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33 lines
1.3 KiB
33 lines
1.3 KiB
\item \self Find a \textit{symbolic encoding} for the \textit{transition relation} of the following \textit{Kripke structure} and
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simplify your formulas. The labels of the states symbolize their symbolic encoding.
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E.g. "110" = "$x_2 \land x_1 \land \lnot x_0$", i.e. the least significant bit corresponds to $x_0$,
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the second-least significant bit to $x_1$, and so forth.
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\begin{center}
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\vspace{-2em}
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\begin{tikzpicture}[auto, node distance=2cm,shorten >=1pt,
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thick,node/.style={circle,draw,minimum size=25pt}]
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\node[node] (s0) {$000$};
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\node[node] (s1) [above right of=s0] {$001$};
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\node[node] (s2) [right of=s1] {$010$};
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\node[node] (s3) [below right of=s2] {$011$};
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\node[node] (s4) [below of=s3] {$100$};
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\node[node] (s5) [below left of=s4] {$101$};
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\node[node] (s6) [left of=s5] {$110$};
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\node[node] (s7) [above left of=s6] {$111$};
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\path[->] (s0) edge (s1);
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\path[->] (s1) edge (s2);
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\path[<->] (s2) edge (s3);
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\path[->] (s3) edge (s4);
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\path[->] (s4) edge (s7);
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\path[->] (s7) edge (s6);
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\path[<->] (s6) edge (s5);
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\path[->] (s3) edge (s6);
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\path[->] (s5) edge (s0);
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\path[->] (s1.30) edge[bend right=90, looseness=15, out=240, in=300] (s1.60);
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\path[->] (s4.30) edge[bend right=90, looseness=15, out=240, in=300] (s4.60);
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\end{tikzpicture}
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\end{center}
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