103 |
104 |
104 |
105 |
105 \end{frame}} |
106 \end{frame}} |
106 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
107 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
107 |
108 |
108 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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109 \mode<presentation>{ |
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110 \begin{frame}[c] |
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111 |
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112 \begin{textblock}{1}(2,5) |
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113 \begin{tabular}{c} |
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114 \includegraphics[scale=0.15]{pics/servers.png}\\[-2mm] |
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115 \small Server |
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116 \end{tabular} |
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117 \end{textblock} |
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118 |
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119 \begin{textblock}{1}(5.6,4) |
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120 \begin{tikzpicture}[scale=1.1] |
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121 \draw[white] (0,1) node (X) {}; |
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122 \draw[white] (2,1) node (Y) {}; |
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123 \draw[white] (0,0) node (X1) {}; |
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124 \draw[white] (2,0) node (Y1) {}; |
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125 \draw[white] (0,-1) node (X2) {}; |
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126 \draw[white] (2,-1) node (Y2) {}; |
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127 \draw[red, <-, line width = 2mm] (X) -- (Y); |
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128 \node [inner sep=5pt,label=above:\textcolor{black}{GET request}] at ($ (X)!.5!(Y) $) {}; |
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129 \draw[red, ->, line width = 2mm] (X1) -- (Y1); |
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130 \node [inner sep=5pt,label=above:\textcolor{black}{webpage}] at ($ (X1)!.5!(Y1) $) {}; |
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131 \draw[red, <-, line width = 2mm] (X2) -- (Y2); |
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132 \node [inner sep=7pt,label=above:\textcolor{black}{POST data}] at ($ (X2)!.5!(Y2) $) {}; |
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133 \end{tikzpicture} |
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134 \end{textblock} |
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135 |
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136 |
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137 \begin{textblock}{1}(9,5.5) |
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138 \begin{tabular}{c} |
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139 \includegraphics[scale=0.15]{pics/laptop.png}\\[-2mm] |
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140 \small Browser |
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141 \end{tabular} |
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142 \end{textblock} |
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143 |
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144 \only<2>{ |
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145 \begin{textblock}{10}(2,13.5) |
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146 \begin{itemize} |
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147 \item programming languages, compilers |
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148 \end{itemize} |
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149 \end{textblock}} |
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150 |
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151 |
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152 \end{frame}} |
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153 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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154 |
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155 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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156 \mode<presentation>{ |
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157 \begin{frame}[c] |
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158 |
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159 transforming strings into structured data\\[10mm] |
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160 |
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161 {\LARGE\bf Lexing}\medskip\\ |
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162 \hspace{5mm}(recognising ``words'')\\[6mm] |
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163 |
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164 {\LARGE\bf Parsing}\medskip\\ |
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165 \hspace{5mm}(recognising ``sentences'') |
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166 |
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167 \end{frame}} |
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168 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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169 |
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170 |
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171 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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172 \mode<presentation>{ |
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173 \begin{frame}[c] |
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174 |
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175 The subject is quite old: |
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176 |
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177 \begin{itemize} |
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178 \item Turing Machines, 1936 |
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179 \item first compiler for COBOL, 1957 (Grace Hopper) |
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180 \item but surprisingly research papers are still published now |
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181 \end{itemize} |
