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\documentclass[dvipsnames,14pt,t]{beamer}
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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\usepackage{../slides}
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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\usepackage{../graphics}
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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\usepackage{../langs}
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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\usepackage{../data}
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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|
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\hfuzz=220pt
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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8 |
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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|
9 |
\pgfplotsset{compat=1.11}
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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10 |
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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\newcommand{\bl}[1]{\textcolor{blue}{#1}}
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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|
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\renewcommand{\slidecaption}{AFL 04, King's College London}
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\begin{document}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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|
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\begin{frame}[t]
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33
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\frametitle{%
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\begin{tabular}{@ {}c@ {}}
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\\[-3mm]
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\LARGE Automata and \\[-2mm]
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\LARGE Formal Languages (4)\\[3mm]
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\end{tabular}}
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25 |
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\normalsize
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\begin{center}
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\begin{tabular}{ll}
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Email: & christian.urban at kcl.ac.uk\\
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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|
30 |
Office: & S1.27 (1st floor Strand Building)\\
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33
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Slides: & KEATS (also home work is there)\\
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\end{tabular}
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\end{center}
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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|
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\end{frame}
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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|
35 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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|
36 |
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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|
37 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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|
38 |
\begin{frame}[c]
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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39 |
\frametitle{Regexps and Automata}
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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|
40 |
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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|
41 |
\begin{center}
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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|
42 |
\begin{tikzpicture}
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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|
43 |
\node (rexp) {\bl{\bf Regexps}};
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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|
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\node (nfa) [right=of rexp] {\bl{\bf NFAs}};
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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|
45 |
\node (dfa) [right=of nfa] {\bl{\bf DFAs}};
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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\node (mdfa) [right=of dfa] {\bl{\bf \begin{tabular}{c}minimal\\ DFAs\end{tabular}}};
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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changeset
|
47 |
\path[->,red, line width=2mm] (rexp) edge node [above=4mm, black]
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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changeset
|
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{\begin{tabular}{c@{\hspace{9mm}}}Thompson's\\[-1mm] construction\end{tabular}} (nfa);
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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changeset
|
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\path[->,red, line width=2mm] (nfa) edge node [above=4mm, black]
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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changeset
|
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{\begin{tabular}{c}subset\\[-1mm] construction\end{tabular}}(dfa);
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Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
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\path[->, red, line width=2mm] (dfa) edge node [below=5mm, black] {minimisation} (mdfa);
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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changeset
|
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\path[->, red, line width=2mm] (dfa) edge [bend left=45] (rexp);
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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|
53 |
\end{tikzpicture}\\
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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|
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\end{center}
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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|
55 |
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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|
56 |
\end{frame}
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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|
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
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changeset
|
58 |
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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changeset
|
59 |
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Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
60 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
61 |
\mode<presentation>{
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Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
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|
62 |
\begin{frame}[t]
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Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
63 |
\frametitle{\bl{$(a?\{n\}) \cdot a\{n\}$}}
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Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
64 |
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272
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
65 |
\begin{tikzpicture}
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Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
66 |
\begin{axis}[xlabel={\pcode{a}s},ylabel={time in secs},
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Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
67 |
enlargelimits=false,
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Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
68 |
xtick={0,5,...,30},
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Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
69 |
xmax=30,
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Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
70 |
ymax=35,
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Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
71 |
ytick={0,5,...,30},
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Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
72 |
scaled ticks=false,
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Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
73 |
axis lines=left,
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Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
74 |
width=10cm,
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Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
75 |
height=7cm,
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Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
76 |
legend entries={Python,Ruby,my NFA},
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
77 |
legend pos=north west,
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Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
78 |
legend cell align=left]
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
79 |
\addplot[blue,mark=*, mark options={fill=white}]
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
80 |
table {re-python.data};
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Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
81 |
\addplot[brown,mark=pentagon*, mark options={fill=white}]
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
82 |
table {re-ruby.data};
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
83 |
\addplot[red,mark=triangle*, mark options={fill=white}]
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
84 |
table {nfasearch.data};
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
85 |
\end{axis}
|
145
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
86 |
\end{tikzpicture}
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Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
87 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
88 |
\end{frame}}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
89 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
90 |
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Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
91 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
92 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
272
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
93 |
\begin{frame}[c]
|
145
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
94 |
\frametitle{DFA to Rexp}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
95 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
96 |
\begin{center}
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272
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
97 |
\begin{tikzpicture}[scale=2,>=stealth',very thick,
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
98 |
every state/.style={minimum size=0pt,
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
99 |
draw=blue!50,very thick,fill=blue!20},]
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
100 |
\node[state, initial] (q0) at ( 0,1) {$q_0$};
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
101 |
\node[state] (q1) at ( 1,1) {$q_1$};
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
102 |
\node[state, accepting] (q2) at ( 2,1) {$q_2$};
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Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
103 |
\path[->] (q0) edge[bend left] node[above] {\alert{$a$}} (q1)
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
104 |
(q1) edge[bend left] node[above] {\alert{$b$}} (q0)
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
105 |
(q2) edge[bend left=50] node[below] {\alert{$b$}} (q0)
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
106 |
(q1) edge node[above] {\alert{$a$}} (q2)
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
107 |
(q2) edge [loop right] node {\alert{$a$}} ()
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
108 |
(q0) edge [loop below] node {\alert{$b$}} ();
|
145
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
109 |
\end{tikzpicture}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
110 |
\end{center}\bigskip
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
111 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
112 |
\begin{center}
|
272
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
113 |
\begin{tabular}{r@ {\hspace{2mm}}c@ {\hspace{2mm}}l@{\hspace{7mm}}l}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
114 |
\bl{$q_0$} & \bl{$=$} & \bl{$\epsilon + q_0\,b + q_1\,b + q_2\,b$} & (start state)\\
|
145
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
115 |
\bl{$q_1$} & \bl{$=$} & \bl{$q_0\,a$}\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
116 |
\bl{$q_2$} & \bl{$=$} & \bl{$q_1\,a + q_2\,a$}\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
117 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
118 |
\end{tabular}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
119 |
\end{center}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
120 |
|
272
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
121 |
\onslide<2->{
|
145
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
122 |
Arden's Lemma:
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
123 |
\begin{center}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
124 |
If \bl{$q = q\,r + s$}\; then\; \bl{$q = s\, r^*$}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
125 |
\end{center}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
126 |
}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
127 |
|
272
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
128 |
\end{frame}
|
145
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
129 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
130 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
131 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
132 |
\mode<presentation>{
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
133 |
\begin{frame}[c]
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
134 |
\frametitle{DFA Minimisation}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
135 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
136 |
\begin{enumerate}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
137 |
\item Take all pairs \bl{$(q, p)$} with \bl{$q \not= p$}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
138 |
\item Mark all pairs that accepting and non-accepting states
|
270
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
139 |
\item For all unmarked pairs \bl{$(q, p)$} and all characters \bl{$c$} test whether
|
145
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
140 |
\begin{center}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
141 |
\bl{$(\delta(q, c), \delta(p,c))$}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
142 |
\end{center}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
143 |
are marked. If yes, then also mark \bl{$(q, p)$}.
