On an infinite sequence of improving Boolean bases☆

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Abstract

We consider complexity of formulas for Boolean functions in finite complete bases. It is shown that, as regards complexity, the basis of all (k+1)-ary functions is essentially better than the basis of all k-ary functions for all k⩾2.

Keywords

Boolean function
Formula
Complexity

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☆

Translated from Discrete Anal. Oper. Res. (Novosibirsk) 4(4) (1997) 79–95. This research was supported by the Russian Foundation of Basic Research (Grant 96-01-01068).

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