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31 lines
1.3 KiB
31 lines
1.3 KiB
\item \self
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Consider a robot moving in this small transition system. The robot has to fulfill tasks in the state $00$ and $10$. \\
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Let the state labelling be as follows: $(x_1 x_0)$.
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\begin{figure}[h!]
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\centering
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\begin{conflictgraph}
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%\tikzset{every loop/.style={min distance=10mm,in=0,out=60,looseness=10}}
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\node[base node] (00) {$00$};
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\node[base node] (01) [right of=00] {$01$};
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\node[base node] (10) [below of=01] {$10$};
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\node[base node] (11) [below of=00] {$11$};
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\path[->] (00) edge [loop above] node {} ();
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\path[->] (10) edge [loop right] node {} ();
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\path[->] (11) edge [loop below] node {} ();
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\path[]
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(00) edge [bend left] node {} (01)
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(01) edge [bend left] node {} (00)
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(01) edge [bend left] node {} (10)
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(10) edge [bend left] node {} (01)
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(00) edge [] node {} (11)
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(10) edge [] node {} (11);
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\end{conflictgraph}
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\end{figure}
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Formulate the following using \emph{Linear Temporal Logic}:
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\begin{enumerate}[(a)]
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\item The robot will infinitely often see state $00$ and $10$.
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\item The robot will never visit state $11$.
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\item After visiting either state $00$ or $10$ the robot will visit state $01$ within the next three time steps.
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\end{enumerate}
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