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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{beamerthemeplaincu}
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\usepackage[absolute,overlay]{textpos}
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\usepackage{ifthen}
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\usepackage{tikz}
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\usepackage{pgf}
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\usepackage{calc}
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\usepackage{ulem}
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\usepackage{courier}
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\usepackage{listings}
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\renewcommand{\uline}[1]{#1}
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\usetikzlibrary{arrows}
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\usetikzlibrary{automata}
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\usetikzlibrary{shapes}
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\usetikzlibrary{shadows}
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\usetikzlibrary{positioning}
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\usetikzlibrary{calc}
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\usepackage{graphicx}
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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\usepackage{pgfplots}
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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changeset
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\usepackage{fontspec}
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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changeset
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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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changeset
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\usepackage{../data}
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% beamer stuff
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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changeset
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\renewcommand{\slidecaption}{AFL 05, King's College London, 23.~October 2013}
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\newcommand{\bl}[1]{\textcolor{blue}{#1}}
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\newcommand{\dn}{\stackrel{\mbox{\scriptsize def}}{=}}% for definitions
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\begin{document}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\mode<presentation>{
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\begin{frame}<1>[t]
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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 (5)\\[3mm]
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\end{tabular}}
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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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Office: & S1.27 (1st floor Strand Building)\\
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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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\end{frame}}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\mode<presentation>{
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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{frame}[c]
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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changeset
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\frametitle{DFA Minimisation}
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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{enumerate}
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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changeset
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\item Take all pairs \bl{$(q, p)$} with \bl{$q \not= p$}
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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changeset
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\item Mark all pairs that accepting and non-accepting states
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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changeset
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\item For all unmarked pairs \bl{$(q, p)$} and all characters \bl{$c$} tests wether
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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{center}
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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changeset
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\bl{$(\delta(q, c), \delta(p,c))$}
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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changeset
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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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changeset
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are marked. If yes, then also mark \bl{$(q, p)$}.
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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changeset
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\item Repeat last step until no chance.
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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changeset
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\item All unmarked pairs can be merged.
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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changeset
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\end{enumerate}
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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changeset
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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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changeset
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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changeset
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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changeset
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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changeset
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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changeset
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\mode<presentation>{
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Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
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\begin{frame}<1-2>[c]
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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{center}
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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{tikzpicture}[>=stealth',very thick,auto,
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Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
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every state/.style={minimum size=0pt,inner sep=2pt,draw=blue!50,very thick,fill=blue!20},]
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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changeset
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\node[state,initial] (q_0) {$q_0$};
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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changeset
|
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\node[state] (q_1) [right=of q_0] {$q_1$};
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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changeset
|
85 |
\node[state] (q_2) [below right=of q_0] {$q_2$};
