16 

    21 \beamertemplateballitem

   917 \frametitle{Rectification}

   922 \frametitle{Rectification $\_ + \_$}

   962 \frametitle{Rectification}

   967 \frametitle{Rectification $\_ \cdot \_$}

  1221 \begin{frame}[c]

  1226 %\begin{frame}[c]

  1222 \begin{center}

  1227 %\begin{center}

  1223 \begin{tabular}{@ {}l@ {\hspace{2mm}}c@ {\hspace{2mm}}l@ {}}

  1228 %\begin{tabular}{@ {}l@ {\hspace{2mm}}c@ {\hspace{2mm}}l@ {}}

  1224 \bl{$zeroable(\ZERO)$}      & \bl{$\dn$} & \bl{$true$}\\

  1229 %\bl{$zeroable(\ZERO)$}      & \bl{$\dn$} & \bl{$true$}\\

  1225 \bl{$zeroable(\ONE)$}         & \bl{$\dn$} & \bl{$\textit{false}$}\\

  1230 %\bl{$zeroable(\ONE)$}         & \bl{$\dn$} & \bl{$\textit{false}$}\\

  1226 \bl{$zeroable(c)$}                & \bl{$\dn$} & \bl{$\textit{false}$}\\

  1231 %\bl{$zeroable(c)$}                & \bl{$\dn$} & \bl{$\textit{false}$}\\

  1227 \bl{$zeroable(r_1 + r_2)$}        & \bl{$\dn$} & \bl{$zeroable(r_1) \wedge zeroable(r_2)$}\\ 

  1232 %\bl{$zeroable(r_1 + r_2)$}        & \bl{$\dn$} & \bl{$zeroable(r_1) \wedge zeroable(r_2)$}\\ 

  1228 \bl{$zeroable(r_1 \cdot r_2)$}    & \bl{$\dn$} & \bl{$zeroable(r_1) \vee zeroable(r_2)$}\\

  1233 %\bl{$zeroable(r_1 \cdot r_2)$}    & \bl{$\dn$} & \bl{$zeroable(r_1) \vee zeroable(r_2)$}\\

  1229 \bl{$zeroable(r^*)$}              & \bl{$\dn$} & \bl{$\textit{false}$}\\

  1234 %\bl{$zeroable(r^*)$}              & \bl{$\dn$} & \bl{$\textit{false}$}\\

  1230 \end{tabular}

  1235 %\end{tabular}

  1231 \end{center}

  1236 %\end{center}

  1232 

  1237 %

  1233 \begin{center}

  1238 %\begin{center}

  1234 \bl{$zeroable(r)$} if and only if \bl{$L(r) = \{\}$}

  1239 %\bl{$zeroable(r)$} if and only if \bl{$L(r) = \{\}$}

  1235 \end{center}

  1240 %\end{center}

  1236 

  1241 %

  1237 

  1242 %

  1238 \end{frame}

  1243 %\end{frame}

  1239 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%   

  1244 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%   

  1240 

  1245 

  1241 

  1246 

  1242   

  1247   

  1243 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

  1248 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

  1244 \begin{frame}[c]

  1249 %\begin{frame}[c]

  1245 \frametitle{\begin{tabular}{c}Last Week\\[-2mm] 

  1250 %\frametitle{\begin{tabular}{c}Last Week\\[-2mm] 

  1246             Regexes and Values\end{tabular}}

  1251 %            Regexes and Values\end{tabular}}

  1247 

  1252 %

  1248 Regular expressions and their corresponding values:

  1253 %Regular expressions and their corresponding values:

