Abstract:
The upper and lower bounds for the number $n(k)$ of significant variables of balanced Boolean function represented by $k$ elementary conjunction are obtained. The boundedness of $n(k)$ for every $k$ was proved by the author previously. Balanced Boolean functions are very important for cryptography; their DNF representations correspond to realizations by circuits, in particular, by programmable logical matrices.
Key words:Boolean function, DNF (disjunctive normal form), Fibonacci numbers.