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182 |
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183 \begin{flushright} |
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184 \includegraphics[scale=0.3]{pics/hopper.jpg}\\ |
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185 \footnotesize\textcolor{gray}{Grace Hopper} |
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186 \end{flushright} |
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187 |
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188 {\footnotesize\textcolor{gray}{(she made it to David Letterman's Tonight Show, \url{http://www.youtube.com/watch?v=aZOxtURhfEU})}} |
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189 |
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190 \end{frame}} |
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191 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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192 |
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193 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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194 \mode<presentation>{ |
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195 \begin{frame}[c] |
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196 \frametitle{\begin{tabular}{c}This Course\end{tabular}} |
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197 |
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198 \begin{itemize} |
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199 \item the ultimate goal is to implement a small web-browser (really small one)\bigskip |
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200 \end{itemize} |
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201 |
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202 Let's start with: |
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203 |
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204 \begin{itemize} |
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205 \item a web-crawler |
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206 \item an email harvester |
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207 \item a web-scraper |
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208 \end{itemize} |
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209 |
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210 \end{frame}} |
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211 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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212 |
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213 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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214 \mode<presentation>{ |
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215 \begin{frame}[t] |
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216 \frametitle{\begin{tabular}{c}A Web Crawler\end{tabular}} |
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217 |
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218 \mbox{}\\[10mm] |
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219 |
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220 \begin{enumerate} |
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221 \item given an URL, read the corresponding webpage |
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222 \item extract all links from it |
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223 \item call the web-crawler again for all these links |
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224 \end{enumerate} |
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225 |
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226 \end{frame}} |
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227 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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228 |
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229 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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230 \mode<presentation>{ |
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231 \begin{frame}[t] |
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232 \frametitle{\begin{tabular}{c}A Web Crawler\end{tabular}} |
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233 |
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234 \mbox{}\\[10mm] |
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235 |
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236 |
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237 \begin{enumerate} |
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238 \item given an URL, read the corresponding webpage |
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239 \item if not possible print, out a problem |
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240 \item if possible, extract all links from it |
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241 \item call the web-crawler again for all these links |
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242 \end{enumerate}\bigskip\pause |
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243 |
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244 \small (we need a bound for the number of recursive calls) |
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245 |
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246 \small (the purpose is to check all links on my own webpage) |
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247 \end{frame}} |
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248 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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249 |
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250 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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251 \mode<presentation>{ |
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252 \begin{frame}[c] |
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253 \frametitle{\begin{tabular}{c}Scala\end{tabular}} |
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254 |
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255 \footnotesize a simple Scala function for reading webpages\\[-3mm] |
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256 |
