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1 \documentclass[dvipsnames,14pt,t]{beamer} |
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2 \usepackage{beamerthemeplainculight} |
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3 \usepackage[T1]{fontenc} |
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4 \usepackage[latin1]{inputenc} |
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5 \usepackage{mathpartir} |
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6 \usepackage[absolute,overlay]{textpos} |
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7 \usepackage{ifthen} |
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8 \usepackage{tikz} |
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9 \usepackage{pgf} |
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10 \usepackage{calc} |
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11 \usepackage{ulem} |
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12 \usepackage{courier} |
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13 \usepackage{listings} |
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14 \renewcommand{\uline}[1]{#1} |
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15 \usetikzlibrary{arrows} |
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16 \usetikzlibrary{automata} |
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17 \usetikzlibrary{shapes} |
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18 \usetikzlibrary{shadows} |
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19 \usetikzlibrary{positioning} |
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20 \usetikzlibrary{calc} |
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21 \usetikzlibrary{plotmarks} |
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22 \usepackage{graphicx} |
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23 |
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24 \definecolor{javared}{rgb}{0.6,0,0} % for strings |
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25 \definecolor{javagreen}{rgb}{0.25,0.5,0.35} % comments |
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26 \definecolor{javapurple}{rgb}{0.5,0,0.35} % keywords |
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27 \definecolor{javadocblue}{rgb}{0.25,0.35,0.75} % javadoc |
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28 |
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29 \lstset{language=Java, |
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30 basicstyle=\ttfamily, |
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31 keywordstyle=\color{javapurple}\bfseries, |
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32 stringstyle=\color{javagreen}, |
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33 commentstyle=\color{javagreen}, |
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34 morecomment=[s][\color{javadocblue}]{/**}{*/}, |
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35 numbers=left, |
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36 numberstyle=\tiny\color{black}, |
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37 stepnumber=1, |
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38 numbersep=10pt, |
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39 tabsize=2, |
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40 showspaces=false, |
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41 showstringspaces=false} |
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42 |
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43 \lstdefinelanguage{scala}{ |
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44 morekeywords={abstract,case,catch,class,def,% |
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45 do,else,extends,false,final,finally,% |
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46 for,if,implicit,import,match,mixin,% |
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47 new,null,object,override,package,% |
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48 private,protected,requires,return,sealed,% |
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49 super,this,throw,trait,true,try,% |
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50 type,val,var,while,with,yield}, |
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51 otherkeywords={=>,<-,<\%,<:,>:,\#,@}, |
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52 sensitive=true, |
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53 morecomment=[l]{//}, |
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54 morecomment=[n]{/*}{*/}, |
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55 morestring=[b]", |
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56 morestring=[b]', |
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57 morestring=[b]""" |
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58 } |
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59 |
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60 \lstset{language=Scala, |
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61 basicstyle=\ttfamily, |
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62 keywordstyle=\color{javapurple}\bfseries, |
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63 stringstyle=\color{javagreen}, |
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64 commentstyle=\color{javagreen}, |
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65 morecomment=[s][\color{javadocblue}]{/**}{*/}, |
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66 numbers=left, |
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67 numberstyle=\tiny\color{black}, |
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68 stepnumber=1, |
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69 numbersep=10pt, |
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70 tabsize=2, |
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71 showspaces=false, |
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72 showstringspaces=false} |
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73 |
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74 % beamer stuff |
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75 \renewcommand{\slidecaption}{AFL 06, King's College London, 31.~October 2012} |
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76 \newcommand{\bl}[1]{\textcolor{blue}{#1}} |
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77 \newcommand{\dn}{\stackrel{\mbox{\scriptsize def}}{=}}% for definitions |
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78 |
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79 |
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80 % The data files, written on the first run. |
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81 \begin{filecontents}{re-python.data} |
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94 24 1.773 |
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96 26 6.993 |
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97 27 14.503 |
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98 28 29.307 |
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99 #29 58.886 |
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100 \end{filecontents} |
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101 |
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102 \begin{filecontents}{re1.data} |
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124 \end{filecontents} |
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125 |
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126 \begin{filecontents}{re2.data} |
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150 \end{filecontents} |
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151 |
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152 \begin{filecontents}{re-internal.data} |
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169 \end{filecontents} |
