Questionnaire-2024/bdds/0008_sol.tex

\begin{cofactors}
$f_{a}$ \= $= b \lor(c \biimp d)$ \\
\>$f_{ab}$ \= $= \true $\\
\>$f_{a\lnot b}$ \= $= c \biimp d$ \\
\>\>$f_{a\lnot bc}$ \= $= d$ \\
\>\>\>$f_{a\lnot b c d}$ \= $= \true$ \\
\>\>\>$f_{a\lnot bc\lnot d}$ \= $= \false$ \\
\>\>$f_{a\lnot b\lnot c}$ \= $= \lnot d = f_{abc}$ \\
$f_{\lnot a}$ \= $=\true $
\end{cofactors}

The final ROBDD:\\
\begin{center}
\begin{bdd}
  \node[func node] (f)                     {$f$};
  \node[cofactor] (a1) [below      of=f]   {$a$};
  \node[phantom]  (aR) [below right of=a1] {};
  \node[cofactor] (b1) [below left of=a1]  {$b$};
  \node[phantom]  (bL) [below left of=b1]  {};
  \node[cofactor] (c1) [below right of=b1] {$c$};
  \node[cofactor] (d1) [below      of=c1]  {$d$};
  \node[phantom]  (dL) [below left of=d1]  {};
  \node[phantom]  (dR) [below right of=d1] {};

  \funcEdge{f}{a1}
  \thenEdge{a1}{b1}
  \elseEdge{a1}{aR}

  \thenEdge{b1}{bL}
  \elseEdge{b1}{c1}

  \thenEdge[bend right]{c1}{d1}
  \negatedEdge[bend left]{c1}{d1}

  \thenEdge{d1}{dL}
  \elseEdge{d1}{dR}
\end{bdd}
\end{center}