\documentclass[12pt]{article} \usepackage{amsmath,amssymb,A4} \pagestyle{empty} \begin{document} \begin{center} Beispiel zur $(k,s)$-Lupanov-Darstellung Boolescher Funktionen \end{center} \begin{itemize} \item eine Funktion $f\,:\,\mathcal{B}^6 \rightarrow \mathcal{B}$ mit $k=3, s=3, s' = 2$ : \begin{tabular}{c c c || c c c c c c c c | c } & & $x_4$ & 0 & 1 & 0 & 1 & 0 & 1 & 0 & 1 & \\ & & $x_5$ & 0 & 0 & 1 & 1 & 0 & 0 & 1 & 1 & \\ & & $x_6$ & 0 & 0 & 0 & 0 & 1 & 1 & 1 & 1 & \\ $x_1$ & $x_2$ & $x_3$ & & & & & & & & & \\ \hline\hline 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 1 & 0 & 0 & \\ 0 & 0 & 1 & 0 & 1 & 1 & 0 & 0 & 1 & 1 & 1 & $A_1$ \\ 0 & 1 & 0 & 1 & 0 & 0 & 1 & 0 & 0 & 0 & 1 & \\ \hline 0 & 1 & 1 & 1 & 0 & 1 & 1 & 0 & 0 & 1 & 0 & \\ 1 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 1 & $A_2$ \\ 1 & 0 & 1 & 1 & 1 & 0 & 1 & 1 & 0 & 0 & 0 & \\ \hline 1 & 1 & 0 & 1 & 0 & 1 & 1 & 0 & 1 & 1 & 0 & \\ 1 & 1 & 1 & 0 & 1 & 0 & 0 & 0 & 0 & 1 & 0 & $A_3$ \\ \end{tabular} \item die Funktion $f_2 \,:\,\mathcal{B}^6 \rightarrow \mathcal{B}$ \begin{tabular}{c c c || c c c c c c c c | c } & & $x_4$ & 0 & 1 & 0 & 1 & 0 & 1 & 0 & 1 & \\ & & $x_5$ & 0 & 0 & 1 & 1 & 0 & 0 & 1 & 1 & \\ & & $x_6$ & 0 & 0 & 0 & 0 & 1 & 1 & 1 & 1 & \\ $x_1$ & $x_2$ & $x_3$ & & & & & & & & & \\ \hline\hline 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & \\ 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & $A_1$ \\ 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & \\ \hline 0 & 1 & 1 & 1 & 0 & 1 & 1 & 0 & 0 & 1 & 0 & \\ 1 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 1 & $A_2$ \\ 1 & 0 & 1 & 1 & 1 & 0 & 1 & 1 & 0 & 0 & 0 & \\ \hline 1 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & \\ 1 & 1 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & $A_3$ \\ \end{tabular} \item die Funktion $f_{2,\mathbf{v}}^{(r)}$ f\"ur $\mathbf{v} = (1\,0\,1)^t$ und f\"ur $\mathbf{v} = (0\,1\,1)^t$ \begin{tabular}{c c c || c | c } $x_1$ & $x_2$ & $x_3$ & & \\ \hline\hline 0 & 0 & 0 & 0 & \\ 0 & 0 & 1 & 0 & $A_1$ \\ 0 & 1 & 0 & 0 & \\ \hline 0 & 1 & 1 & 1 & \\ 1 & 0 & 0 & 0 & $A_2$ \\ 1 & 0 & 1 & 1 & \\ \hline 1 & 1 & 0 & 0 & \\ 1 & 1 & 1 & 0 & $A_3$ \\ \end{tabular} \hskip25mm \begin{tabular}{c c c || c | c } $x_1$ & $x_2$ & $x_3$ & & \\ \hline\hline 0 & 0 & 0 & 0 & \\ 0 & 0 & 1 & 0 & $A_1$ \\ 0 & 1 & 0 & 0 & \\ \hline 0 & 1 & 1 & 0 & \\ 1 & 0 & 0 & 1 & $A_2$ \\ 1 & 0 & 1 & 1 & \\ \hline 1 & 1 & 0 & 0 & \\ 1 & 1 & 1 & 0 & $A_3$ \\ \end{tabular} \item die Funktion $f_{2,\mathbf{v}}^{(c)}$ f\"ur $\mathbf{v} = (1\,0\,1)^t$ und f\"ur $\mathbf{v} = (0\,1\,1)^t$ \begin{tabular}{c || c c c c c c c c } $x_4$ & 0 & 1 & 0 & 1 & 0 & 1 & 0 & 1 \\ $x_5$ & 0 & 0 & 1 & 1 & 0 & 0 & 1 & 1 \\ $x_6$ & 0 & 0 & 0 & 0 & 1 & 1 & 1 & 1 \\ \hline & 1 & 0 & 0 & 1 & 0 & 0 & 0 & 0 \end{tabular} \hskip5mm \begin{tabular}{c || c c c c c c c c } $x_4$ & 0 & 1 & 0 & 1 & 0 & 1 & 0 & 1 \\ $x_5$ & 0 & 0 & 1 & 1 & 0 & 0 & 1 & 1 \\ $x_6$ & 0 & 0 & 0 & 0 & 1 & 1 & 1 & 1 \\ \hline & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 \end{tabular} \end{itemize} \end{document}