ASSOCIATORS IN THE N-SCHEME OF THE MARKOV ALGORITHM

Abstract

The prescriptions defining the association of words and morphisms in the N-scheme of the Markov algorithm synthesized to replace its well–known g-scheme are investigated. The prescriptions for processing words from the expanded and ordered Markov alphabet using the N-scheme of his algorithm are considered. The analysis of consequences for algorithms arising from some prescriptions used in the N-scheme of the Markov algorithm is carried out. Examples of Markov occurrences of words using word associators and morphisms are illustrated with figures showing the structure of n-category associators. The homology of Markov systems defined by associators is found. One of the Markov systems, which is a homology, consisting of N-schemes of the Markov algorithm, in which the control channel is also an N-scheme of the Markov algorithm, is singled out. It is shown that the alphabets M and MK together with the numbers-types should be used to increase the reliability of algorithms, since these alphabets provide for overcoming loops, in other words, do not allow algorithms to enter an infinite cycle. This variant of the Markov system is analyzed in order to study its properties. The distinctive properties of such a system are highlighted. The method of association of several homogeneous morphisms is considered. A method for setting the tuning mode using the control channel in the Markov system is proposed. It is noted that the method can be extended in case of entering initial, controlled parameters in order to check the safety and technical condition of the equipment. It is indicated that there are several prescriptions responsible for the association of words and morphisms in the N-scheme of the Markov algorithm, which are structurally related to the composition of associators. It is noted that the composition of the Markov alphabet word associators is sufficient, but perhaps not necessary for solving some applied problems, therefore, no restrictions are imposed on its composition and methods of expansion or ordering. It is concluded that in systems where clear and fuzzy (isolated morphisms) are used together, it is allowed to determine the composition of the associators of isolated morphisms by introducing new prescriptions.