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Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
86 |
\node[state] (q_3) [right=of q_2] {$q_3$};
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Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
87 |
\node[state, accepting] (q_4) [right=of q_1] {$q_4$};
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Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
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\path[->] (q_0) edge node [above] {\alert{$a$}} (q_1);
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Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
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\path[->] (q_1) edge node [above] {\alert{$a$}} (q_4);
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Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
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\path[->] (q_4) edge [loop right] node {\alert{$a, b$}} ();
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Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
91 |
\path[->] (q_3) edge node [right] {\alert{$a$}} (q_4);
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Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
92 |
\path[->] (q_2) edge node [above] {\alert{$a$}} (q_3);
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Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
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\path[->] (q_1) edge node [right] {\alert{$b$}} (q_2);
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Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
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\path[->] (q_0) edge node [above] {\alert{$b$}} (q_2);
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Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
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\path[->] (q_2) edge [loop left] node {\alert{$b$}} ();
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Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
96 |
\path[->] (q_3) edge [bend left=95, looseness=1.3] node [below] {\alert{$b$}} (q_0);
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Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
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\end{tikzpicture}
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Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
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\end{center}
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Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
99 |
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Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
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\mbox{}\\[-20mm]\mbox{}
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Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
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102 |
\begin{center}
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Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
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\begin{tikzpicture}[scale=0.8,line width=0.8mm]
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Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
104 |
\draw (0,0) -- (4,0);
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Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
105 |
\draw (0,1) -- (4,1);
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Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
106 |
\draw (0,2) -- (3,2);
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Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
107 |
\draw (0,3) -- (2,3);
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Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
108 |
\draw (0,4) -- (1,4);
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Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
109 |
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Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
110 |
\draw (0,0) -- (0, 4);
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Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
111 |
\draw (1,0) -- (1, 4);
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Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
112 |
\draw (2,0) -- (2, 3);
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Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
113 |
\draw (3,0) -- (3, 2);
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Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
114 |
\draw (4,0) -- (4, 1);
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Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
115 |
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Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
116 |
\draw (0.5,-0.5) node {$q_0$};
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Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
117 |
\draw (1.5,-0.5) node {$q_1$};
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Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
118 |
\draw (2.5,-0.5) node {$q_2$};
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Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
119 |
\draw (3.5,-0.5) node {$q_3$};
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Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
120 |
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Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
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121 |
\draw (-0.5, 3.5) node {$q_1$};
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Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
122 |
\draw (-0.5, 2.5) node {$q_2$};
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Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
123 |
\draw (-0.5, 1.5) node {$q_3$};
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Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
124 |
\draw (-0.5, 0.5) node {$q_4$};
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Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
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125 |
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Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
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126 |
\draw (0.5,0.5) node {\large$\star$};
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Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
127 |
\draw (1.5,0.5) node {\large$\star$};
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Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
128 |
\draw (2.5,0.5) node {\large$\star$};
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Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
129 |
\draw (3.5,0.5) node {\large$\star$};
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Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
130 |
\end{tikzpicture}\\
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Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
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131 |
\end{center}
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132 |
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133 |
\end{frame}}
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134 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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135 |
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\mode<presentation>{
|
147
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
138 |
\begin{frame}<1-2>[c]
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44
|
139 |
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147
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
140 |
\begin{center}
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Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
141 |
