diff options
| -rw-r--r-- | controle-20200123.tex | 32 |
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 |