  1249 

  1254 %

  1250 \begin{center}

  1255 %\begin{center}

  1251 \begin{columns}

  1256 %\begin{columns}

  1252 \begin{column}{3cm}

  1257 %\begin{column}{3cm}

  1253 \begin{tabular}{@{}rrl@{}}

  1258 %\begin{tabular}{@{}rrl@{}}

  1254   \bl{$r$} & \bl{$::=$}  & \bl{$\ZERO$}\\

  1259 %  \bl{$r$} & \bl{$::=$}  & \bl{$\ZERO$}\\

  1255            & \bl{$\mid$} & \bl{$\ONE$}   \\

  1260 %           & \bl{$\mid$} & \bl{$\ONE$}   \\

  1256            & \bl{$\mid$} & \bl{$c$}          \\

  1261 %           & \bl{$\mid$} & \bl{$c$}          \\

  1257            & \bl{$\mid$} & \bl{$r_1 \cdot r_2$}\\

  1262 %           & \bl{$\mid$} & \bl{$r_1 \cdot r_2$}\\

  1258            & \bl{$\mid$} & \bl{$r_1 + r_2$}   \\

  1263 %           & \bl{$\mid$} & \bl{$r_1 + r_2$}   \\

  1259   \\

  1264 %  \\

  1260            & \bl{$\mid$} & \bl{$r^*$}         \\

  1265 %           & \bl{$\mid$} & \bl{$r^*$}         \\

  1261   \end{tabular}

  1266 %  \end{tabular}

  1262 \end{column}

  1267 %\end{column}

  1263 \begin{column}{3cm}

  1268 %\begin{column}{3cm}

  1264 \begin{tabular}{@{\hspace{-7mm}}rrl@{}}

  1269 %\begin{tabular}{@{\hspace{-7mm}}rrl@{}}

  1265   \bl{$v$} & \bl{$::=$}  & \\

  1270 %  \bl{$v$} & \bl{$::=$}  & \\

  1266            &             & \bl{$Empty$}   \\

  1271 %           &             & \bl{$Empty$}   \\

  1267            & \bl{$\mid$} & \bl{$Char(c)$}          \\

  1272 %           & \bl{$\mid$} & \bl{$Char(c)$}          \\

  1268            & \bl{$\mid$} & \bl{$Seq(v_1,v_2)$}\\

  1273 %           & \bl{$\mid$} & \bl{$Seq(v_1,v_2)$}\\

  1269            & \bl{$\mid$} & \bl{$Left(v)$}   \\

  1274 %           & \bl{$\mid$} & \bl{$Left(v)$}   \\

  1270            & \bl{$\mid$} & \bl{$Right(v)$}  \\

  1275 %           & \bl{$\mid$} & \bl{$Right(v)$}  \\

  1271            & \bl{$\mid$} & \bl{$Stars [v_1,\ldots\,v_n]$} \\

  1276 %           & \bl{$\mid$} & \bl{$Stars [v_1,\ldots\,v_n]$} \\

  1272   \end{tabular}

  1277 %  \end{tabular}

  1273 \end{column}

  1278 %\end{column}

  1274 \end{columns}

  1279 %\end{columns}

  1275 \end{center}

  1280 %\end{center}

  1276 

  1281 %

  1277 

  1282 %\end{frame}

  1278 \end{frame}

  1283 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%   

  1279 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%   

  1284 

  1280 

  1285 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

  1281 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

  1286 %\begin{frame}[c]

  1282 \begin{frame}[c]

  1287 %

  1283 

  1288 %\begin{textblock}{10}(3,5)

  1284 \begin{textblock}{10}(3,5)

  1289 %\begin{tikzpicture}[scale=2,node distance=1.3cm,every node/.style={minimum size=8mm}]

  1285 \begin{tikzpicture}[scale=2,node distance=1.3cm,every node/.style={minimum size=8mm}]

  1290 %\node (r1)  {\bl{$r_1$}};

  1286 \node (r1)  {\bl{$r_1$}};

  1291 %\node (r2) [right=of r1] {\bl{$r_2$}};

  1287 \node (r2) [right=of r1] {\bl{$r_2$}};

  1292 %\draw[->,line width=1mm]  (r1) -- (r2) node[above,midway] {\bl{$der\,a$}};

  1288 \draw[->,line width=1mm]  (r1) -- (r2) node[above,midway] {\bl{$der\,a$}};

  1293 %\node (r3) [right=of r2] {\bl{$r_3$}};

  1289 \node (r3) [right=of r2] {\bl{$r_3$}};

  1294 %\draw[->,line width=1mm]  (r2) -- (r3) node[above,midway] {\bl{$der\,b$}};

  1290 \draw[->,line width=1mm]  (r2) -- (r3) node[above,midway] {\bl{$der\,b$}};

  1295 %\node (r4) [right=of r3] {\bl{$r_4$}};

  1291 \node (r4) [right=of r3] {\bl{$r_4$}};

  1296 %\draw[->,line width=1mm]  (r3) -- (r4) node[above,midway] {\bl{$der\,c$}};

  1292 \draw[->,line width=1mm]  (r3) -- (r4) node[above,midway] {\bl{$der\,c$}};

  1297 %\draw (r4) node[anchor=west] {\;\raisebox{3mm}{\bl{$nullable$}}};