|
270
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
144 |
\item Repeat last step until no change.
|
145
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
145 |
\item All unmarked pairs can be merged.
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
146 |
\end{enumerate}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
147 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
148 |
\end{frame}}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
149 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
144
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
150 |
|
265
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
151 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
270
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
152 |
\begin{frame}[c]
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
153 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
154 |
\begin{center}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
155 |
\begin{tikzpicture}[>=stealth',very thick,auto,
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
156 |
every state/.style={minimum size=0pt,inner sep=2pt,draw=blue!50,very thick,fill=blue!20},]
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
157 |
\node[state,initial] (q_0) {$q_0$};
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
158 |
\node[state] (q_1) [right=of q_0] {$q_1$};
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
159 |
\node[state] (q_2) [below right=of q_0] {$q_2$};
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
160 |
\node[state] (q_3) [right=of q_2] {$q_3$};
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
161 |
\node[state, accepting] (q_4) [right=of q_1] {$q_4$};
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
162 |
\path[->] (q_0) edge node [above] {\alert{$a$}} (q_1);
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
163 |
\path[->] (q_1) edge node [above] {\alert{$a$}} (q_4);
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
164 |
\path[->] (q_4) edge [loop right] node {\alert{$a, b$}} ();
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
165 |
\path[->] (q_3) edge node [right] {\alert{$a$}} (q_4);
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
166 |
\path[->] (q_2) edge node [above] {\alert{$a$}} (q_3);
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
167 |
\path[->] (q_1) edge node [right] {\alert{$b$}} (q_2);
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
168 |
\path[->] (q_0) edge node [above] {\alert{$b$}} (q_2);
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
169 |
\path[->] (q_2) edge [loop left] node {\alert{$b$}} ();
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
170 |
\path[->] (q_3) edge [bend left=95, looseness=1.3] node [below] {\alert{$b$}} (q_0);
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
171 |
\end{tikzpicture}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
172 |
\end{center}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
173 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
174 |
\mbox{}\\[-20mm]\mbox{}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
175 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
176 |
\begin{center}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
177 |
\begin{tikzpicture}[scale=0.8,line width=0.8mm]
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
178 |
\draw (0,0) -- (4,0);
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
179 |
\draw (0,1) -- (4,1);
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
180 |
\draw (0,2) -- (3,2);
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
181 |
\draw (0,3) -- (2,3);
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
182 |
\draw (0,4) -- (1,4);
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
183 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
184 |
\draw (0,0) -- (0, 4);
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
185 |
\draw (1,0) -- (1, 4);
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
186 |
\draw (2,0) -- (2, 3);
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
187 |
\draw (3,0) -- (3, 2);
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
188 |
\draw (4,0) -- (4, 1);
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
189 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
190 |
\draw (0.5,-0.5) node {$q_0$};
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
191 |
\draw (1.5,-0.5) node {$q_1$};
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
192 |
\draw (2.5,-0.5) node {$q_2$};
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
193 |
\draw (3.5,-0.5) node {$q_3$};
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
194 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
195 |
\draw (-0.5, 3.5) node {$q_1$};
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
196 |
\draw (-0.5, 2.5) node {$q_2$};
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
197 |
\draw (-0.5, 1.5) node {$q_3$};
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
198 |
\draw (-0.5, 0.5) node {$q_4$};
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
199 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
200 |
\draw (0.5,0.5) node {\large$\star$};
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
201 |
\draw (1.5,0.5) node {\large$\star$};
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
202 |
\draw (2.5,0.5) node {\large$\star$};
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
203 |
\draw (3.5,0.5) node {\large$\star$};
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
204 |
\end{tikzpicture}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
205 |
\end{center}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
206 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
207 |
\end{frame}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
208 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
209 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
210 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
211 |
\begin{frame}[c]
|
265
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
212 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
213 |
\begin{center}
|
272
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
214 |
\begin{tabular}{@{\hspace{-8mm}}cc@{}}
|
265
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
215 |
\begin{tikzpicture}[>=stealth',very thick,auto,
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
216 |
every state/.style={minimum size=0pt,inner sep=2pt,draw=blue!50,very thick,fill=blue!20},]
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
217 |
\node[state,initial] (q_0) {$q_0$};
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
218 |
\node[state] (q_1) [right=of q_0] {$q_1$};
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
219 |
\node[state] (q_2) [below right=of q_0] {$q_2$};
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
220 |
\node[state] (q_3) [right=of q_2] {$q_3$};
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
221 |
\node[state, accepting] (q_4) [right=of q_1] {$q_4$};
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
222 |
\path[->] (q_0) edge node [above] {\alert{$a$}} (q_1);
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
223 |
\path[->] (q_1) edge node [above] {\alert{$a$}} (q_4);
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
224 |
\path[->] (q_4) edge [loop right] node {\alert{$a, b$}} ();
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
225 |
\path[->] (q_3) edge node [right] {\alert{$a$}} (q_4);
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
226 |
\path[->] (q_2) edge node [above] {\alert{$a$}} (q_3);
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
227 |
\path[->] (q_1) edge node [right] {\alert{$b$}} (q_2);
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
228 |
\path[->] (q_0) edge node [above] {\alert{$b$}} (q_2);
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
229 |
\path[->] (q_2) edge [loop left] node {\alert{$b$}} ();
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
230 |
\path[->] (q_3) edge [bend left=95, looseness=1.3] node [below] {\alert{$b$}} (q_0);
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
231 |
\end{tikzpicture}
|
272
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
232 |
&
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
233 |
\raisebox{9mm}{\begin{tikzpicture}[scale=0.6,line width=0.8mm]