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170 |
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171 \begin{filecontents}{re3.data} |
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193 \end{filecontents} |
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194 \begin{document} |
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195 |
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196 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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197 \mode<presentation>{ |
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198 \begin{frame}<1>[t] |
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199 \frametitle{% |
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200 \begin{tabular}{@ {}c@ {}} |
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201 \\[-3mm] |
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202 \LARGE Automata and \\[-2mm] |
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203 \LARGE Formal Languages (6)\\[3mm] |
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204 \end{tabular}} |
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205 |
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206 \normalsize |
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207 \begin{center} |
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208 \begin{tabular}{ll} |
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209 Email: & christian.urban at kcl.ac.uk\\ |
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210 Of$\!$fice: & S1.27 (1st floor Strand Building)\\ |
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211 Slides: & KEATS (also home work is there)\\ |
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212 \end{tabular} |
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213 \end{center} |
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214 |
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215 |
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216 \end{frame}} |
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217 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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218 |
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219 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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220 \mode<presentation>{ |
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221 \begin{frame}[c] |
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222 |
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223 ``I hate coding. I do not want to look at code.'' |
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224 |
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225 \end{frame}} |
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226 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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227 |
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228 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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229 \mode<presentation>{ |
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230 \begin{frame}[c] |
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231 |
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232 ``I am appalled. You do not show code anymore.'' |
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233 |
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234 \end{frame}} |
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235 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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236 |
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237 |
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238 |
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239 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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240 \mode<presentation>{ |
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241 \begin{frame}[c] |
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242 \frametitle{\begin{tabular}{c}ReDoS\end{tabular}} |
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243 |
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244 \begin{itemize} |
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245 \item \alert{R}egular \alert{e}xpression \alert{D}enial \alert{o}f \alert{S}ervice\bigskip |
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246 \item ``Regular Expressions Will Stab You in the Back''\bigskip |
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247 \item Evil regular expressions\medskip |
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248 \begin{itemize} |
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249 \item \bl{$(a?\{n\})a\{n\}$} |
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250 \item \bl{$(a^+)^+$} |
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251 \item \bl{$([a-zA-Z]^+)^*$} |
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252 \item \bl{$(a + aa)^+$} |
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253 \item \bl{$(a + a?)^+$} |
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254 \end{itemize} |
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255 \end{itemize} |
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256 |
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257 \end{frame}} |
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258 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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259 |
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260 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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261 \mode<presentation>{ |
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262 \begin{frame}[c] |
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263 \frametitle{\begin{tabular}{c}Regexp Matching\end{tabular}} |
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264 |
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265 Given a regular expression |
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266 |
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267 \begin{enumerate} |
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268 \item you might convert it into a DFA (subset construction) |
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269 \item you might try all possible paths in an NFA via backtracking |
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270 \item you might try all paths in an NFA in parallel |
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271 \item you might try to convert the DFA ``lazily'' |
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272 \end{enumerate}\bigskip |
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273 |
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274 Often No~2 is implemented (sometimes there are even good reasons for doing this). |
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275 |
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276 \end{frame}} |
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277 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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278 |
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279 |
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280 |
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281 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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282 \mode<presentation>{ |
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283 \begin{frame}[c] |
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284 \frametitle{\begin{tabular}{c}\bl{$(a?\{n\})a\{n\}$} in Python\end{tabular}} |
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285 |
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286 \begin{tikzpicture}[y=.2cm, x=.3cm] |