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257 {\lstset{language=Scala}\fontsize{8}{10}\selectfont |
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258 \texttt{\lstinputlisting{app0.scala}}}\pause |
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259 {\lstset{language=Scala}\fontsize{8}{10}\selectfont |
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260 \texttt{\lstinline{get_page("""http://www.inf.kcl.ac.uk/staff/urbanc/""")}}}\pause\bigskip |
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261 |
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262 |
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263 \footnotesize slightly more complicated for handling errors properly:\\[-3mm] |
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264 |
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265 \footnotesize |
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266 {\lstset{language=Scala}\fontsize{8}{10}\selectfont |
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267 \texttt{\lstinputlisting{app1.scala}}} |
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268 |
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269 |
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270 \end{frame}} |
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271 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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272 |
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273 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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274 \mode<presentation>{ |
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275 \begin{frame}[t] |
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276 \frametitle{\begin{tabular}{c}A Regular Expression\end{tabular}} |
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277 |
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278 \begin{itemize} |
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279 \item \ldots{} is a pattern or template for specifying strings |
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280 \end{itemize}\bigskip |
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281 |
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282 \begin{center} |
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283 \only<1>{{\lstset{language=Scala}\fontsize{18}{19}\selectfont\bf |
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284 \texttt{"https?://[$\hat{\hspace{2mm}}$"]*"}}}% |
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285 \only<2>{{\lstset{language=Scala}\fontsize{18}{19}\selectfont\bf |
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286 \texttt{"""\textbackslash{}"https?://[$\hat{\hspace{2mm}}$\textbackslash{}"]*\textbackslash{}"""".r}}} |
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287 \end{center}\bigskip\bigskip |
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288 |
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289 matches for example\\ |
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290 \;{\lstset{language=Scala}\fontsize{12}{14}\selectfont\bf |
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291 \texttt{"http://www.foobar.com"}}\\ |
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292 \;{\lstset{language=Scala}\fontsize{12}{14}\selectfont\bf |
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293 \texttt{"https://www.tls.org"}}\\ |
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294 |
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295 \end{frame}} |
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296 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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297 |
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298 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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299 \mode<presentation>{ |
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300 \begin{frame}[c] |
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301 |
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302 {\lstset{language=Scala}\fontsize{18}{19}\selectfont\bf |
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303 \texttt{rexp.findAllIn(string)}}\medskip |
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304 |
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305 returns a list of all (sub)strings that match the regular expression\bigskip\bigskip |
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306 |
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307 {\lstset{language=Scala}\fontsize{18}{19}\selectfont\bf |
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308 \texttt{rexp.findFirstIn(string)}}\medskip |
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309 |
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310 returns either {\bf\texttt{None}} if no (sub)string matches |
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311 or {\bf\texttt{Some(s)}} with the first (sub)string |
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312 |
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313 \end{frame}} |
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314 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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315 |
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316 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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317 \mode<presentation>{ |
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318 \begin{frame}[c] |
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319 |
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320 {\lstset{language=Scala}\fontsize{8}{10}\selectfont |
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321 \texttt{\lstinputlisting{app2.scala}}}\medskip |
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322 |
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323 {\lstset{language=Scala}\fontsize{8}{10}\selectfont |
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324 \texttt{crawl(some\_start\_URL, 2)}}\ |
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325 |
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326 \end{frame}} |
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327 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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328 |