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
234 |
\draw (0,0) -- (4,0);
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
235 |
\draw (0,1) -- (4,1);
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
236 |
\draw (0,2) -- (3,2);
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
237 |
\draw (0,3) -- (2,3);
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
238 |
\draw (0,4) -- (1,4);
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
239 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
240 |
\draw (0,0) -- (0, 4);
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
241 |
\draw (1,0) -- (1, 4);
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
242 |
\draw (2,0) -- (2, 3);
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
243 |
\draw (3,0) -- (3, 2);
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
244 |
\draw (4,0) -- (4, 1);
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
245 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
246 |
\draw (0.5,-0.5) node {$q_0$};
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
247 |
\draw (1.5,-0.5) node {$q_1$};
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
248 |
\draw (2.5,-0.5) node {$q_2$};
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
249 |
\draw (3.5,-0.5) node {$q_3$};
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
250 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
251 |
\draw (-0.5, 3.5) node {$q_1$};
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
252 |
\draw (-0.5, 2.5) node {$q_2$};
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
253 |
\draw (-0.5, 1.5) node {$q_3$};
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
254 |
\draw (-0.5, 0.5) node {$q_4$};
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
255 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
256 |
\draw (0.5,0.5) node {\large$\star$};
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
257 |
\draw (1.5,0.5) node {\large$\star$};
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
258 |
\draw (2.5,0.5) node {\large$\star$};
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
259 |
\draw (3.5,0.5) node {\large$\star$};
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
260 |
\draw (0.5,1.5) node {\large$\star$};
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
261 |
\draw (2.5,1.5) node {\large$\star$};
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
262 |
\draw (0.5,3.5) node {\large$\star$};
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
263 |
\draw (1.5,2.5) node {\large$\star$};
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
264 |
\end{tikzpicture}}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
265 |
\end{tabular}
|
265
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
266 |
\end{center}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
267 |
|
272
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
268 |
|
265
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
269 |
\mbox{}\\[-20mm]\mbox{}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
270 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
271 |
\begin{center}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
272 |
\begin{tikzpicture}[>=stealth',very thick,auto,
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
273 |
every state/.style={minimum size=0pt,inner sep=2pt,draw=blue!50,very thick,fill=blue!20},]
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
274 |
\node[state,initial] (q_02) {$q_{0, 2}$};
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
275 |
\node[state] (q_13) [right=of q_02] {$q_{1, 3}$};
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
276 |
\node[state, accepting] (q_4) [right=of q_13] {$q_{4\phantom{,0}}$};
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
277 |
\path[->] (q_02) edge [bend left] node [above] {\alert{$a$}} (q_13);
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
278 |
\path[->] (q_13) edge [bend left] node [below] {\alert{$b$}} (q_02);
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
279 |
\path[->] (q_02) edge [loop below] node {\alert{$b$}} ();
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
280 |
\path[->] (q_13) edge node [above] {\alert{$a$}} (q_4);
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
281 |
\path[->] (q_4) edge [loop above] node {\alert{$a, b$}} ();
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
282 |
\end{tikzpicture}\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
283 |
minimal automaton
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
284 |
\end{center}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
285 |
|
270
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
286 |
\end{frame}
|
265
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
287 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
288 |
|
144
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
289 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
272
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
290 |
\begin{frame}[c]
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
291 |
\frametitle{Alternatives}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
292 |
\mbox{}\\[-17mm]\mbox{}
|
139
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
293 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
294 |
\begin{center}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
295 |
\begin{tikzpicture}[>=stealth',very thick,auto,
|
272
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
296 |
every state/.style={minimum size=0pt,
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
297 |
inner sep=2pt,draw=blue!50,very thick,fill=blue!20}]
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
298 |
\only<1>{\node[state,initial] (q_0) {$q_0$};}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
299 |
\only<2->{\node[state,accepting] (q_0) {$q_0$};}
|
139
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
300 |
\node[state] (q_1) [right=of q_0] {$q_1$};
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
301 |
\node[state] (q_2) [below right=of q_0] {$q_2$};
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
302 |
\node[state] (q_3) [right=of q_2] {$q_3$};
|
272
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
303 |
\only<1>{\node[state, accepting] (q_4) [right=of q_1] {$q_4$};}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
304 |
\only<2->{\node[state, initial right] (q_4) [right=of q_1] {$q_4$};}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
305 |
\only<1-2>{
|
139
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
306 |
\path[->] (q_0) edge node [above] {\alert{$a$}} (q_1);
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
307 |
\path[->] (q_1) edge node [above] {\alert{$a$}} (q_4);
|
272
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
308 |
\path[->] (q_4) edge [loop above] node {\alert{$a, b$}} ();
|
139
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
309 |
\path[->] (q_3) edge node [right] {\alert{$a$}} (q_4);
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
310 |
\path[->] (q_2) edge node [above] {\alert{$a$}} (q_3);
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
311 |
\path[->] (q_1) edge node [right] {\alert{$b$}} (q_2);
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
312 |
\path[->] (q_0) edge node [above] {\alert{$b$}} (q_2);
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
313 |
\path[->] (q_2) edge [loop left] node {\alert{$b$}} ();
|
272
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
314 |
\path[->] (q_3) edge [bend left=95, looseness=1.3] node [below] {\alert{$b$}} (q_0);}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
315 |
\only<3->{
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
316 |
\path[<-] (q_0) edge node [above] {\alert{$a$}} (q_1);
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
317 |
\path[<-] (q_1) edge node [above] {\alert{$a$}} (q_4);
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
318 |
\path[<-] (q_4) edge [loop above] node {\alert{$a, b$}} ();
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
319 |
\path[<-] (q_3) edge node [right] {\alert{$a$}} (q_4);
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
320 |
\path[<-] (q_2) edge node [above] {\alert{$a$}} (q_3);
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
321 |