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287 %axis |
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288 \draw (0,0) -- coordinate (x axis mid) (30,0); |
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289 \draw (0,0) -- coordinate (y axis mid) (0,30); |
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290 %ticks |
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291 \foreach \x in {0,5,...,30} |
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292 \draw (\x,1pt) -- (\x,-3pt) |
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293 node[anchor=north] {\x}; |
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294 \foreach \y in {0,5,...,30} |
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295 \draw (1pt,\y) -- (-3pt,\y) |
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296 node[anchor=east] {\y}; |
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297 %labels |
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298 \node[below=0.6cm] at (x axis mid) {\bl{a}s}; |
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299 \node[rotate=90, left=1.2cm] at (y axis mid) {secs}; |
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300 |
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301 %plots |
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302 \draw[color=blue] plot[mark=*, mark options={fill=white}] |
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303 file {re-python.data}; |
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304 \only<2->{ |
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305 \draw[color=red] plot[mark=triangle*, mark options={fill=white} ] |
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306 file {re1.data};} |
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307 \only<3->{ |
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308 \draw[color=green] plot[mark=square*, mark options={fill=white} ] |
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309 file {re2.data};} |
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310 |
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311 %legend |
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312 \begin{scope}[shift={(4,20)}] |
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313 \draw[color=blue] (0,0) -- |
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314 plot[mark=*, mark options={fill=white}] (0.25,0) -- (0.5,0) |
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315 node[right]{\small Python}; |
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316 \only<2->{\draw[yshift=\baselineskip, color=red] (0,0) -- |
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317 plot[mark=triangle*, mark options={fill=white}] (0.25,0) -- (0.5,0) |
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318 node[right]{\small Scala V1};} |
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319 \only<3->{ |
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320 \draw[yshift=2\baselineskip, color=green] (0,0) -- |
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321 plot[mark=square*, mark options={fill=white}] (0.25,0) -- (0.5,0) |
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322 node[right]{\small Scala V2 with simplifications};} |
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323 \end{scope} |
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324 \end{tikzpicture} |
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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 |
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334 \begin{tikzpicture}[y=.7cm, x=.0009cm] |
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335 %axis |
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336 \draw (0,0) -- coordinate (x axis mid) (10000,0); |
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337 \draw (0,0) -- coordinate (y axis mid) (0,6); |
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338 %ticks |
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339 \foreach \x in {0,2000,...,10000} |
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340 \draw (\x,1pt) -- (\x,-3pt) |
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341 node[anchor=north] {\x}; |
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342 \foreach \y in {0,1,...,6} |
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343 \draw (1pt,\y) -- (-3pt,\y) |
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344 node[anchor=east] {\y}; |
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345 %labels |
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346 \node[below=0.6cm] at (x axis mid) {\bl{a}s}; |
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347 \node[rotate=90, left=1.2cm] at (y axis mid) {secs}; |
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348 |
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349 %plots |
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350 \draw[color=blue] plot[mark=*, mark options={fill=white}] |
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351 file {re-internal.data}; |
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352 \only<2->{ |
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353 \draw[color=red] plot[mark=triangle*, mark options={fill=white} ] |
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354 file {re3.data};} |
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355 |
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356 %legend |
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357 \begin{scope}[shift={(2000,4)}] |
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358 \draw[color=blue] (0,0) -- |
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359 plot[mark=*, mark options={fill=white}] (0.25,0) -- (0.5,0) |
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360 node[right]{\small Scala Internal}; |
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361 \only<2->{ |
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362 \draw[yshift=\baselineskip, color=red] (0,0) -- |
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363 plot[mark=triangle*, mark options={fill=white}] (0.25,0) -- (0.5,0) |
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364 node[right]{\small Scala V3 with explicit $\_\{\_\}$};} |
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365 \end{scope} |
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366 \end{tikzpicture} |
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367 |
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368 \end{frame}} |
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369 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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370 |
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371 |
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372 |
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373 \newcommand{\qq}{\mbox{\texttt{"}}} |
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374 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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375 \mode<presentation>{ |
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376 \begin{frame}[c] |
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377 \frametitle{\begin{tabular}{c}Grammars\end{tabular}} |
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378 |
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379 A (context-free) grammar \bl{$G$} consists of |
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380 |
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381 \begin{itemize} |
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382 \item a finite set of nonterminal symbols (upper case) |
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383 \item a finite terminal symbols or tokens (lower case) |
