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authorDavid A. Madore <david+git@madore.org>2019-01-18 22:06:59 (GMT)
committerDavid A. Madore <david+git@madore.org>2019-01-23 12:47:10 (GMT)
commit6293ae6685fb45a014e52efc131352ba05c2c546 (patch)
tree62b0e712b153fec442a62baa794204222d1235ce
parentdde7a775ea3a9c358cb25e74c3f87a977e91df9d (diff)
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Adopt convention of underlining the epsilon symbol in regexps.
-rw-r--r--controle-20190205.tex20
1 files changed, 10 insertions, 10 deletions
diff --git a/controle-20190205.tex b/controle-20190205.tex
index 39f5c07..41ce6d2 100644
--- a/controle-20190205.tex
+++ b/controle-20190205.tex
@@ -314,7 +314,7 @@ transition qui en part :
\node (S2) at (70bp,-35bp) [draw,circle,state] {$2$};
\node (Sink) at (140bp,0bp) [draw,circle,state] {$\bot$};
\node (SF) at (210bp,0bp) [draw,circle,state,final] {$F$};
-\draw [->] (SI) -- node[auto] {$\varepsilon$} (S0);
+\draw [->] (SI) -- node[auto] {$\underline{\varepsilon}$} (S0);
\draw [->] (S0) to[out=75,in=180] node[auto,near end] {$a$} (S1);
\draw [->] (S0) to[out=285,in=180] node[auto,below] {$b$} (S2);
\draw [->] (S1) to[out=270,in=15] node[auto,above] {$b$} (S0);
@@ -322,9 +322,9 @@ transition qui en part :
\draw [->] (S1) -- node[auto,near end] {$a$} (Sink);
\draw [->] (S2) -- node[auto,below,near end] {$b$} (Sink);
\draw [->] (Sink) to[loop above] node[auto] {$a|b$} (Sink);
-\draw [->] (S1) to[out=15,in=135] node[auto,near end] {$\varepsilon$} (SF);
-\draw [->] (S2) to[out=345,in=225] node[auto,near end] {$\varepsilon$} (SF);
-\draw [->] (Sink) -- node[auto] {$\varepsilon$} (SF);
+\draw [->] (S1) to[out=15,in=135] node[auto,near end] {$\underline{\varepsilon}$} (SF);
+\draw [->] (S2) to[out=345,in=225] node[auto,near end] {$\underline{\varepsilon}$} (SF);
+\draw [->] (Sink) -- node[auto] {$\underline{\varepsilon}$} (SF);
\end{tikzpicture}
\end{center}
On élimine ensuite l'état $\bot$ :
@@ -335,13 +335,13 @@ On élimine ensuite l'état $\bot$ :
\node (S1) at (70bp,35bp) [draw,circle,state] {$1$};
\node (S2) at (70bp,-35bp) [draw,circle,state] {$2$};
\node (SF) at (210bp,0bp) [draw,circle,state,final] {$F$};
-\draw [->] (SI) -- node[auto] {$\varepsilon$} (S0);
+\draw [->] (SI) -- node[auto] {$\underline{\varepsilon}$} (S0);
\draw [->] (S0) to[out=75,in=180] node[auto,near end] {$a$} (S1);
\draw [->] (S0) to[out=285,in=180] node[auto,below] {$b$} (S2);
\draw [->] (S1) to[out=270,in=15] node[auto,above] {$b$} (S0);
\draw [->] (S2) to[out=90,in=345] node[auto] {$a$} (S0);
-\draw [->] (S1) to[out=15,in=135] node[auto,near end] {$\varepsilon|a(a|b){*}$} (SF);
-\draw [->] (S2) to[out=345,in=225] node[auto,near end] {$\varepsilon|b(a|b){*}$} (SF);
+\draw [->] (S1) to[out=15,in=135] node[auto,near end] {$\underline{\varepsilon}|a(a|b){*}$} (SF);
+\draw [->] (S2) to[out=345,in=225] node[auto,near end] {$\underline{\varepsilon}|b(a|b){*}$} (SF);
\end{tikzpicture}
\end{center}
Puis les états $1$ et $2$ peuvent être éliminés simultanément :
@@ -350,14 +350,14 @@ Puis les états $1$ et $2$ peuvent être éliminés simultanément :
\node (SI) at (-70bp,0bp) [draw,circle,state,initial] {$I$};
\node (S0) at (0bp,0bp) [draw,circle,state] {$0$};
\node (SF) at (210bp,0bp) [draw,circle,state,final] {$F$};
-\draw [->] (SI) -- node[auto] {$\varepsilon$} (S0);
-\draw [->] (S0) -- node[auto] {$a(\varepsilon|a(a|b){*})|b(\varepsilon|b(a|b){*})$} (SF);
+\draw [->] (SI) -- node[auto] {$\underline{\varepsilon}$} (S0);
+\draw [->] (S0) -- node[auto] {$a(\underline{\varepsilon}|a(a|b){*})|b(\underline{\varepsilon}|b(a|b){*})$} (SF);
\draw [->] (S0) to[loop above] node[auto] {$ab|ba$} (S0);
\end{tikzpicture}
\end{center}
Et l'expression rationnelle finalement obtenue est la suivante :
\[
-(ab|ba){*}(a(\varepsilon|a(a|b){*})|b(\varepsilon|b(a|b){*}))
+(ab|ba){*}(a(\underline{\varepsilon}|a(a|b){*})|b(\underline{\varepsilon}|b(a|b){*}))
\]
On pouvait aussi donner, entre autres choses :
\[