\path[<-] (q_1) edge node [right] {\alert{$b$}} (q_2);
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
322 |
\path[<-] (q_0) edge node [above] {\alert{$b$}} (q_2);
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
323 |
\path[<-] (q_2) edge [loop left] node {\alert{$b$}} ();
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
324 |
\path[<-] (q_3) edge [bend left=95, looseness=1.3] node [below] {\alert{$b$}} (q_0);}
|
139
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
325 |
\end{tikzpicture}
|
272
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
326 |
\end{center}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
327 |
\mbox{}\\[-18mm]
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
328 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
329 |
\begin{itemize}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
330 |
\item<2-> exchange initial / accepting states
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
331 |
\item<3-> reverse all edges
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
332 |
\item<4-> subset construction $\Rightarrow$ DFA
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
333 |
\item<5-> repeat once more \onslide<6->{$\Rightarrow$ minimal DFA}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
334 |
\end{itemize}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
335 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
336 |
\end{frame}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
337 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
338 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
339 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
340 |
\begin{frame}[c]
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
341 |
\frametitle{Regular Languages}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
342 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
343 |
Two equivalent definitions:\bigskip
|
139
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
344 |
|
272
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
345 |
\begin{quote}\rm A language is \alert{regular} iff there exists a
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
346 |
regular expression that recognises all its strings.
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
347 |
\end{quote}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
348 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
349 |
\begin{quote}\rm A language is \alert{regular} iff there exists an
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
350 |
automaton that recognises all its strings.
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
351 |
\end{quote}\bigskip\bigskip
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
352 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
353 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
354 |
\small
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
355 |
for example $a^nb^n$ is not regular
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
356 |
\end{frame}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
357 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
358 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
359 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
360 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
361 |
\begin{frame}[c]
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
362 |
\frametitle{Negation}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
363 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
364 |
Regular languages are closed under negation:\bigskip
|
139
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
365 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
366 |
\begin{center}
|
272
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
367 |
\begin{tikzpicture}[scale=2,>=stealth',very thick,
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
368 |
every state/.style={minimum size=0pt,
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
369 |
draw=blue!50,very thick,fill=blue!20}]
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
370 |
\only<1>{\node[state,initial] (q0) at ( 0,1) {$q_0$};}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
371 |
\only<2>{\node[state,initial,accepting] (q0) at ( 0,1) {$q_0$};}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
372 |
\only<1>{\node[state] (q1) at ( 1,1) {$q_1$};}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
373 |
\only<2>{\node[state,accepting] (q1) at ( 1,1) {$q_1$};}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
374 |
\only<1>{\node[state, accepting] (q2) at ( 2,1) {$q_2$};}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
375 |
\only<2>{\node[state] (q2) at ( 2,1) {$q_2$};}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
376 |
\path[->] (q0) edge[bend left] node[above] {\alert{$a$}} (q1)
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
377 |
(q1) edge[bend left] node[above] {\alert{$b$}} (q0)
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
378 |
(q2) edge[bend left=50] node[below] {\alert{$b$}} (q0)
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
379 |
(q1) edge node[above] {\alert{$a$}} (q2)
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
380 |
(q2) edge [loop right] node {\alert{$a$}} ()
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
381 |
(q0) edge [loop below] node {\alert{$b$}} ();
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
382 |
\end{tikzpicture}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
383 |
\end{center}\bigskip\bigskip
|
139
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
384 |
|
272
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
385 |
\onslide<2>{But requires that the automaton is \alert{completed}!}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
386 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
387 |
\end{frame}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
388 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
389 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
390 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
391 |
\begin{frame}[c]
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
392 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
393 |
\mbox{\lstinputlisting[language=While]{../progs/fib.while}}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
394 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
395 |
\end{frame}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
396 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
397 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
398 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
399 |
\begin{frame}[c]
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
400 |
\frametitle{??}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
401 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
402 |
\mbox{\lstinputlisting[language=While]{../progs/collatz.while}}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
403 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
404 |
\end{frame}
|
139
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
405 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
406 |
|
35
|
407 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
408 |
\begin{frame}[c]
|
272
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
409 |
\frametitle{A Compiler}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
410 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
411 |
\begin{tikzpicture}[scale=1]
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
412 |
\draw[line width=1mm] (-0.3, 0) rectangle (1.5,2);
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
413 |
\draw[line width=1mm] (-1.8, 0) rectangle (-3.6,2);
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
414 |
\draw (4.4,1) node {Code Gen};
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
415 |
\draw (0.6,1.7) node {\small Parser};
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
416 |
\draw (-2.7,1.7) node {\small Lexer};
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
417 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
418 |
\draw[red,->,line width = 2mm] (1.7,1) -- (3.2,1);
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
419 |
\draw[red,<-,line width = 2mm] (-0.6,1) -- (-1.6,1);
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
420 |
