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26 lines
947 B
26 lines
947 B
\item For the following binary decision diagram:
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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=10mm,
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l sep=5mm}
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[$f$, rectangle, draw, tikz={\draw [fulldot=.5] () to (a.north);}
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[$a$, name=a, tikz={\draw [line] () to (b1.north); \draw [fulldot=.5] () to (c.north);}
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[$b$, name=b1, tikz={\draw [line, bend right] () to (d.north west); \draw [dot=.5, bend left] () to (d.north east);}
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[$d$, name=d, tikz={\draw [line] () to (254:4.6); \draw [fulldot=.5] () to (265:4.42);}]
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]
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[$c$, name=c, tikz={\draw [line] () to (d.east); \draw [fulldot=.5] () to (291:3.53);}]
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]
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]
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\end{forest}
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\end{center}
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Check if the following models are satisfying:
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\begin{align*}
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\Model_1 =~& \{a = \top, b = \top, c = \bot, d = \bot\},\\
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\Model_2 =~& \{a = \bot, b = \bot, c = \top, d = \top\},\text{~and~}
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\end{align*}
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compute \DNF{f}.
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