Abstract
Let Ω be the basis consisting of a negation and logical “and” and “or” operations over any number of inputs. Every Boolean function of n variables can be realised by a Boolean circuit over Ω using at most 2.122 · 2 n 2 + n + 1 gates ( 2 · 2 n 2 + n + 1 for even n). We also show that almost all Boolean functions have circuit complexity at least 1.914 · 2 n 2 − 4n .
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