\draw[red,<-,line width = 2mm] (-3.8,1) -- (-4.8,1);
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
421 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
422 |
\draw (-4.6,1.7) node {\small string};
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
423 |
\draw (-1.1,1.7) node {\small tokens};
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
424 |
\draw ( 2.3,1.7) node {\small AST};
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
425 |
\end{tikzpicture}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
426 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
427 |
\end{frame}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
428 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
429 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
430 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
431 |
\begin{frame}[t]
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
432 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
433 |
\tt
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
434 |
\begin{center}\large
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
435 |
\code{"if true then then 42 else +"}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
436 |
\end{center}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
437 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
438 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
439 |
\begin{tabular}{@{}l}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
440 |
KEYWORD: \\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
441 |
\hspace{5mm}{if}, {then}, {else},\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
442 |
WHITESPACE:\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
443 |
\hspace{5mm}{" "}, {$\backslash$n},\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
444 |
IDENT:\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
445 |
\hspace{5mm}LETTER $\cdot$ (LETTER + DIGIT + {\_})$^*$\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
446 |
NUM:\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
447 |
\hspace{5mm}(NONZERODIGIT $\cdot$ DIGIT$^*$) + {0}\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
448 |
OP:\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
449 |
\hspace{5mm}{+}\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
450 |
COMMENT:\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
451 |
\hspace{5mm}{$\slash$*} $\cdot$ (ALL$^*$ $\cdot$ {$\sim$(*$\slash$)} $\cdot$ ALL$^*$) $\cdot$ {*$\slash$}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
452 |
\end{tabular}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
453 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
454 |
\end{frame}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
455 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
456 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
457 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
458 |
\begin{frame}[t]
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
459 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
460 |
\tt
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
461 |
\begin{center}\large
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
462 |
\code{"if true then then 42 else +"}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
463 |
\end{center}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
464 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
465 |
\only<1>{
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
466 |
\small\begin{tabular}{l}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
467 |
KEYWORD(if),\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
468 |
WHITESPACE,\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
469 |
IDENT(true),\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
470 |
WHITESPACE,\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
471 |
KEYWORD(then),\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
472 |
WHITESPACE,\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
473 |
KEYWORD(then),\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
474 |
WHITESPACE,\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
475 |
NUM(42),\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
476 |
WHITESPACE,\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
477 |
KEYWORD(else),\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
478 |
WHITESPACE,\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
479 |
OP(+)
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
480 |
\end{tabular}}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
481 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
482 |
\only<2>{
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
483 |
\small\begin{tabular}{l}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
484 |
KEYWORD(if),\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
485 |
IDENT(true),\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
486 |
KEYWORD(then),\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
487 |
KEYWORD(then),\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
488 |
NUM(42),\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
489 |
KEYWORD(else),\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
490 |
OP(+)
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
491 |
\end{tabular}}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
492 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
493 |
\end{frame}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
494 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
495 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
496 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
497 |
\begin{frame}[c]
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
498 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
499 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
500 |
There is one small problem with the tokenizer. How should we
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
501 |
tokenize:
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
502 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
503 |
\begin{center}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
504 |
\large\code{"x-3"}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
505 |
\end{center}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
506 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
507 |
\tt
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
508 |
\begin{tabular}{@{}l}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
509 |
ID: \ldots\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
510 |
OP:\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
511 |
\hspace{5mm}\texttt{"+"}, \texttt{"-"}\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
512 |
NUM:\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
513 |
\hspace{5mm}(NONZERODIGIT $\cdot$ DIGIT$^*$) + {''0''}\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
514 |
NUMBER:\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
515 |
\hspace{5mm}NUM + (\texttt{"-"} $\cdot$ NUM)\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
516 |
\end{tabular}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
517 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
518 |
\end{frame}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
519 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
520 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
521 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
522 |
\begin{frame}[c]
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
523 |
\frametitle{POSIX: Two Rules}
|
33
|
524 |
|
38
|
525 |
\begin{itemize}
|
272
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
526 |
\item Longest match rule (``maximal munch rule''): The
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
527 |
longest initial substring matched by any regular expression is taken
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
528 |
as next token.\bigskip
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
529 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
530 |
\item Rule priority:
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
531 |
For a particular longest initial substring, the first regular
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
532 |
expression that can match determines the token.