  1293 \draw (r4) node[anchor=west] {\;\raisebox{3mm}{\bl{$nullable$}}};

  1298 %\node (v4) [below=of r4] {\bl{$v_4$}};

  1294 \node (v4) [below=of r4] {\bl{$v_4$}};

  1299 %\draw[->,line width=1mm]  (r4) -- (v4);

  1295 \draw[->,line width=1mm]  (r4) -- (v4);

  1300 %\node (v3) [left=of v4] {\bl{$v_3$}};

  1296 \node (v3) [left=of v4] {\bl{$v_3$}};

  1301 %\draw[->,line width=1mm]  (v4) -- (v3) node[below,midway] {\bl{$inj\,c$}};

  1297 \draw[->,line width=1mm]  (v4) -- (v3) node[below,midway] {\bl{$inj\,c$}};

  1302 %\node (v2) [left=of v3] {\bl{$v_2$}};

  1298 \node (v2) [left=of v3] {\bl{$v_2$}};

  1303 %\draw[->,line width=1mm]  (v3) -- (v2) node[below,midway] {\bl{$inj\,b$}};

  1299 \draw[->,line width=1mm]  (v3) -- (v2) node[below,midway] {\bl{$inj\,b$}};

  1304 %\node (v1) [left=of v2] {\bl{$v_1$}};

  1300 \node (v1) [left=of v2] {\bl{$v_1$}};

  1305 %\draw[->,line width=1mm]  (v2) -- (v1) node[below,midway] {\bl{$inj\,a$}};

  1301 \draw[->,line width=1mm]  (v2) -- (v1) node[below,midway] {\bl{$inj\,a$}};

  1306 %\draw[->,line width=0.5mm]  (r3) -- (v3);

  1302 \draw[->,line width=0.5mm]  (r3) -- (v3);

  1307 %\draw[->,line width=0.5mm]  (r2) -- (v2);

  1303 \draw[->,line width=0.5mm]  (r2) -- (v2);

  1308 %\draw[->,line width=0.5mm]  (r1) -- (v1);

  1304 \draw[->,line width=0.5mm]  (r1) -- (v1);

  1309 %\draw (r4) node[anchor=north west] {\;\raisebox{-8mm}{\bl{$mkeps$}}};

  1305 \draw (r4) node[anchor=north west] {\;\raisebox{-8mm}{\bl{$mkeps$}}};

  1310 %\end{tikzpicture}

  1306 \end{tikzpicture}

  1311 %\end{textblock}

  1307 \end{textblock}

  1312 %

  1308 

  1313 %\begin{textblock}{6}(1,0.8)

  1309 \begin{textblock}{6}(1,0.8)

  1314 %\begin{bubble}[6cm]

  1310 \begin{bubble}[6cm]

  1315 %\small

  1311 \small

  1316 %\begin{tabular}{ll}

  1312 \begin{tabular}{ll}

  1317 %\bl{$r_1$}: & \bl{$a \cdot (b \cdot c)$}\\

  1313 \bl{$r_1$}: & \bl{$a \cdot (b \cdot c)$}\\

  1318 %\bl{$r_2$}: & \bl{$\ONE \cdot (b \cdot c)$}\\

  1314 \bl{$r_2$}: & \bl{$\ONE \cdot (b \cdot c)$}\\

  1319 %\bl{$r_3$}: & \bl{$(\ZERO \cdot (b \cdot c)) + (\ONE \cdot c)$}\\

  1315 \bl{$r_3$}: & \bl{$(\ZERO \cdot (b \cdot c)) + (\ONE \cdot c)$}\\

  1320 %\bl{$r_4$}: & \bl{$(\ZERO \cdot (b \cdot c)) + ((\ZERO \cdot c) + \ONE)$}\\

  1316 \bl{$r_4$}: & \bl{$(\ZERO \cdot (b \cdot c)) + ((\ZERO \cdot c) + \ONE)$}\\

  1321 %\end{tabular}

  1317 \end{tabular}

  1322 %\end{bubble}

  1318 \end{bubble}

  1323 %\end{textblock}

  1319 \end{textblock}

  1324 %

  1320 

  1325 %\begin{textblock}{6}(1,11.4)

  1321 \begin{textblock}{6}(1,11.4)

  1326 %\begin{bubble}[7.6cm]

  1322 \begin{bubble}[7.6cm]