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329 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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330 \mode<presentation>{ |
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331 \begin{frame}[c] |
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332 |
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333 \footnotesize |
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334 a version that only ``crawls'' links in my domain: |
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335 |
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336 {\lstset{language=Scala}\fontsize{8}{10}\selectfont |
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337 \texttt{\lstinputlisting{app3.scala}}} |
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338 |
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339 |
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340 \end{frame}} |
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341 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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342 |
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343 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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344 \mode<presentation>{ |
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345 \begin{frame}[c] |
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346 |
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347 \footnotesize |
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348 a little email ``harvester'': |
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349 |
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350 {\lstset{language=Scala}\fontsize{8}{10}\selectfont |
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351 \texttt{\lstinputlisting{app4.scala}}}\bigskip |
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352 |
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353 \tiny |
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354 \textcolor{gray}{\url{http://net.tutsplus.com/tutorials/other/8-regular-expressions-you-should-know/}} |
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355 |
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356 \end{frame}} |
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357 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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358 |
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359 \newcommand{\bl}[1]{\textcolor{blue}{#1}} |
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360 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
109 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
361 \mode<presentation>{ |
110 \mode<presentation>{ |
362 \begin{frame}[c] |
111 \begin{frame}[c] |
363 \frametitle{\begin{tabular}{c}Regular Expressions\end{tabular}} |
112 \frametitle{\begin{tabular}{c}Regular Expressions\end{tabular}} |
364 |
113 |
376 \end{frame}} |
125 \end{frame}} |
377 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
126 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
378 |
127 |
379 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
128 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
380 \mode<presentation>{ |
129 \mode<presentation>{ |
381 \begin{frame}[t] |
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382 \frametitle{\begin{tabular}{c}Regular Expressions\end{tabular}} |
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383 |
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384 {\lstset{language=Scala}\fontsize{8}{10}\selectfont |
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385 \texttt{\lstinputlisting{app51.scala}}} |
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386 |
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387 |
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388 \end{frame}} |
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389 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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390 |
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391 \newcommand{\dn}{\stackrel{\mbox{\scriptsize def}}{=}}% for definitions |
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392 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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393 \mode<presentation>{ |
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394 \begin{frame}[c] |
130 \begin{frame}[c] |
395 \frametitle{\begin{tabular}{c}The Meaning of a\\[-2mm] Regular Expression\end{tabular}} |
131 \frametitle{\begin{tabular}{c}The Meaning of a\\[-2mm] Regular Expression\end{tabular}} |
396 |
132 |
397 \begin{textblock}{15}(1,4) |
133 \begin{textblock}{15}(1,4) |
398 \begin{tabular}{@ {}rcl} |
134 \begin{tabular}{@ {}rcl} |
399 \bl{$L$($\varnothing$)} & \bl{$\dn$} & \bl{$\varnothing$}\\ |
135 \bl{$L$($\varnothing$)} & \bl{$\dn$} & \bl{$\varnothing$}\\ |
400 \bl{$L$($\epsilon$)} & \bl{$\dn$} & \bl{$\{$""$\}$}\\ |
136 \bl{$L$($\epsilon$)} & \bl{$\dn$} & \bl{$\{$""$\}$}\\ |
401 \bl{$L$(c)} & \bl{$\dn$} & \bl{$\{$"c"$\}$}\\ |
137 \bl{$L$(c)} & \bl{$\dn$} & \bl{$\{$"c"$\}$}\\ |
402 \bl{$L$(r$_1$ + r$_2$)} & \bl{$\dn$} & \bl{$L$(r$_1$) $\cup$ $L$(r$_2$)}\\ |
138 \bl{$L$(r$_1$ + r$_2$)} & \bl{$\dn$} & \bl{$L$(r$_1$) $\cup$ $L$(r$_2$)}\\ |
403 \bl{$L$(r$_1$ $\cdot$ r$_2$)} & \bl{$\dn$} & \bl{$\{$ s$_1$ @ s$_2$ $|$ s$_1$ $\in$ $L$(r$_1$) $\wedge$ s$_2$ $\in$ |
139 \bl{$L$(r$_1$ $\cdot$ r$_2$)} & \bl{$\dn$} & \bl{$L$(r$_1$) @ $L$(r$_2$)}\\ |
404 $L$(r$_2$) $\}$}\\ |
140 \bl{$L$(r$^*$)} & \bl{$\dn$} & \bl{$\bigcup_{n \ge 0}$ $L$(r)$^n$}\\ |
405 \bl{$L$(r$^*$)} & \bl{$\dn$} & \onslide<4->{\bl{$\bigcup_{n \ge 0}$ $L$(r)$^n$}}\\ |
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406 \end{tabular}\bigskip |
141 \end{tabular}\bigskip |
407 |
142 |
408 \onslide<2->{ |
143 \hspace{5mm}\textcolor{gray}{$L$(r)$^0$ $\;\dn\;$ $\{$""$\}$}\\ |
409 \hspace{5mm}\bl{$L$(r)$^0$ $\;\dn\;$ $\{$""$\}$}\\ |
144 \textcolor{gray}{$L$(r)$^{n+1}$ $\;\dn\;$ $L$(r) @ $L$(r)$^n$} |
410 \bl{$L$(r)$^{n+1}$ $\;\dn\;$ $L$(r) @ $L$(r)$^n$}\hspace{9mm}\onslide<3->{\small\textcolor{gray}{(append on sets)}\\ |
145 \end{textblock} |
411 \small\hspace{5cm}\textcolor{gray}{$\{$ s$_1$ @ s$_2$ $|$ s$_1$ $\in$ $L$(r) $\wedge$ s$_2$ $\in$ |