\begin{tabular}{@{\hspace{-8mm}}cc@{}}
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Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
142 |
\begin{tikzpicture}[>=stealth',very thick,auto,
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Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
143 |
every state/.style={minimum size=0pt,inner sep=2pt,draw=blue!50,very thick,fill=blue!20},]
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Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
144 |
\node[state,initial] (q_0) {$q_0$};
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Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
145 |
\node[state] (q_1) [right=of q_0] {$q_1$};
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Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
146 |
\node[state] (q_2) [below right=of q_0] {$q_2$};
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Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
147 |
\node[state] (q_3) [right=of q_2] {$q_3$};
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Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
148 |
\node[state, accepting] (q_4) [right=of q_1] {$q_4$};
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Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
149 |
\path[->] (q_0) edge node [above] {\alert{$a$}} (q_1);
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Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
150 |
\path[->] (q_1) edge node [above] {\alert{$a$}} (q_4);
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Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
151 |
\path[->] (q_4) edge [loop right] node {\alert{$a, b$}} ();
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Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
152 |
\path[->] (q_3) edge node [right] {\alert{$a$}} (q_4);
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Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
153 |
\path[->] (q_2) edge node [above] {\alert{$a$}} (q_3);
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Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
154 |
\path[->] (q_1) edge node [right] {\alert{$b$}} (q_2);
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Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
155 |
\path[->] (q_0) edge node [above] {\alert{$b$}} (q_2);
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Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
156 |
\path[->] (q_2) edge [loop left] node {\alert{$b$}} ();
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Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
157 |
\path[->] (q_3) edge [bend left=95, looseness=1.3] node [below] {\alert{$b$}} (q_0);
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Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
158 |
\end{tikzpicture}
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Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
159 |
&
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Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
160 |
\raisebox{9mm}{\begin{tikzpicture}[scale=0.6,line width=0.8mm]
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
161 |
\draw (0,0) -- (4,0);
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
162 |
\draw (0,1) -- (4,1);
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
163 |
\draw (0,2) -- (3,2);
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
164 |
\draw (0,3) -- (2,3);
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
165 |
\draw (0,4) -- (1,4);
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
166 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
167 |
\draw (0,0) -- (0, 4);
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
168 |
\draw (1,0) -- (1, 4);
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
169 |
\draw (2,0) -- (2, 3);
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
170 |
\draw (3,0) -- (3, 2);
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Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
171 |
\draw (4,0) -- (4, 1);
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
172 |
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Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
173 |
\draw (0.5,-0.5) node {$q_0$};
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Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
174 |
\draw (1.5,-0.5) node {$q_1$};
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
175 |
\draw (2.5,-0.5) node {$q_2$};
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
176 |
\draw (3.5,-0.5) node {$q_3$};
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
177 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
178 |
\draw (-0.5, 3.5) node {$q_1$};
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
179 |
\draw (-0.5, 2.5) node {$q_2$};
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
180 |
\draw (-0.5, 1.5) node {$q_3$};
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
181 |
\draw (-0.5, 0.5) node {$q_4$};
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
182 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
183 |
\draw (0.5,0.5) node {\large$\star$};
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
184 |
\draw (1.5,0.5) node {\large$\star$};
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
185 |
\draw (2.5,0.5) node {\large$\star$};
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
186 |
\draw (3.5,0.5) node {\large$\star$};
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
187 |
\draw (0.5,1.5) node {\large$\star$};
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
188 |
\draw (2.5,1.5) node {\large$\star$};
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
189 |
\draw (0.5,3.5) node {\large$\star$};
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
190 |
\draw (1.5,2.5) node {\large$\star$};
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
191 |
\end{tikzpicture}}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
192 |
\end{tabular}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
193 |
\end{center}
|
|
44
|
194 |
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|
195 |
|
147
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
196 |
\mbox{}\\[-20mm]\mbox{}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
197 |
|
|
44
|
198 |
\begin{center}
|
147
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
199 |
\begin{tikzpicture}[>=stealth',very thick,auto,
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
200 |
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
|
201 |
\node[state,initial] (q_02) {$q_{0, 2}$};
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
202 |
\node[state] (q_13) [right=of q_02] {$q_{1, 3}$};
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
203 |
\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
|
204 |
\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
|
205 |
\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
|
206 |
\path[->] (q_02) edge [loop below] node {\alert{$b$}} ();
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
207 |
\path[->] (q_13) edge node [above] {\alert{$a$}} (q_4);
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
208 |
\path[->] (q_4) edge [loop above] node {\alert{$a, b$}} ();
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
209 |
\end{tikzpicture}\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
210 |
minimal automaton
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
211 |
\end{center}
|
|
44
|
212 |
|
|
|
213 |
\end{frame}}
|
|
|
214 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
|
215 |
|
147
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
216 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
217 |
|
|
44
|
218 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
|
219 |
\mode<presentation>{
|
|
|
220 |
\begin{frame}[c]
|
|
|
221 |
|
147
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
222 |
