## On a classification of Post classes.(Russian)Zbl 0671.06009

Let $$B_ 1$$ and $$B_ 2$$ be two bases of a closed class K of Boolean functions. One defines $$B_ 1\leq B_ 2$$ by the existence of a constant $$c>0$$ such that $$L_{B_ 1}(f)\leq cL_{B_ 2}(f)$$ for every $$f\in K$$, where $$L_ B(f)$$ denotes the least number of functions in B generating f. The class K is said to be elementary provided $$B_ 1\leq B_ 2$$ and $$B_ 2\leq B_ 1$$ for every two bases $$B_ 1$$ and $$B_ 2$$ of K. The author determines all elementary classes in the Post classification.
Reviewer: S.Rudeanu

### MSC:

 06E30 Boolean functions 94C10 Switching theory, application of Boolean algebra; Boolean functions (MSC2010)

### Keywords:

closed class; elementary classes; Post classification
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