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author committer David A. Madore 2020-01-21 11:51:42 +0100 David A. Madore 2020-01-21 11:51:42 +0100 2f36233558948bb9771fab7f9bfa24c0fe4b6d04 (patch) 33e856233315a6bede17491935d07febfad246df 51080734543552b21da1ba1986928ef5f3db888c (diff) inf105-2f36233558948bb9771fab7f9bfa24c0fe4b6d04.zipinf105-2f36233558948bb9771fab7f9bfa24c0fe4b6d04.tar.gzinf105-2f36233558948bb9771fab7f9bfa24c0fe4b6d04.tar.bz2
Exercise on state elimination.
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 diff --git a/controle-20200123.tex b/controle-20200123.texindex b05f9d0..d77ec87 100644--- a/controle-20200123.tex+++ b/controle-20200123.tex@@ -124,7 +124,37 @@ Git: \input{vcline.tex} \exercice -Dans cet exercice, on pose $\Sigma = \{a\}$ (alphabet à une seule lettre).+Soit $\mathscr{A}$ l'automate suivant sur l'alphabet $\Sigma :=+\{a,b,c\}$ :++\begin{center}+\begin{tikzpicture}[>=latex,line join=bevel,automaton]+\node (S0) at (0bp,0bp) [draw,circle,state,initial] {$0$};+\node (S1) at (70bp,35bp) [draw,circle,state] {$1$};+\node (S2) at (70bp,-35bp) [draw,circle,state] {$2$};+\node (S3) at (140bp,0bp) [draw,circle,state,final] {$3$};+\draw [->] (S0) -- node[auto,near end] {$\varepsilon$} (S1);+\draw [->] (S0) -- node[auto,below] {$\varepsilon$} (S2);+\draw [->] (S1) to[out=225,in=135] node[auto,left] {$a$} (S2);+\draw [->] (S2) to[out=45,in=315] node[auto,right] {$b$} (S1);+\draw [->] (S2) to[loop below] node[auto] {$c$} (S2);+\draw [->] (S1) -- node[auto] {$\varepsilon$} (S3);+\draw [->] (S2) -- node[auto,below,near end] {$\varepsilon$} (S3);+\end{tikzpicture}+\end{center}++\vskip-\baselineskip\vskip-.5ex\noindent En lui appliquant la méthode+d'élimination des états, déterminer une expression rationnelle+dénotant le langage qu'il reconnaît.+++%+%+%++\exercice++Dans cet exercice, on pose $\Sigma := \{a\}$ (alphabet à une seule lettre). \medskip