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