Questionnaire-2024/bdds/1034_sol.tex

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\begin{tabbing}
$f$ \= $= (p \oplus q) \land \lnot r$\\
	\>$ f_p $ \= $= \lnot q \land \lnot r$ \\
	    \>\>$ f_{pq} $ \= $= \bot$ \\
	    \>\>$ f_{p \lnot q} $ \= $= \lnot r$ \\
	        \>\>\>$ f_{p \lnot q r} $ \= $= \bot$ \\
	        \>\>\>$ f_{p \lnot q \lnot r} $ \= $= \top$ \\
	\>$ f_{\lnot p} = q \land \lnot r$ \\
	    \>\>$ f_{\lnot pq} $ \= $= \lnot r = f_{p \lnot q}$ \\
	    \>\>$ f_{\lnot p \lnot q} $ \= $= \bot$ \\
\end{tabbing}
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\begin{minipage}{0.5\textwidth}
The final ROBDD:
\begin{center}
\begin{forest}
for tree={circle, draw, no edge,
            minimum size=2em,
            inner sep=0pt,
            s sep=6mm,
            l sep=6mm}
[$f$, rectangle, draw,  tikz={\draw [fulldot=.3] () to (p.north);}
    [$f_q$, rectangle, draw,  tikz={\draw [fulldot=.3] () to (q1.north);}]
    [$p$, name=p, tikz={\draw [line] () to (q1.north east); \draw [dot=.3] () to (q2.north west);}
        [$q$, name=q1, tikz={\draw [line] () to (-2,-3.5); \draw [dot=.3] () to (r.north west);}
            [$f_{p \lnot q}$, rectangle, draw,  tikz={\draw [fulldot=.3] () to (r.west);}]
        ]
        [$q$, name=q2, tikz={\draw [line] () to (r.north east); \draw [dot=.3] () to (2,-3.5);}
            [$r$, name=r, tikz={\draw [line] () to (-0.5,-4.8); \draw [fulldot=.3] () to (0.5, -4.8);}]
            [$f_{\lnot pq}$, rectangle, draw,  tikz={\draw [fulldot=.3] () to (r.east);}]
            [,phantom]
        ]
    ]
    [$f_{\lnot q}$, rectangle, draw,  tikz={\draw [fulldot=.3] () to (q2.north);}]
]
\end{forest}
\end{center}

\end{minipage}