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
533 |
\end{itemize}\bigskip\bigskip\pause
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
534 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
535 |
\small
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
536 |
\hfill most posix matchers are buggy\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
537 |
\footnotesize
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
538 |
\hfill \url{http://www.haskell.org/haskellwiki/Regex_Posix}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
539 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
540 |
%\url{http://www.technologyreview.com/tr10/?year=2011}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
541 |
%finite deterministic automata/ nondeterministic automaton
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
542 |
%\item problem with infix operations, for example i-12
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
543 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
544 |
\end{frame}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
545 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
546 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
547 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
548 |
\begin{frame}[c]
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
549 |
\frametitle{Sulzmann Matcher}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
550 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
551 |
We want to match the string \bl{$abc$} using \bl{$r_1$}:
|
38
|
552 |
|
272
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
553 |
\begin{center}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
554 |
\begin{tikzpicture}[scale=2,node distance=1.3cm,every node/.style={minimum size=8mm}]
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
555 |
\node (r1) {\bl{$r_1$}};
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
556 |
\node (r2) [right=of r1] {\bl{$r_2$}};
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
557 |
\draw[->,line width=1mm] (r1) -- (r2) node[above,midway] {\bl{$der\,a$}};\pause
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
558 |
\node (r3) [right=of r2] {\bl{$r_3$}};
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
559 |
\draw[->,line width=1mm] (r2) -- (r3) node[above,midway] {\bl{$der\,b$}};\pause
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
560 |
\node (r4) [right=of r3] {\bl{$r_4$}};
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
561 |
\draw[->,line width=1mm] (r3) -- (r4) node[above,midway] {\bl{$der\,c$}};\pause
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
562 |
\draw (r4) node[anchor=west] {\;\raisebox{3mm}{\bl{$nullable$}}};\pause
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
563 |
\node (v4) [below=of r4] {\bl{$v_4$}};
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
564 |
\draw[->,line width=1mm] (r4) -- (v4);\pause
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
565 |
\node (v3) [left=of v4] {\bl{$v_3$}};
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
566 |
\draw[->,line width=1mm] (v4) -- (v3) node[below,midway] {\bl{$inj\,c$}};\pause
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
567 |
\node (v2) [left=of v3] {\bl{$v_2$}};
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
568 |
\draw[->,line width=1mm] (v3) -- (v2) node[below,midway] {\bl{$inj\,b$}};\pause
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
569 |
\node (v1) [left=of v2] {\bl{$v_1$}};
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
570 |
\draw[->,line width=1mm] (v2) -- (v1) node[below,midway] {\bl{$inj\,a$}};\pause
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
571 |
\draw[->,line width=0.5mm] (r3) -- (v3);
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
572 |
\draw[->,line width=0.5mm] (r2) -- (v2);
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
573 |
\draw[->,line width=0.5mm] (r1) -- (v1);
|
273
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
574 |
\draw (r4) node[anchor=north west] {\;\raisebox{-8mm}{\bl{$mkeps$}}};
|
272
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
575 |
\end{tikzpicture}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
576 |
\end{center}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
577 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
578 |
\end{frame}
|
33
|
579 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
580 |
|
273
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
581 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
582 |
\begin{frame}[c]
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
583 |
\frametitle{Regexes and Values}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
584 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
585 |
Regular expressions and their corresponding values:
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
586 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
587 |
\begin{center}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
588 |
\begin{columns}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
589 |
\begin{column}{3cm}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
590 |
\begin{tabular}{@{}rrl@{}}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
591 |
\bl{$r$} & \bl{$::=$} & \bl{$\varnothing$}\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
592 |
& \bl{$\mid$} & \bl{$\epsilon$} \\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
593 |
& \bl{$\mid$} & \bl{$c$} \\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
594 |
& \bl{$\mid$} & \bl{$r_1 \cdot r_2$}\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
595 |
& \bl{$\mid$} & \bl{$r_1 + r_2$} \\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
596 |
\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
597 |
& \bl{$\mid$} & \bl{$r^*$} \\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
598 |
\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
599 |
\end{tabular}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
600 |
\end{column}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
601 |
\begin{column}{3cm}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
602 |
\begin{tabular}{@{\hspace{-7mm}}rrl@{}}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
603 |
\bl{$v$} & \bl{$::=$} & \\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
604 |
& & \bl{$Empty$} \\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
605 |
& \bl{$\mid$} & \bl{$Char(c)$} \\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
606 |
& \bl{$\mid$} & \bl{$Seq(v_1\,v_2)$}\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
607 |
& \bl{$\mid$} & \bl{$Left(v)$} \\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
608 |
& \bl{$\mid$} & \bl{$Right(v)$} \\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
609 |
& \bl{$\mid$} & \bl{$[]$} \\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
610 |
& \bl{$\mid$} & \bl{$[v_1,\ldots\,v_n]$} \\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
611 |
\end{tabular}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
612 |
\end{column}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
613 |
\end{columns}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
614 |
\end{center}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
615 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
616 |
\end{frame}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
617 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
618 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
619 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
620 |
\begin{frame}[c]
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
621 |
\frametitle{Mkeps}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
622 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
623 |
Finding a (posix) value for recognising the empty string
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
624 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
625 |
\begin{center}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
626 |
\begin{tabular}{lcl}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
627 |
\bl{$mkeps\,\epsilon$} & \bl{$\dn$} & \bl{$Empty$}\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
628 |