  1327 %\small

  1323 \small

  1328 %\begin{tabular}{ll}

  1324 \begin{tabular}{ll}

  1329 %\bl{$v_1$}: & \bl{$Seq(Char(a), Seq(Char(b), Char(c)))$}\\

  1325 \bl{$v_1$}: & \bl{$Seq(Char(a), Seq(Char(b), Char(c)))$}\\

  1330 %\bl{$v_2$}: & \bl{$Seq(Empty, Seq(Char(b), Char(c)))$}\\

  1326 \bl{$v_2$}: & \bl{$Seq(Empty, Seq(Char(b), Char(c)))$}\\

  1331 %\bl{$v_3$}: & \bl{$Right(Seq(Empty, Char(c)))$}\\

  1327 \bl{$v_3$}: & \bl{$Right(Seq(Empty, Char(c)))$}\\

  1332 %\bl{$v_4$}: & \bl{$Right(Right(Empty))$}\\

  1328 \bl{$v_4$}: & \bl{$Right(Right(Empty))$}\\

  1333 %\end{tabular}

  1329 \end{tabular}

  1334 %\end{bubble}

  1330 \end{bubble}

  1335 %\end{textblock}

  1331 \end{textblock}

  1336 %

  1332 

  1337 %\begin{textblock}{6}(12,11.4)

  1333 \begin{textblock}{6}(12,11.4)

  1338 %\begin{bubble}[2cm]

  1334 \begin{bubble}[2cm]

  1339 %\small

  1335 \small

  1340 %\begin{tabular}{ll}

  1336 \begin{tabular}{ll}

  1341 %\bl{$|v_1|$}: & \bl{$abc$}\\

  1337 \bl{$|v_1|$}: & \bl{$abc$}\\

  1342 %\bl{$|v_2|$}: & \bl{$bc$}\\

  1338 \bl{$|v_2|$}: & \bl{$bc$}\\

  1343 %\bl{$|v_3|$}: & \bl{$c$}\\

  1339 \bl{$|v_3|$}: & \bl{$c$}\\

  1344 %\bl{$|v_4|$}: & \bl{$[]$}

  1340 \bl{$|v_4|$}: & \bl{$[]$}

  1345 %\end{tabular}

  1341 \end{tabular}

  1346 %\end{bubble}

  1342 \end{bubble}

  1347 %\end{textblock}

  1343 \end{textblock}

  1348 %

  1344 

  1349 %

  1345 

  1350 %%\end{frame}

  1346 \end{frame}

  1351 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%   

  1347 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%   

  1352 %

  1348 

  1353 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

  1349 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

  1354 %\begin{frame}[c]

  1350 \begin{frame}[c]

  1355 %\frametitle{Simplification}

  1351 \frametitle{Simplification}

  1356 %

  1352 

  1357 %\begin{itemize}

  1353 \begin{itemize}

  1358 %\item If we simplify after the derivative, then we are builing the

  1354 \item If we simplify after the derivative, then we are builing the

  1359 %value for the simplified regular expression, but \emph{not} for the original

  1355 value for the simplified regular expression, but \emph{not} for the original

  1360 %regular expression.

  1356 regular expression.

  1361 %\end{itemize}

  1357 \end{itemize}

  1362 %

  1358 

  1363 %\begin{center}

  1359 \begin{center}

  1364 %\begin{tikzpicture}[scale=2,node distance=1.3cm,every node/.style={minimum size=8mm}]

  1360 \begin{tikzpicture}[scale=2,node distance=1.3cm,every node/.style={minimum size=8mm}]

  1365 %\node (r1)  {\bl{$r_1$}};

  1361 \node (r1)  {\bl{$r_1$}};

  1366 %\node (r2) [right=of r1] {\bl{$r_2$}};

  1362 \node (r2) [right=of r1] {\bl{$r_2$}};

  1367 %\draw[->,line width=1mm]  (r1) -- (r2) node[above,midway] {\bl{$der\,a$}};

  1363 \draw[->,line width=1mm]  (r1) -- (r2) node[above,midway] {\bl{$der\,a$}};

  1368 %\node (r3) [right=of r2] {\bl{$r_3$}};

  1364 \node (r3) [right=of r2] {\bl{$r_3$}};

  1369 %\draw[->,line width=1mm]  (r2) -- (r3) node[above,midway] {\bl{$der\,b$}};

  1365 \draw[->,line width=1mm]  (r2) -- (r3) node[above,midway] {\bl{$der\,b$}};

  1370 %\node (r4) [right=of r3] {\bl{$r_4$}};

