-scheme, Markov’s algorithm, and differs from it in its conclusion, which cannot be considered normal according to Markov. Fundamentally new methods for synthesizing computer systems are being developed that can be used to classify economic interactions in organizational systems when solving the problem of combating money laundering and terrorist financing. A mathematical abstraction, which is the logical associator L, has been introduced into scientific circulation for the cNnet-scheme of the Markov algorithm. This logical associator is understood as open, replenished with new ways of logical processing of words and their morphisms, implementing the open logical architecture of Markov networks. Separate logical associators are synthesized. These individual associators are considered, among other things, as applied examples of logics in the Markov algorithm (network). Examples of such logics in a Markov network are time logics, category (group) logics, internal category (group) logics. Conclusions are drawn that logical associators in the cNnet-scheme of the Markov algorithm need to be developed in further applied research in order to synthesize a wider range of methods for the logical processing of words and morphisms. The presented results of the study of logics can be applied in the problem of combating money laundering and terrorist financing when analyzing economic interactions in organizational systems. This set should include both relatively simple and fairly knowledge-intensive methods, which will allow choosing the most suitable of them, for example, to minimize economic or time costs for design, without reducing the operational characteristics of the software and hardware that implement them.