510.5+681.3The properties of the class of information-lossless automata represented by recurrent relations over a finite ring are investigated. For these automata, the structure of classes of equivalent states is investigated, problems of parametric identification and identification of the initial state are solved, and the variation in the behavior of such automata as a result of variation of their parameters or initial states is characterized.

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A general scheme is investigated that is destined for obtaining estimates based on the cardinality of subsets of a fixed set of automata over some finite commutative-associative ring with unit element. A scheme is proposed to solve parametric systems of polynomial equations based on classes of associated elements of the ring. Some general characteristics of automata over the ring are established.

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