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90feb62..41c2272 100644 --- a/presentation/automata.tex +++ b/presentation/automata.tex @@ -704,4 +704,88 @@ $\tVarX\{\ta \ror \epsilon\} \cdot \tVarX\{\tb \ror \epsilon\}$ \end{center} + + \pagebreak + + ~\newline + \begin{center} + \begin{tikzpicture}[node distance=10mm,on grid,>=stealth',auto, + state/.style={rectangle,draw=black,inner sep=2pt,minimum size=4mm}] + \node (start) {}; + \node[state] (a1) [right=of start] {$\ta$}; + \node[state] (a2) [below=of a1] {$\ta$}; + \node (end) [right=of a1] {}; + + \draw[fill=black] (start) circle (0.5mm); + \draw[fill=black] (end) circle (0.5mm); + \draw (end) circle (1mm); + + \path[->] + (start.center) edge node[above, left=-5pt,very near end,yshift=1mm] {} (a1) + (start.center) edge[] node[] {} (a2) + (a1) edge[] node[above, left=-5pt,very near end,yshift=1mm] {} (end.west) + (a2) edge (end.west); + \end{tikzpicture} + + \end{center} + \vspace{-15pt} + \begin{center} + $\ta \ror \ta$ + \end{center} + + ~\newline + \begin{center} + \begin{tikzpicture}[node distance=10mm,on grid,>=stealth',auto, + state/.style={rectangle,draw=black,inner sep=2pt,minimum size=4mm}] + \node (start) {}; + \node[state] (a1) [right=of start] {$\ta$}; + \node[state] (a2) [below=of a1] {$\ta$}; + \node (end) [right=of a1] {}; + + \draw[fill=black] (start) circle (0.5mm); + \draw[fill=black] (end) circle (0.5mm); + \draw (end) circle (1mm); + + \path[->] + (start.center) edge node[above, left=-5pt,very near end,yshift=1mm] {} (a1) + (start.center) edge[] node[] {} (a2) + (a1) edge[] node[above, left=-5pt,very near end,yshift=1mm] {} (end.west) + (a2) edge (end.west); + \end{tikzpicture} + + \end{center} + \vspace{-15pt} + \begin{center} + $\ta \ror \ta$ + \end{center} + + ~\newline + \begin{center} + \begin{tikzpicture}[node distance=10mm,on grid,>=stealth',auto, + state/.style={rectangle,draw=black,inner sep=2pt,minimum size=4mm}] + \node (start) {}; + \node[state] (a1) [right=of start] {$\ta$}; + \node[state] (b) [right=of a1] {$\tb$}; + \node[state] (refX) [right=of b] {$\tRefX$}; + \node (end) [right=of refX] {}; + + \draw[fill=black] (start) circle (0.5mm); + \draw[fill=black] (end) circle (0.5mm); + \draw (end) circle (1mm); + + \path[->] + (start.center) edge node[above, left=-5pt,very near end,yshift=2mm] {o(x)} (a1) + (a1) edge[] node[above, left=-6.5pt,very near end,yshift=2mm] {c(x)} (b) + (b) edge[bend right=120] node[above, yshift=-1mm] {o(x)} (a1) + (b) edge[bend right=45] node[below] {} (end.west) + (b) edge (refX) + (refX) edge (end.west); + \end{tikzpicture} + + \end{center} + \vspace{-15pt} + \begin{center} + $(\tVarX \{ \ta \} \cdot \tb)^+ \cdot (\tRefX \ror \epsilon)$ + \end{center} + \end{document}