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384 \item a start symbol (which must be a nonterminal) |
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385 \item a set of rules |
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386 \begin{center} |
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387 \bl{$A \rightarrow \text{rhs}$} |
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388 \end{center} |
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389 |
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390 where \bl{rhs} are sequences involving terminals and nonterminals.\medskip\pause |
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391 |
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392 We can also allow rules |
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393 \begin{center} |
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394 \bl{$A \rightarrow \text{rhs}_1 | \text{rhs}_2 | \ldots$} |
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395 \end{center} |
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396 \end{itemize} |
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397 |
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398 |
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399 \end{frame}} |
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400 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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401 |
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402 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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403 \mode<presentation>{ |
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404 \begin{frame}[c] |
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405 \frametitle{\begin{tabular}{c}Palindromes\end{tabular}} |
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406 |
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407 \begin{center} |
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408 \bl{\begin{tabular}{lcl} |
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409 $S$ & $\rightarrow$ & $\epsilon$ \\ |
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410 $S$ & $\rightarrow$ & $a\cdot S\cdot a$ \\ |
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411 $S$ & $\rightarrow$ & $b\cdot S\cdot b$ \\ |
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412 \end{tabular}} |
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413 \end{center}\pause |
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414 |
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415 or |
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416 |
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417 \begin{center} |
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418 \bl{\begin{tabular}{lcl} |
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419 $S$ & $\rightarrow$ & $\epsilon \;|\; a\cdot S\cdot a \;|\;b\cdot S\cdot b$ \\ |
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420 \end{tabular}} |
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421 \end{center} |
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422 |
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423 |
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424 \end{frame}} |
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425 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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426 |
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427 |
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428 |
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429 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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430 \mode<presentation>{ |
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431 \begin{frame}[c] |
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432 \frametitle{\begin{tabular}{c}Arithmetic Expressions\end{tabular}} |
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433 |
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434 \begin{center} |
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435 \bl{\begin{tabular}{lcl} |
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436 $E$ & $\rightarrow$ & $num\_token$ \\ |
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437 $E$ & $\rightarrow$ & $E \cdot + \cdot E$ \\ |
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438 $E$ & $\rightarrow$ & $E \cdot - \cdot E$ \\ |
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439 $E$ & $\rightarrow$ & $E \cdot * \cdot E$ \\ |
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440 $E$ & $\rightarrow$ & $( \cdot E \cdot )$ |
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441 \end{tabular}} |
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442 \end{center}\pause |
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443 |
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444 \bl{\texttt{1 + 2 * 3 + 4}} |
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445 |
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446 \end{frame}} |
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447 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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448 |
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449 |
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450 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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451 \mode<presentation>{ |
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452 \begin{frame}[c] |
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453 \frametitle{\begin{tabular}{c}Parse Trees\end{tabular}} |
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454 |
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455 \begin{center} |
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456 \bl{\begin{tabular}{lcl} |
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457 $E$ & $\rightarrow$ & $F \;|\; F \cdot * \cdot F$\\ |
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458 $F$ & $\rightarrow$ & $T \;|\; T \cdot + \cdot T \;|\; T \cdot - \cdot T$\\ |
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459 $T$ & $\rightarrow$ & $num\_token \;|\; ( \cdot E \cdot )$\\ |
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460 \end{tabular}} |
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461 \end{center} |
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462 |
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463 \begin{center} |
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464 \begin{tikzpicture}[level distance=8mm, blue] |
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465 \node {$E$} |
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466 child {node {$F$} |
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467 child {node {$T$} |
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468 child {node {(\,$E$\,)} |
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469 child {node{$F$ *{} $F$} |
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470 child {node {$T$} child {node {2}}} |
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471 child {node {$T$} child {node {3}}} |
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472 } |
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473 } |
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474 } |
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475 child {node {+}} |
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476 child {node {$T$} |
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477 child {node {(\,$E$\,)} |
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478 child {node {$F$} |
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479 child {node {$T$ +{} $T$} |
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480 child {node {3}} |
