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115 \item A \alert{\bf language} is a set of strings, for example\medskip |
115 \item A \alert{\bf language} is a set of strings, for example\medskip |
116 \begin{center} |
116 \begin{center} |
117 \bl{$\{[], hello, \textit{foobar}, a, abc\}$} |
117 \bl{$\{[], hello, \textit{foobar}, a, abc\}$} |
118 \end{center}\bigskip |
118 \end{center}\bigskip |
119 |
119 |
120 \item \alert{\bf Concatenation} of strings and sets |
120 \item \alert{\bf Concatenation} of strings and languages |
121 |
121 |
122 \begin{center} |
122 \begin{center} |
123 \begin{tabular}{rcl} |
123 \begin{tabular}{rcl} |
124 \bl{$\textit{foo}\;@\;bar$} & \bl{$=$} & \bl{$\textit{foobar}$}\medskip\\ |
124 \bl{$\textit{foo}\;@\;bar$} & \bl{$=$} & \bl{$\textit{foobar}$}\medskip\\ |
125 \bl{$A\;@\;B$} & \bl{$\dn$} & \bl{$\{ s_1\,@\,s_2 \;\mid\; s_1 \in A \wedge s_2 \in B\}$} |
125 \bl{$A\;@\;B$} & \bl{$\dn$} & \bl{$\{ s_1\,@\,s_2 \;\mid\; s_1 \in A \wedge s_2 \in B\}$} |
150 & \bl{$\mid$} & \bl{$r_1 + r_2$} & alternative / choice\\ |
150 & \bl{$\mid$} & \bl{$r_1 + r_2$} & alternative / choice\\ |
151 & \bl{$\mid$} & \bl{$r^*$} & star (zero or more)\\ |
151 & \bl{$\mid$} & \bl{$r^*$} & star (zero or more)\\ |
152 \end{tabular} |
152 \end{tabular} |
153 \end{textblock} |
153 \end{textblock} |
154 |
154 |
155 |
155 |
156 \only<2->{\footnotesize |
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157 \begin{textblock}{9}(2,0.5) |
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158 \begin{bubble}[9.8cm] |
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159 \lstinputlisting{../progs/app01.scala} |
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160 \end{bubble} |
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161 \end{textblock}} |
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162 |
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163 \end{frame} |
156 \end{frame} |
164 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
157 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
165 |
158 |
166 |
159 |
167 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
160 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
196 \begin{frame}[c] |
189 \begin{frame}[c] |
197 |
190 |
198 \large |
191 \large |
199 \begin{center} |
192 \begin{center} |
200 What is \bl{$L(a^*)$}? |
193 What is \bl{$L(a^*)$}? |
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194 \end{center} |
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195 |
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196 \end{frame} |
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197 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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198 |
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199 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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200 \begin{frame}[c] |
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201 \frametitle{\begin{tabular}{c} |
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202 When Are Two Regular\\ |
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203 Expressions Equivalent?\end{tabular}} |
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204 \large |
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205 \begin{center} |
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206 \bl{$r_1 \equiv r_2 \;\;\dn\;\; L(r_1) = L(r_2)$} |
201 \end{center} |
207 \end{center} |
202 |
208 |
203 \end{frame} |
209 \end{frame} |
204 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
210 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
205 |
211 |