A New Formulation of a Criterion for the Minimal Logarithmic Growth Rate

Abstract

We obtain a new formulation of a criterion for the minimal logarithmic growth rate for an arbitrary finite set with a given set of operations. It turns out that a finite set with operations has the minimal logarithmic growth rate if and only if the set of operations is not entirely contained in any of the precomplete (maximal) classes other than the classes preserving subsets and the classes of functions that preserve predicates given by permutations decomposable into cycles of the same prime length.