\bl{$mkeps\,r_1 + r_2$} & \bl{$\dn$} & \bl{if $nullable(r_1)$} \\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
629 |
& & \bl{then $Left(mkeps(r_1))$}\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
630 |
& & \bl{else $Right(mkeps(r_2))$}\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
631 |
\bl{$mkeps\,r_1 \cdot r_2$} & \bl{$\dn$} & \bl{$Seq(mkeps(r_1),mkeps(r_2))$}\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
632 |
\bl{$mkeps\,r^*$} & \bl{$\dn$} & \bl{$[]$} \\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
633 |
\end{tabular}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
634 |
\end{center}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
635 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
636 |
\end{frame}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
637 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
638 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
639 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
640 |
\begin{frame}[c]
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
641 |
\frametitle{Inject}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
642 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
643 |
Injecting (``Adding'') a character to a value\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
644 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
645 |
\begin{center}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
646 |
\begin{tabular}{l@{\hspace{1mm}}c@{\hspace{1mm}}l}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
647 |
\bl{$inj\,(c)\,c\,Empty$} & \bl{$\dn$} & \bl{$Char\,c$}\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
648 |
\bl{$inj\,(r_1 + r_2)\,c\,Left(v)$} & \bl{$\dn$} & \bl{$Left(inj\,r_1\,c\,v)$}\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
649 |
\bl{$inj\,(r_1 + r_2)\,c\,Right(v)$} & \bl{$\dn$} & \bl{$Right(inj\,r_2\,c\,v)$}\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
650 |
\bl{$inj\,(r_1 \cdot r_2)\,c\,Seq(v_1,v_2)$} & \bl{$\dn$} & \bl{$Seq(inj\,r_1\,c\,v_1,v_2)$}\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
651 |
\bl{$inj\,(r_1 \cdot r_2)\,c\,Left(Seq(v_1,v_2))$} & \bl{$\dn$} & \bl{$Seq(inj\,r_1\,c\,v_1,v_2)$}\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
652 |
\bl{$inj\,(r_1 \cdot r_2)\,c\,Right(v)$} & \bl{$\dn$} & \bl{$Seq(mkeps(r_1),inj\,r_2\,c\,v)$}\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
653 |
\bl{$inj\,(r^*)\,c\,Sequ(v,vs)$} & \bl{$\dn$} & \bl{$inj\,r\,c\,v\,::\,vs$}\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
654 |
\end{tabular}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
655 |
\end{center}\bigskip
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
656 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
657 |
\footnotesize
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
658 |
\bl{$inj$}: 1st arg $\mapsto$ a rexp; 2nd arg $\mapsto$ a character; 3rd arg $\mapsto$ a value
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
659 |
\end{frame}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
660 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
661 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
662 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
663 |
\begin{frame}[c]
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
664 |
\frametitle{Lexing}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
665 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
666 |
\begin{center}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
667 |
\begin{tabular}{l@{\hspace{1mm}}c@{\hspace{1mm}}l}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
668 |
\bl{$lex\,r\,[]$} & \bl{$\dn$} & \bl{if $nullable(r)$ then $mkeps(r)$ else $error$}\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
669 |
\bl{$lex\,r\,c::s$} & \bl{$\dn$} & \bl{$inj\,r\,c\,lex(der(c,r), s)$}\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
670 |
\end{tabular}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
671 |
\end{center}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
672 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
673 |
\footnotesize
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
674 |
\bl{$lex$}: returns a value
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
675 |
\end{frame}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
676 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
677 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
678 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
679 |
\begin{frame}[c]
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
680 |
\frametitle{Records}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
681 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
682 |
\begin{itemize}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
683 |
\item new regex: \bl{$(x:r)$}\hspace{7mm}new value: \bl{$Rec(x,v)$}\medskip\pause
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
684 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
685 |
\item \bl{$nullable(x:r) \dn nullable(r)$}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
686 |
\item \bl{$der\,c\,(x:r) \dn (x:der\,c\,r)$}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
687 |
\item \bl{$mkeps(x:r) \dn Rec(x, mkeps(r))$}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
688 |
\item \bl{$inj\,(x:r)\,c\,v \dn Rec(x, inj\,r\,c\,v)$}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
689 |
\end{itemize}\bigskip\bigskip\pause
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
690 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
691 |
\small
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
692 |
for extracting subpatterns \bl{$(z: ((x:ab) + (y:ba))$}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
693 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
694 |
\end{frame}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
695 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
696 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
697 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
698 |
\begin{frame}[c]
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
699 |
\frametitle{While Tokens}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
700 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
701 |
\begin{center}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
702 |
\begin{tabular}{rcl}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
703 |
\pcode{WHILE\_REGS} & $\dn$ & \raisebox{-1mm}{\large(}\pcode{("k" : KEYWORD)} +\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
704 |
& & \phantom{(}\pcode{("i" : ID)} +\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
705 |
& & \phantom{(}\pcode{("o" : OP)} + \\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
706 |
& & \phantom{(}\pcode{("n" : NUM)} + \\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
707 |
& & \phantom{(}\pcode{("s" : SEMI)} +\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
708 |
& & \phantom{(}\pcode{("p" : (LPAREN + RPAREN))} +\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
709 |
& & \phantom{(}\pcode{("b" : (BEGIN + END))} +\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
710 |
& & \phantom{(}\pcode{("w" : WHITESPACE)}\raisebox{-1mm}{\large)$^*$}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
711 |
\end{tabular}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
712 |
\end{center}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
713 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
714 |
\end{frame}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
715 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
716 |
|
274
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
717 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
718 |
\begin{frame}[c]
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
719 |
\frametitle{Simplification}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
720 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
721 |
\begin{itemize}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
722 |
\item If we simplify after the derivative, then we ar builing the
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
723 |
value for the simplified regular expression, but \emph{not} for the original
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
724 |
regular expression.
