A METHOD FOR SYNTHESIZING TOPOS OF HASHES IN THE CATEGORICAL cN-SCHEME OF THE MARKOV ALGORITHM. Part 1

Abstract

In organizational systems, economic interactions are studied. The purpose of this study is to synthesize a problem-oriented management subsystem for combating money laundering and terrorist financing. To achieve this goal, the problem of synthesizing a constructive way of processing such interactions is solved. The method is based on the development of the N-scheme of the Markov algorithm with an output that cannot be considered normal according to Markov. This algorithm scheme allows us to consider a quadruple consisting of words in the ordered and extended Markov alphabet A2, morphism numbers N, source numbers i, and the alphabet M. From the N-scheme of the Markov algorithm, its categorical version is synthesized. The need for this scheme of the Markov algorithm is due to the solution of the problem of folding Markov occurrences of words into each other of large length for their more compact representation. The idea of organizing a convolution for the entire topos is tested separately. The term “topos of hashes” is introduced into scientific circulation. This topos is considered as an alternative way to represent blocks of chains of Markov occurrences. The hash topos is formed from hash trees known in blockchain technology. This idea follows from previous studies of classifiers in topos, as well as the possibility of splitting chains of Markov occurrences into blocks. The convolution is considered using gamma and hash functions. In the course of the study, it was possible to theoretically show the connection between Markov algorithms and blockchain technology, taking into account the fact that each chain of occurrences of words in each other is considered as a category, and these chains are formed in different sources, otherwise worlds, and the way they are synthesized may have signs of a creative process, then a connection was found between the theories of categories, algorithms, blockchain technology and intuitionistic models by S. Kripke and L. E. Ya. Brouwer.