I have matrix $H_1:$ $$ \begin{pmatrix} 1 & 1 \\ 0 & 1 \\ \end{pmatrix} $$
And aim is to achieve $H_k$: $$ \begin{pmatrix} H_{k-1} & H_{k-1} \\ \overline H_{k-1} & H_{k-1} \\ \end{pmatrix} $$
The basis is only disjunction. How to find minimal complexity $L(H_k)$ of this problem?
EDIT:
$H_2$ $$ \begin{pmatrix} 1 & 1 & 1 & 1 \\ 0 & 1 & 0 & 1 \\ 0 & 0 & 1 & 1 \\ 1 & 0 & 0 & 1 \\ \end{pmatrix} $$
EDIT 2:
$H_1$ also can be interpreted as: \begin{align}y_1 = x1 \cup x2 \\ y_2 = x2 \end{align}
$H_2$ also can be interpreted as: \begin{align}y_1 = x_1 \cup x_2 \cup x_3 \cup x_4 \\ y_2 = x_2 \cup x_4 \\ y_3 = x_3 \cup x_4 \\ y_4 = x_1 \cup x_4 \end{align}