  1366 \node (r4) [right=of r3] {\bl{$r_4$}};

  1371 %\draw[->,line width=1mm]  (r3) -- (r4) node[above,midway] {\bl{$der\,c$}};

  1367 \draw[->,line width=1mm]  (r3) -- (r4) node[above,midway] {\bl{$der\,c$}};

  1372 %\draw (r4) node[anchor=west] {\;\raisebox{3mm}{\bl{$nullable$}}};

  1368 \draw (r4) node[anchor=west] {\;\raisebox{3mm}{\bl{$nullable$}}};

  1373 %\node (v4) [below=of r4] {\bl{$v_4$}};

  1369 \node (v4) [below=of r4] {\bl{$v_4$}};

  1374 %\draw[->,line width=1mm]  (r4) -- (v4);

  1370 \draw[->,line width=1mm]  (r4) -- (v4);

  1375 %\node (v3) [left=of v4] {\bl{$v_3$}};

  1371 \node (v3) [left=of v4] {\bl{$v_3$}};

  1376 %\draw[->,line width=1mm]  (v4) -- (v3) node[below,midway] {\bl{$inj\,c$}};

  1372 \draw[->,line width=1mm]  (v4) -- (v3) node[below,midway] {\bl{$inj\,c$}};

  1377 %\node (v2) [left=of v3] {\bl{$v_2$}};

  1373 \node (v2) [left=of v3] {\bl{$v_2$}};

  1378 %\draw[->,line width=1mm]  (v3) -- (v2) node[below,midway] {\bl{$inj\,b$}};

  1374 \draw[->,line width=1mm]  (v3) -- (v2) node[below,midway] {\bl{$inj\,b$}};

  1379 %\node (v1) [left=of v2] {\bl{$v_1$}};

  1375 \node (v1) [left=of v2] {\bl{$v_1$}};

  1380 %\draw[->,line width=1mm]  (v2) -- (v1) node[below,midway] {\bl{$inj\,a$}};

  1376 \draw[->,line width=1mm]  (v2) -- (v1) node[below,midway] {\bl{$inj\,a$}};

  1381 %\draw[->,line width=0.5mm]  (r3) -- (v3);

  1377 \draw[->,line width=0.5mm]  (r3) -- (v3);

  1382 %\draw[->,line width=0.5mm]  (r2) -- (v2);

  1378 \draw[->,line width=0.5mm]  (r2) -- (v2);

  1383 %\draw[->,line width=0.5mm]  (r1) -- (v1);

  1379 \draw[->,line width=0.5mm]  (r1) -- (v1);

  1384 %\draw (r4) node[anchor=north west] {\;\raisebox{-8mm}{\bl{$mkeps$}}};

  1380 \draw (r4) node[anchor=north west] {\;\raisebox{-8mm}{\bl{$mkeps$}}};

  1385 %\end{tikzpicture}

  1381 \end{tikzpicture}

  1386 %\end{center}

  1382 \end{center}

  1387 %

  1383 

  1388 %\small

  1384 \small

  1389 %\hspace{4.5cm}\bl{$(b \cdot c) + (\ZERO + \ONE)$}

  1385 \hspace{4.5cm}\bl{$(b \cdot c) + (\ZERO + \ONE)$}

  1390 %$\mapsto$

  1386 $\mapsto$

  1391 %\bl{$(b \cdot c) + \ONE$}

  1387 \bl{$(b \cdot c) + \ONE$}

  1392 %

  1388 

  1393 %\end{frame}

  1389 \end{frame}

  1394 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%  

  1390 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%  

  1395 %

  1391 

  1396 %% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

  1392 % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

  1454 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

  1458 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

  1455 \begin{frame}[c]

  1459 %\begin{frame}[c]

  1456 \frametitle{Records}

  1460 %\frametitle{Records}

  1457 

  1461 %

  1458 \begin{itemize}

  1462 %\begin{itemize}

  1459 \item new regex: \bl{$(x:r)$}\hspace{7mm}new value: \bl{$Rec(x,v)$}\medskip\pause

  1463 %\item new regex: \bl{$(x:r)$}\hspace{7mm}new value: \bl{$Rec(x,v)$}\medskip\pause

