Исследование структуры множества линейных БПИ-автоматов над кольцом Zpk

Abstract

For linear information-lossless automata over the ring Zp , we have established conditions and estimated cardinalities for sets of automata characterized via basic characteristics of automata theory (the transition graph is complete with a loop at each vertex, permutation and reduced automata, automata with twin states). For the investigated automata, a criterion of equivalence is established, the problem of parametric identification is resolved, and the canonical presentati- ons, in which all linear transformation are reduced to component-wise multiplication in the ring and to the application of reversible matrices, are designed.