Abstract:
We investigate representations of Boolean functions by formulas. In terms of the residual functions, we describe Boolean functions realised by repetition-free formulas in pre-elementary bases $\{\vee,\cdot,-,0,1,x_1(x_2\vee\ldots\vee x_n)\vee x_2\cdot\ldots\cdot x_n\}$ where $n\ge4$.