Questionnaire-2024/bdds/1023.tex

\item For the following binary decision diagram:


Note: Else-edges are marked with circles. Filled circles represent the \emph{complemented} attribute. Dangling edges are assumed to point to the constant node \texttt{true}.

\begin{center}
\begin{forest}
for tree={circle, draw, no edge,
          minimum size=2em,
          inner sep=0pt,
          s sep=10mm,
          l sep=5mm}
[$f$, rectangle, draw,  tikz={\draw [fulldot=.5] () to (a.north);}
   [$a$, name=a, tikz={\draw [line] () to (b1.north); \draw [fulldot=.5] () to (c.north);}
      [$b$, name=b1, tikz={\draw [line, bend right] () to (d.north west); \draw [dot=.5, bend left] () to (d.north east);}
         [$d$, name=d, tikz={\draw [line] () to (254:4.6); \draw [fulldot=.5] () to (265:4.42);}]
      ]
      [$c$, name=c, tikz={\draw [line] () to (d.east); \draw [fulldot=.5] () to (291:3.53);}]
   ]
]
\end{forest}
\end{center}

Check if the following models are satisfying:
\begin{align*}
  \Model_1 =~& \{a = \top, b = \top, c = \bot, d = \bot\},\\
  \Model_2 =~& \{a = \bot, b = \bot, c = \top, d = \top\},\text{~and~}
\end{align*}
compute \DNF{f}.