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
725 |
\end{itemize}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
726 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
727 |
\begin{center}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
728 |
\begin{tikzpicture}[scale=2,node distance=1.3cm,every node/.style={minimum size=8mm}]
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
729 |
\node (r1) {\bl{$r_1$}};
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
730 |
\node (r2) [right=of r1] {\bl{$r_2$}};
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
731 |
\draw[->,line width=1mm] (r1) -- (r2) node[above,midway] {\bl{$der\,a$}};
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
732 |
\node (r3) [right=of r2] {\bl{$r_3$}};
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
733 |
\draw[->,line width=1mm] (r2) -- (r3) node[above,midway] {\bl{$der\,b$}};
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
734 |
\node (r4) [right=of r3] {\bl{$r_4$}};
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
735 |
\draw[->,line width=1mm] (r3) -- (r4) node[above,midway] {\bl{$der\,c$}};
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
736 |
\draw (r4) node[anchor=west] {\;\raisebox{3mm}{\bl{$nullable$}}};
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
737 |
\node (v4) [below=of r4] {\bl{$v_4$}};
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
738 |
\draw[->,line width=1mm] (r4) -- (v4);
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
739 |
\node (v3) [left=of v4] {\bl{$v_3$}};
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
740 |
\draw[->,line width=1mm] (v4) -- (v3) node[below,midway] {\bl{$inj\,c$}};
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
741 |
\node (v2) [left=of v3] {\bl{$v_2$}};
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
742 |
\draw[->,line width=1mm] (v3) -- (v2) node[below,midway] {\bl{$inj\,b$}};
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
743 |
\node (v1) [left=of v2] {\bl{$v_1$}};
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
744 |
\draw[->,line width=1mm] (v2) -- (v1) node[below,midway] {\bl{$inj\,a$}};
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
745 |
\draw[->,line width=0.5mm] (r3) -- (v3);
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
746 |
\draw[->,line width=0.5mm] (r2) -- (v2);
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
747 |
\draw[->,line width=0.5mm] (r1) -- (v1);
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
748 |
\draw (r4) node[anchor=north west] {\;\raisebox{-8mm}{\bl{$mkeps$}}};
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
749 |
\end{tikzpicture}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
750 |
\end{center}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
751 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
752 |
\end{frame}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
753 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
754 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
755 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
756 |
\begin{frame}[c]
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
757 |
\frametitle{Rectification}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
758 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
759 |
\def\arraystretch{1.05}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
760 |
\begin{center}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
761 |
\begin{tabular}{l@{\hspace{2mm}}c@{\hspace{2mm}}l@{\hspace{5mm}}l}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
762 |
& & & \hspace{5mm}rectification \\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
763 |
& & & \hspace{5mm}functions:\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
764 |
\bl{$r \cdot \varnothing$} & $\mapsto$ & \bl{$\varnothing$} & \\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
765 |
\bl{$\varnothing \cdot r$} & $\mapsto$ & \bl{$\varnothing$} & \\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
766 |
\bl{$r \cdot \epsilon$} & $\mapsto$ & \bl{$r$} & \bl{$\lambda f_1\,f_2\,v.\, Seq(f_1\,v, f_2\,Empty)$}\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
767 |
\bl{$\epsilon \cdot r$} & $\mapsto$ & \bl{$r$} & \bl{$\lambda f_1\,f_2\,v.\, Seq(f_1\,Empty, f_2\,v)$}\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
768 |
\bl{$r + \varnothing$} & $\mapsto$ & \bl{$r$} & \bl{$\lambda f_1\,f_2\,v.\, Left(f_1\,v)$}\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
769 |
\bl{$\varnothing + r$} & $\mapsto$ & \bl{$r$} & \bl{$\lambda f_1\,f_2\,v.\, Right(f_2\,v)$}\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
770 |
\bl{$r + r$} & $\mapsto$ & \bl{$r$} & \bl{$\lambda f_1\,f_2\,v.\, Left(f_1\,v)$}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
771 |
\end{tabular}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
772 |
\end{center}\medskip\pause
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
773 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
774 |
\small
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
775 |
old \bl{$simp$} returns a rexp;\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
776 |
new \bl{$simp$} returns a rexp and a rectification~fun.
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
777 |
\end{frame}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
778 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
779 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
780 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
781 |
\begin{frame}[c]
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
782 |
\frametitle{Lexing with Simplification}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
783 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
784 |
\begin{center}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
785 |
\begin{tabular}{l@{\hspace{1mm}}c@{\hspace{1mm}}l}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
786 |
\bl{$lex\,r\,[]$} & \bl{$\dn$} & \bl{if $nullable(r)$ then $mkeps(r)$ else $error$}\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
787 |
\bl{$lex\,r\,c::s$} & \bl{$\dn$} & \bl{let $(r', frect) = simp(der(c, r))$}\smallskip\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
788 |
& & \bl{$inj\,r\,c\,(frect(lex(r', s)))$}\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
789 |
\end{tabular}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
790 |
\end{center}\bigskip
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
791 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
792 |
\begin{center}\small
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
793 |
\begin{tikzpicture}[node distance=1.1cm,every node/.style={minimum size=7mm}]
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
794 |
\node (r1) {\bl{$r_1$}};
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
795 |
\node (r2) [right=of r1] {\bl{$r_2$}};
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
796 |
\draw[->,line width=1mm] (r1) -- (r2) node[above,midway] {\bl{$der\,a$}};
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
797 |
\node (r3) [right=of r2] {\bl{$r_3$}};
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
798 |
\draw[->,line width=1mm] (r2) -- (r3) node[above,midway] {\bl{$der\,b$}};
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
799 |
\node (r4) [right=of r3] {\bl{$r_4$}};
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
800 |
\draw[->,line width=1mm] (r3) -- (r4) node[above,midway] {\bl{$der\,c$}};
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
801 |
\draw (r4) node[anchor=west] {\;\raisebox{3mm}{\bl{$nullable$}}};
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
802 |
\node (v4) [below=of r4] {\bl{$v_4$}};
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
803 |
\draw[->,line width=1mm] (r4) -- (v4);
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
804 |
\node (v3) [left=of v4] {\bl{$v_3$}};
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
805 |
\draw[->,line width=1mm] (v4) -- (v3) node[below,midway] {\bl{$inj\,c$}};
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
806 |
\node (v2) [left=of v3] {\bl{$v_2$}};
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
807 |
\draw[->,line width=1mm] (v3) -- (v2) node[below,midway] {\bl{$inj\,b$}};
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
808 |
\node (v1) [left=of v2] {\bl{$v_1$}};
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
809 |
\draw[->,line width=1mm] (v2) -- (v1) node[below,midway] {\bl{$inj\,a$}};
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
810 |
\draw[->,line width=0.5mm] (r3) -- (v3);
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
811 |
\draw[->,line width=0.5mm] (r2) -- (v2);
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
812 |
\draw[->,line width=0.5mm] (r1) -- (v1);
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
813 |
\draw (r4) node[anchor=north west] {\;\raisebox{-8mm}{\bl{$mkeps$}}};
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
814 |
\end{tikzpicture}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
815 |
\end{center}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
816 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
817 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
818 |
\end{frame}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
819 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
820 |
|
33
|
821 |
\end{document}
|
|
822 |
|
|
823 |
%%% Local Variables:
|
|
824 |
%%% mode: latex
|
|
825 |
%%% TeX-master: t
|
|
826 |
%%% End:
|
|
827 |
|