\begin{center}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
223 |
\begin{tikzpicture}[>=stealth',very thick,auto,
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
224 |
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
|
225 |
\only<1>{\node[state,initial] (q_0) {$q_0$};}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
226 |
\only<2->{\node[state,accepting] (q_0) {$q_0$};}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
227 |
\node[state] (q_1) [right=of q_0] {$q_1$};
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
228 |
\node[state] (q_2) [below right=of q_0] {$q_2$};
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
229 |
\node[state] (q_3) [right=of q_2] {$q_3$};
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
230 |
\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
|
231 |
\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
|
232 |
\only<1-2>{
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
233 |
\path[->] (q_0) edge node [above] {\alert{$a$}} (q_1);
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
234 |
\path[->] (q_1) edge node [above] {\alert{$a$}} (q_4);
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
235 |
\path[->] (q_4) edge [loop above] node {\alert{$a, b$}} ();
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
236 |
\path[->] (q_3) edge node [right] {\alert{$a$}} (q_4);
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
237 |
\path[->] (q_2) edge node [above] {\alert{$a$}} (q_3);
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
238 |
\path[->] (q_1) edge node [right] {\alert{$b$}} (q_2);
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
239 |
\path[->] (q_0) edge node [above] {\alert{$b$}} (q_2);
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
240 |
\path[->] (q_2) edge [loop left] node {\alert{$b$}} ();
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
241 |
\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
|
242 |
\only<3->{
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
243 |
\path[<-] (q_0) edge node [above] {\alert{$a$}} (q_1);
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
244 |
\path[<-] (q_1) edge node [above] {\alert{$a$}} (q_4);
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
245 |
\path[<-] (q_4) edge [loop above] node {\alert{$a, b$}} ();
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
246 |
\path[<-] (q_3) edge node [right] {\alert{$a$}} (q_4);
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
247 |
\path[<-] (q_2) edge node [above] {\alert{$a$}} (q_3);
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
248 |
\path[<-] (q_1) edge node [right] {\alert{$b$}} (q_2);
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
249 |
\path[<-] (q_0) edge node [above] {\alert{$b$}} (q_2);
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
250 |
\path[<-] (q_2) edge [loop left] node {\alert{$b$}} ();
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
251 |
\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
|
252 |
\end{tikzpicture}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
253 |
\end{center}
|
|
44
|
254 |
|
|
|
255 |
\begin{itemize}
|
147
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
256 |
\item<2-> exchange initial / accepting states
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
257 |
\item<3-> reverse all edges
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
258 |
\item<4-> subset construction $\Rightarrow$ DFA
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
259 |
\item<5-> repeat once more \onslide<6->{$\Rightarrow$ minimal DFA}
|
|
44
|
260 |
|
|
|
261 |
\end{itemize}
|
|
|
262 |
|
|
|
263 |
\end{frame}}
|
|
|
264 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
|
265 |
|
|
|
266 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
|
267 |
\mode<presentation>{
|
|
|
268 |
\begin{frame}[c]
|
|
|
269 |
|
153
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
270 |
\mbox{\lstinputlisting[language=while]{../progs/fib.while}}
|
|
44
|
271 |
|
|
|
272 |
\end{frame}}
|
|
|
273 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
|
274 |
|
|
|
275 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
|
276 |
\mode<presentation>{
|
|
|
277 |
\begin{frame}[c]
|
|
|
278 |
|
153
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
279 |
\mbox{\lstinputlisting[language=while]{../progs/collatz.while}}
|
|
44
|
280 |
|
|
|
281 |
\end{frame}}
|
|
|
282 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
|
283 |
|
|
46
|
284 |
|
148
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
285 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
286 |
\mode<presentation>{
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
287 |
\begin{frame}[c]
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
288 |
|
157
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
289 |
\mbox{\lstinputlisting[language=while]{../progs/collatz.while}}
|
148
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
290 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
291 |
\begin{textblock}{6}(10,2)
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
292 |
\begin{tikzpicture}[scale=0.46]
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
293 |
\begin{axis}[axis x line=bottom, axis y line=left, ylabel=secs,
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
294 |
xlabel=n,
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
295 |
enlargelimits=0.05,
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
296 |
ybar interval=0.7, legend style=small]
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
297 |
\addplot file {interpreted2.data};
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
298 |
\addplot file {compiled2.data};
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
299 |
%\legend{interpreted, compiled}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
300 |
\end{axis}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
301 |
\end{tikzpicture}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
302 |
\end{textblock}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
303 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
304 |
\end{frame}}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
305 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
150
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
306 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
307 |
\mode<presentation>{
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
308 |
\begin{frame}[c]
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
309 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
310 |
\begin{tikzpicture}[scale=1]
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
311 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
312 |
\draw[line width=1mm] (-.3, 0) rectangle (1.5,2);
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
313 |
\draw (4.2,1) node {Code Gen};
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
314 |
\draw (0.6,1.7) node {\footnotesize Parser};
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
315 |
\draw (-2.7,1.7) node {\footnotesize Lexer};
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
316 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
317 |
\draw[line width=1mm] (-1.8, 0) rectangle (-3.6,2);
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
318 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
319 |
\draw[white] (1.7,1) node (X) {};
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
320 |
\draw[white] (3.2,1) node (Y) {};
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
321 |
\draw[red, ->, line width = 2mm] (X) -- (Y);
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
322 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
323 |
\draw[red, <-, line width = 2mm] (-0.6,1) -- (-1.6,1);
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
324 |
\draw[red, <-, line width = 2mm] (-3.8,1) -- (-4.8,1);
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
325 |
