FUNDAMENTALNAYA
I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

2000, VOLUME 6, NUMBER 1, PAGES 133-142

A. S. Doumov

Abstract

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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 $d$ .

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Last modified: April 11, 2000