On a Modification of Lupanov's Method with More Uniform Distribution of Fan-out

In this paper we suggest a modification of classical Lupanov’s method [8] that allows building circuits over the basis {&,∨,¬} for Boolean functions of n variables with size at most 2n n ( 1 + 3 log n+O(1) n ) , and with more uniform distribution of outgoing arcs by circuit gates. For almost all Boolean functions of n variables in the circuits for these functions, which are built using our method, the fraction of gates with fanout 2 is asymptotically at least 1/32. This fact disproves upper bound [15] on the number of circuits with exact number of gates with fan-out at least 2.