  1460 

  1464 %

  1461 \item \bl{$nullable(x:r) \dn nullable(r)$}

  1465 %\item \bl{$nullable(x:r) \dn nullable(r)$}

  1462 \item \bl{$der\,c\,(x:r) \dn der\,c\,r$}

  1466 %\item \bl{$der\,c\,(x:r) \dn der\,c\,r$}

  1463 \item \bl{$mkeps(x:r) \dn Rec(x, mkeps(r))$}

  1467 %\item \bl{$mkeps(x:r) \dn Rec(x, mkeps(r))$}

  1464 \item \bl{$inj\,(x:r)\,c\,v \dn Rec(x, inj\,r\,c\,v)$}

  1468 %\item \bl{$inj\,(x:r)\,c\,v \dn Rec(x, inj\,r\,c\,v)$}

  1465 \end{itemize}\bigskip\bigskip\pause

  1469 %\end{itemize}\bigskip\bigskip\pause

  1466 

  1470 %

  1467 \small

  1471 %\small

  1468 for extracting subpatterns \bl{$(z: ((x:ab) + (y:ba))$}

  1472 %for extracting subpatterns \bl{$(z: ((x:ab) + (y:ba))$}

  1469 

  1473 %

  1470 \end{frame}

  1474 %\end{frame}

  1471 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

  1475 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

  1650  

  1654 

  1655 \begin{frame}[t]

  1656 \begin{mybox3}{}

  1657   Are dfas completed by definition as in do they have a to have transitions

  1658   for every char at every state?

  1659 \end{mybox3}

  1660 \end{frame}

  1661 

  1662 \begin{frame}[t]

  1663 \begin{mybox3}{}

  1664   How can you tell if a language will be regular or irregular?

  1665 \end{mybox3}

  1666 \end{frame}

  1667 

  1668 \begin{frame}<1-12>[c]

  1669 \end{frame}

  1670 

  1671 \begin{frame}[c]

  1672   \small

  1673   \begin{itemize}

  1674 \item[$\bullet$] contentwise probably the most enjoyable module I have had so far at KCL 

  1675 

  1676 \item[$\bullet$] I personally found the coursework sheets a bit unclear. For example I couldnt see what was required from the CFUN section but once explained it actually was very easy and didnt take long to get working

  1677 

  1678 \item[$\bullet$] Please can tutorial sessions be recorded \& linked on Keats.

  1679   

  1680 \item[$\bullet$] One of the best taught modules I've had, with a genuinely interested and engaging lecturer. Thanks Dr.~Urban!

  1681 \end{itemize}

  1682 \end{frame}

  1683 

  1684 \begin{frame}[c]

  1685   \small

  1686   \begin{itemize}

  1687 \item[$\bullet$] Dr.~Urban is honestly a great lecturer, he's incredibly helpful and responsive. He also teaches at a very good pace and explains things clearly so students who sometimes struggle with the content like myself can keep up. It's a pleasure to learn from him.

  1688   

  1689 \item[$\bullet$] I just wish the Coursework content was explained better, in such a way that allows students to get on with the coursework as soon as possible.

  1690   

  1691 \item[$\bullet$] I'm thoroughly enjoying the module so far. I find that the handouts and homework really solidify my knowledge and the feedback is extremely useful. I enjoy doing the homework and then using the feedback alongside the workshop to correct where I have gone wrong.

  1692   

  1693 \item[$\bullet$] I enjoy this module and think it is taught well. The homework is very useful.

  1694 \end{itemize}

  1695 \end{frame}

  1696 

  1697 \begin{frame}[c]

  1698   \begin{center}

  1699   \begin{tabular}{cc}  

  1700   \includegraphics[scale=0.3]{s1.png} &

  1701   \includegraphics[scale=0.3]{s2.png} \\

  1702   \includegraphics[scale=0.3]{s3.png} &

  1703   \includegraphics[scale=0.3]{s4.png} \\

  1704   \end{tabular}                                      

  1705   \end{center}

  1706 \end{frame}

  1707 

  1708 \begin{frame}[c]

  1709   \begin{center}

  1710   \begin{tabular}{cc}  

  1711   \includegraphics[scale=0.3]{s5.png} &

  1712   \includegraphics[scale=0.3]{s6.png} \\

  1713   \includegraphics[scale=0.3]{s7.png} &

  1714   \includegraphics[scale=0.3]{s8.png} \\

  1715   \end{tabular}                                      

  1716   \end{center}

  1717 \end{frame}

  1718 

  1719 \begin{frame}[c]

  1720   \begin{center}

  1721   \begin{tabular}{cc}  

  1722   \includegraphics[scale=0.3]{s9.png} 

  1723   \end{tabular}                                      

  1724   \end{center}

  1725 \end{frame}