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481 child {node {4}} |
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482 } |
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483 }} |
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484 }}; |
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485 \end{tikzpicture} |
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486 \end{center} |
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487 |
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488 \begin{textblock}{5}(1, 6.5) |
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489 \bl{\texttt{(2*3)+(3+4)}} |
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490 \end{textblock} |
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491 |
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492 \end{frame}} |
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493 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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494 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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495 \mode<presentation>{ |
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496 \begin{frame}[c] |
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497 \frametitle{\begin{tabular}{c}Ambiguous Grammars\end{tabular}} |
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498 |
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499 A grammar is \alert{ambiguous} if there is a string that has at least parse trees. |
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500 |
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501 |
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502 \begin{center} |
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503 \bl{\begin{tabular}{lcl} |
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504 $E$ & $\rightarrow$ & $num\_token$ \\ |
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505 $E$ & $\rightarrow$ & $E \cdot + \cdot E$ \\ |
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506 $E$ & $\rightarrow$ & $E \cdot - \cdot E$ \\ |
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507 $E$ & $\rightarrow$ & $E \cdot * \cdot E$ \\ |
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508 $E$ & $\rightarrow$ & $( \cdot E \cdot )$ |
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509 \end{tabular}} |
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510 \end{center} |
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511 |
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512 \bl{\texttt{1 + 2 * 3 + 4}} |
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513 |
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514 \end{frame}} |
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515 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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516 |
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517 |
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518 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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519 \mode<presentation>{ |
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520 \begin{frame}[c] |
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521 \frametitle{\begin{tabular}{c}Chomsky Normal Form\end{tabular}} |
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522 |
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523 All rules must be of the form |
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524 |
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525 \begin{center} |
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526 \bl{$A \rightarrow a$} |
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527 \end{center} |
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528 |
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529 or |
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530 |
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531 \begin{center} |
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532 \bl{$A \rightarrow B\cdot C$} |
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533 \end{center} |
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534 |
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535 |
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536 |
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537 \end{frame}} |
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538 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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539 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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540 \mode<presentation>{ |
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541 \begin{frame}[c] |
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542 \frametitle{\begin{tabular}{c}CYK Algorithm\end{tabular}} |
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543 |
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544 |
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545 \begin{center} |
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546 \bl{\begin{tabular}{@ {}lcl} |
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547 $S$ & $\rightarrow$ & $N\cdot P$ \\ |
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548 $P$ & $\rightarrow$ & $V\cdot N$ \\ |
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549 $N$ & $\rightarrow$ & $N\cdot N$ \\ |
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550 $N$ & $\rightarrow$ & $\texttt{students} \;|\; \texttt{Jeff} \;|\; \texttt{geometry} \;|\; \texttt{trains} $ \\ |
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551 $V$ & $\rightarrow$ & $\texttt{trains}$ |
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552 \end{tabular}} |
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553 \end{center} |
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554 |
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555 \bl{\texttt{Jeff trains geometry students}} |
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556 |
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557 \end{frame}} |
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558 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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559 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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560 \mode<presentation>{ |
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561 \begin{frame}[c] |
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562 \frametitle{\begin{tabular}{c}CYK Algorithm\end{tabular}} |
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563 |
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564 |
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565 \begin{itemize} |
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566 \item runtime is \bl{$O(n^3)$}\bigskip |
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567 \item grammars need to be transferred into CNF |
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568 \end{itemize} |
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569 |
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570 \end{frame}} |
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571 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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572 |
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573 \end{document} |
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574 |
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575 %%% Local Variables: |
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576 %%% mode: latex |
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577 %%% TeX-master: t |
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578 %%% End: |
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579 |