\end{tikzpicture}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
326 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
327 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
328 |
\end{frame}}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
329 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
148
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
330 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
331 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
332 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
333 |
\mode<presentation>{
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
334 |
\begin{frame}[t]
|
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 |
\consolas
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
337 |
\begin{center}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
338 |
"if true then then 42 else +"
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
339 |
\end{center}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
340 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
341 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
342 |
\begin{tabular}{@{}l}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
343 |
KEYWORD: \\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
344 |
\hspace{5mm}{if}, {then}, {else},\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
345 |
WHITESPACE:\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
346 |
\hspace{5mm}{" "}, {$\backslash$n},\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
347 |
IDENT:\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
348 |
\hspace{5mm}LETTER $\cdot$ (LETTER + DIGIT + {\_})$^*$\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
349 |
NUM:\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
350 |
\hspace{5mm}(NONZERODIGIT $\cdot$ DIGIT$^*$) + {0}\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
351 |
OP:\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
352 |
\hspace{5mm}{+}\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
353 |
COMMENT:\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
354 |
\hspace{5mm}{$\slash$*} $\cdot$ (ALL$^*$ $\cdot$ {*$\slash$} $\cdot$ ALL$^*$) $\cdot$ {*$\slash$}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
355 |
\end{tabular}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
356 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
357 |
\end{frame}}
|
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 |
\mode<presentation>{
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
362 |
\begin{frame}[t]
|
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 |
\consolas
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
365 |
\begin{center}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
366 |
"if true then then 42 else +"
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
367 |
\end{center}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
368 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
369 |
\only<1>{
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
370 |
\small\begin{tabular}{l}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
371 |
KEYWORD(if),\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
372 |
WHITESPACE,\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
373 |
IDENT(true),\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
374 |
WHITESPACE,\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
375 |
KEYWORD(then),\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
376 |
WHITESPACE,\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
377 |
KEYWORD(then),\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
378 |
WHITESPACE,\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
379 |
NUM(42),\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
380 |
WHITESPACE,\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
381 |
KEYWORD(else),\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
382 |
WHITESPACE,\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
383 |
OP(+)
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
384 |
\end{tabular}}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
385 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
386 |
\only<2>{
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
387 |
\small\begin{tabular}{l}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
388 |
KEYWORD(if),\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
389 |
IDENT(true),\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
390 |
KEYWORD(then),\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
391 |
KEYWORD(then),\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
392 |
NUM(42),\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
393 |
KEYWORD(else),\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
394 |
OP(+)
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
395 |
\end{tabular}}
|
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 |
\end{frame}}
|
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 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
400 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
401 |
\mode<presentation>{
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
402 |
\begin{frame}[c]
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
403 |
|
150
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
404 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
405 |
There is one small problem with the tokenizer. How should we
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
406 |
tokenize:
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
407 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
408 |
\begin{center}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
409 |
{\consolas "x - 3"}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
410 |
\end{center}
|
149
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
411 |
|
150
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
412 |
\consolas
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
413 |
\begin{tabular}{@{}l}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
414 |
OP:\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
415 |
\hspace{5mm}\texttt{"+"}, \texttt{"-"}\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
416 |
NUM:\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
417 |
\hspace{5mm}(NONZERODIGIT $\cdot$ DIGIT$^*$) + {''0''}\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
418 |
NUMBER:\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
419 |
\hspace{5mm}NUM + (\texttt{"-"} $\cdot$ NUM)\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
420 |
\end{tabular}
|
149
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
421 |
|
148
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
422 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
423 |
\end{frame}}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
424 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
425 |
|
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 |
\mode<presentation>{
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
428 |
\begin{frame}[c]
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
429 |
\frametitle{\begin{tabular}{c}Two Rules\end{tabular}}
|
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{itemize}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
432 |
\item Longest match rule (``maximal munch rule''): The
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
433 |
longest initial substring matched by any regular expression is taken
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
434 |
as next token.\bigskip
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
435 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
436 |
\item Rule priority:
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
437 |
For a particular longest initial substring, the first regular
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
438 |
expression that can match determines the token.