146 |
412 $L$(r)$^n$ $\}$}} |
147 \end{frame}} |
413 } |
148 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
414 \end{textblock} |
149 |
415 |
150 \newcommand{\YES}{\textcolor{gray}{yes}} |
416 \end{frame}} |
151 \newcommand{\NO}{\textcolor{gray}{no}} |
417 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
152 \newcommand{\FORALLR}{\textcolor{gray}{$\forall$ r.}} |
418 |
153 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
419 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
154 \mode<presentation>{ |
420 \mode<presentation>{ |
155 \begin{frame}[c] |
421 \begin{frame}[c] |
156 \frametitle{\begin{tabular}{c}Reg Exp Equivalences\end{tabular}} |
422 \frametitle{\begin{tabular}{c}The Meaning of a Matching\end{tabular}} |
157 |
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158 \begin{center} |
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159 \begin{tabular}{lrcl@ {\hspace{7mm}}l} |
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160 &\bl{(a + b) + c} & \bl{$\equiv^?$} & \bl{a + (b + c)} & \onslide<2->{\YES}\\ |
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161 &\bl{a + a} & \bl{$\equiv^?$} & \bl{a} & \onslide<3->{\YES}\\ |
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162 &\bl{(a $\cdot$ b) $\cdot$ c} & \bl{$\equiv^?$} & \bl{a $\cdot$ (b $\cdot$ c)} & \onslide<4->{\YES}\\ |
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163 &\bl{a $\cdot$ a} & \bl{$\equiv^?$} & \bl{a} & \onslide<5->{\NO}\\ |
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164 &\bl{$\epsilon^*$} & \bl{$\equiv^?$} & \bl{$\epsilon$} & \onslide<6->{\YES}\\ |
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165 &\bl{$\varnothing^*$} & \bl{$\equiv^?$} & \bl{$\varnothing$} & \onslide<7->{\NO}\\ |
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166 \FORALLR &\bl{r $\cdot$ $\epsilon$} & \bl{$\equiv^?$} & \bl{r} & \onslide<8->{\YES}\\ |
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167 \FORALLR &\bl{r + $\epsilon$} & \bl{$\equiv^?$} & \bl{r} & \onslide<9->{\NO}\\ |
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168 \FORALLR &\bl{r + $\varnothing$} & \bl{$\equiv^?$} & \bl{r} & \onslide<10->{\YES}\\ |
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169 \FORALLR &\bl{r $\cdot$ $\varnothing$} & \bl{$\equiv^?$} & \bl{r} & \onslide<11->{\NO}\\ |
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170 &\bl{c $\cdot$ (a + b)} & \bl{$\equiv^?$} & \bl{(c $\cdot$ a) + (c $\cdot$ b)} & \onslide<12->{\YES}\\ |
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171 &\bl{a$^*$} & \bl{$\equiv^?$} & \bl{$\epsilon$ + (a $\cdot$ a$^*$)} & \onslide<13->{\YES} |
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172 \end{tabular} |
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173 \end{center} |
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174 |
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175 \end{frame}} |
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176 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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177 |
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178 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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179 \mode<presentation>{ |
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180 \begin{frame}[c] |
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181 \frametitle{\begin{tabular}{c}The Meaning of Matching\end{tabular}} |
423 |
182 |
424 \large |
183 \large |
425 a regular expression \bl{r} matches a string \bl{s} is defined as |
184 a regular expression \bl{r} matches a string \bl{s} is defined as |
426 |
185 |
427 \begin{center} |
186 \begin{center} |
428 \bl{s $\in$ $L$(r)}\\ |
187 \bl{s $\in$ $L$(r)}\\ |
429 \end{center} |
188 \end{center}\bigskip\bigskip\pause |
430 |
189 |
431 \end{frame}} |
190 \small |
432 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
191 if \bl{r$_1$ $\equiv$ r$_2$}, then \bl{$s$ $\in$ $L$(r$_1$)} iff \bl{$s$ $\in$ $L$(r$_2$)} |
433 |
192 |
434 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
193 \end{frame}} |
435 \mode<presentation>{ |
194 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
436 \begin{frame}[c] |
195 |
437 \frametitle{\begin{tabular}{c}Nullability\end{tabular}} |
196 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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197 \mode<presentation>{ |
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198 \begin{frame}[t] |
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199 \frametitle{\begin{tabular}{c}A Matching Algorithm\end{tabular}} |
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200 |
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201 \begin{itemize} |
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202 \item given a regular expression \bl{r} and a string \bl{s}, say yes or no for whether |
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203 \begin{center} |
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204 \bl{s $\in$ $L$(r)} |
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205 \end{center}\bigskip\bigskip\pause |
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206 \only<2>{\item foo}% |
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207 \only<3>{\item bar} |
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208 \end{itemize} |
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209 |
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210 |
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211 \end{frame}} |
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212 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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213 |
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214 |
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215 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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216 \mode<presentation>{ |
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217 \begin{frame}[c] |
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218 \frametitle{\begin{tabular}{c}An Matching Algorithm\end{tabular}} |
438 |
219 |
439 \small |
220 \small |
440 whether a regular expression matches the empty string:\medskip |
221 whether a regular expression matches the empty string:\medskip |
441 |
222 |
442 |
223 |