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49 lines
2.1 KiB
49 lines
2.1 KiB
\begin{minipage}{0.5\textwidth}
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\begin{tabbing}
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$f$ \= $= (p \leftrightarrow q) \land (r \leftrightarrow s)$\\
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\>$ f_r $ \= $= (p \leftrightarrow q) \land s$ \\
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\>\>$ f_{rs} $ \= $= (p \leftrightarrow q)$ \\
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\>\>\>$ f_{rsp} $ \= $= q$ \\
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\>\>\>\>$ f_{rspq} $ \= $= \top$ \\
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\>\>\>\>$ f_{rsp \lnot q} $ \= $= \bot$ \\
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\>\>\>$ f_{rs \lnot p} $ \= $= \lnot q = \lnot f_{rsp}$ \\
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\>\>$ f_{r \lnot s} $ \= $= \bot$ \\
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\>$ f_{\lnot r} = (p \leftrightarrow q) \land \lnot s$ \\
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\>\>$ f_{\lnot rs} $ \= $= \bot$ \\
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\>\>$ f_{\lnot r \lnot s} $ \= $= (p \leftrightarrow q) = f_{rs}$ \\
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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 [line] () to (r.north);}
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[$f_r$, rectangle, draw, tikz={\draw [line] () to (s1.north west);}]
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[$r$, name=r, tikz={\draw [line] () to (s1.north); \draw [fulldot=.5] () to (s2.north);}
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[$f_{\lnot r \lnot s}$, rectangle, draw, tikz={\draw [line] () to (p.north west);}]
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[$f_{rs}$ , rectangle, draw, tikz={\draw [line] () to (p.north west);}]
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[$s$, name=s1, tikz={\draw [line] () to (p.north); \draw [fulldot=.5] () to (-0.2, -3.5);}
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[$f_{\lnot rsp}$, rectangle, draw, tikz={\draw [line] () to (q.north west);}]
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[$p$, name=p, tikz={\draw [line, bend right=14] () to (q.north); \draw [fulldot=.5, bend left=14] () to (q.north east);}
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[$q$, name=q, tikz={\draw [line] () to (-2.3, -6.2); \draw [fulldot=.5] () to (-1.5, -6.2);}
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]
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[,phantom]
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]
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[,phantom]
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[,phantom]
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]
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[$s$, name=s2, tikz={\draw [line] () to (0.2,-3.5); \draw [fulldot=.5, bend left=70] () to (p.east);}]
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[,phantom]
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[,phantom]
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]
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[$f_{\lnot r}$, rectangle, draw, tikz={\draw [fulldot=.5] () to (s2.north east);}]
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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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