On the lifetime of configurations in homogeneous structures

The paper deals with the relationship between the lifetime of configurations and the number of states of a cell in homogeneous structures. For $K_V(n)$, which is a class of all homogeneous structures with $n$ states of the cell and the neighbourhood $V$ that includes all the vectors no longer than one, and $L_V(x)$, which is the reverse function for $x^{x^{|V|}}$, it has been established that the number $n\sim L_V(D)$ of states of the cell is necessary and sufficient in order that for any positive integer $d$, $ d\le D$, in the mentioned class of homogeneous structures, a structure $S$ could be found in which the lifetime of a certain one-cell configuration equals $d$.