Исследование структуры множества линейных БПИ-автоматов над кольцом Zpk

摘要

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