Exercise on state elimination.

1 files changed, 31 insertions, 1 deletions

diff --git a/controle-20200123.tex b/controle-20200123.tex
index 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