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
439 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
440 |
\end{itemize}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
441 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
442 |
%\url{http://www.technologyreview.com/tr10/?year=2011}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
443 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
444 |
%finite deterministic automata/ nondeterministic automaton
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
445 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
446 |
%\item problem with infix operations, for example i-12
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
447 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
448 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
449 |
\end{frame}}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
450 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
149
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
451 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
452 |
\mode<presentation>{
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
453 |
\begin{frame}[t]
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
454 |
\frametitle{\begin{tabular}{c}Nullable\end{tabular}}
|
|
46
|
455 |
|
149
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
456 |
\small
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
457 |
\ldots{}whether a regular expression can match the empty string:
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
458 |
\begin{center}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
459 |
\begin{tabular}{@ {}l@ {\hspace{2mm}}c@ {\hspace{2mm}}l@ {}}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
460 |
\bl{$nullable(\varnothing)$} & \bl{$\dn$} & \bl{$f\!\/alse$}\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
461 |
\bl{$nullable(\epsilon)$} & \bl{$\dn$} & \bl{$true$}\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
462 |
\bl{$nullable (c)$} & \bl{$\dn$} & \bl{$f\!alse$}\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
463 |
\bl{$nullable (r_1 + r_2)$} & \bl{$\dn$} & \bl{$nullable(r_1) \vee nullable(r_2)$} \\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
464 |
\bl{$nullable (r_1 \cdot r_2)$} & \bl{$\dn$} & \bl{$nullable(r_1) \wedge nullable(r_2)$} \\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
465 |
\bl{$nullable (r^*)$} & \bl{$\dn$} & \bl{$true$} \\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
466 |
\end{tabular}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
467 |
\end{center}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
468 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
469 |
\end{frame}}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
470 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
471 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
472 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
473 |
\mode<presentation>{
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
474 |
\begin{frame}[c]
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
475 |
\frametitle{\begin{tabular}{c}Zeroable\end{tabular}}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
476 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
477 |
\small
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
478 |
\ldots{}whether a regular expression can match nothing:
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
479 |
\begin{center}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
480 |
\begin{tabular}{@ {}l@ {\hspace{2mm}}c@ {\hspace{2mm}}l@ {}}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
481 |
\bl{$zeroable(\varnothing)$} & \bl{$\dn$} & \bl{$true$}\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
482 |
\bl{$zeroable(\epsilon)$} & \bl{$\dn$} & \bl{$f\!alse$}\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
483 |
\bl{$zeroable (c)$} & \bl{$\dn$} & \bl{$f\!alse$}\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
484 |
\bl{$zeroable (r_1 + r_2)$} & \bl{$\dn$} & \bl{$zeroable(r_1) \wedge zeroable(r_2)$} \\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
485 |
\bl{$zeroable (r_1 \cdot r_2)$} & \bl{$\dn$} & \bl{$zeroable(r_1) \vee zeroable(r_2)$} \\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
486 |
\bl{$zeroable (r^*)$} & \bl{$\dn$} & \bl{$f\!alse$} \\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
487 |
\end{tabular}
|
150
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
488 |
\end{center}\bigskip\pause
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
489 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
490 |
\begin{center}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
491 |
\bl{$zeroable(r) \Leftrightarrow L(r) = \varnothing$}
|
149
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
492 |
\end{center}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
493 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
494 |
\end{frame}}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
495 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
46
|
496 |
|
150
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
497 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
498 |
\mode<presentation>{
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
499 |
\begin{frame}[c]
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
500 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
501 |
\begin{itemize}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
502 |
\item The star-case in our proof about the matcher needs the following lemma
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
503 |
\begin{center}
|
151
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
504 |
\bl{$Der\,c\,A^* = (Der\,c\,A)\,@\, A^*$}
|
150
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 |
\end{itemize}\bigskip\bigskip
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
507 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
508 |
\begin{itemize}
|
151
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
509 |
\item \bl{$A^* = \{""\} \cup A\,@\,A^*$}
|
150
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
510 |
\item If \bl{\texttt{""} $\in A$}, then\\ \bl{$Der\,c\,(A @ B) = (Der\,c\,A) @ B \cup (Der\,c\,B)$}\medskip
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
511 |
\item If \bl{\texttt{""} $\not\in A$}, then\\ \bl{$Der\,c\,(A @ B) = (Der\,c\,A) @ B$}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
512 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
513 |
\end{itemize}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
514 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
515 |
\end{frame}}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
516 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
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 |
|
|
44
|
519 |
\end{document}
|
|
|
520 |
|
|
|
521 |
%%% Local Variables:
|
|
|
522 |
%%% mode: latex
|
|
|
523 |
%%% TeX-master: t
|
|
|
524 |
%%% End:
|
|
|
525 |
|