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\documentclass[dvipsnames,14pt,t]{beamer}
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\usepackage{beamerthemeplaincu}
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%%\usepackage[T1]{fontenc}
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\usepackage[latin1]{inputenc}
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\usepackage{mathpartir}
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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{plotmarks}
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\usetikzlibrary{calc}
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\usepackage{graphicx}
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\definecolor{javared}{rgb}{0.6,0,0} % for strings
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\definecolor{javagreen}{rgb}{0.25,0.5,0.35} % comments
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\definecolor{javapurple}{rgb}{0.5,0,0.35} % keywords
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\definecolor{javadocblue}{rgb}{0.25,0.35,0.75} % javadoc
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\makeatletter
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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\lst@CCPutMacro\lst@ProcessOther {"2D}{\lst@ttfamily{-{}}{-{}}}
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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\@empty\z@\@empty
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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\makeatother
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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\lstset{language=Java,
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basicstyle=\consolas,
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keywordstyle=\color{javapurple}\bfseries,
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stringstyle=\color{javagreen},
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commentstyle=\color{javagreen},
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morecomment=[s][\color{javadocblue}]{/**}{*/},
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numbers=left,
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numberstyle=\tiny\color{black},
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stepnumber=1,
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numbersep=10pt,
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tabsize=2,
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showspaces=false,
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showstringspaces=false}
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\lstdefinelanguage{scala}{
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morekeywords={abstract,case,catch,class,def,%
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do,else,extends,false,final,finally,%
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for,if,implicit,import,match,mixin,%
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new,null,object,override,package,%
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private,protected,requires,return,sealed,%
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super,this,throw,trait,true,try,%
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type,val,var,while,with,yield},
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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otherkeywords={=>,<-,<\%,<:,>:,\#,@,->},
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sensitive=true,
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morecomment=[l]{//},
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morecomment=[n]{/*}{*/},
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morestring=[b]",
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morestring=[b]',
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morestring=[b]"""
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}
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\lstset{language=Scala,
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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basicstyle=\consolas,
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keywordstyle=\color{javapurple}\bfseries,
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stringstyle=\color{javagreen},
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commentstyle=\color{javagreen},
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morecomment=[s][\color{javadocblue}]{/**}{*/},
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numbers=left,
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numberstyle=\tiny\color{black},
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stepnumber=1,
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numbersep=10pt,
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tabsize=2,
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showspaces=false,
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showstringspaces=false}
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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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\renewcommand{\slidecaption}{AFL 02, King's College London, 2.~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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Christian Urban <christian dot urban at kcl dot ac dot uk>
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% The data files, written on the first run.
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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\begin{filecontents}{re-python.data}
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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changeset
|
86 |
1 0.029
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
87 |
5 0.029
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
88 |
10 0.029
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
89 |
15 0.032
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
90 |
16 0.042
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
91 |
17 0.042
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
92 |
18 0.055
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
93 |
19 0.084
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
94 |
20 0.136
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
95 |
21 0.248
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
96 |
22 0.464
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
97 |
23 0.899
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
98 |
24 1.773
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
99 |
25 3.505
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
100 |
26 6.993
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
101 |
27 14.503
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
102 |
28 29.307
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
103 |
#29 58.886
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
104 |
\end{filecontents}
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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|
105 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
106 |
\begin{filecontents}{re-ruby.data}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
107 |
1 0.00006
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
108 |
2 0.00003
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
109 |
3 0.00001
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
110 |
4 0.00001
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
111 |
5 0.00001
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
112 |
6 0.00002
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
113 |
7 0.00002
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
114 |
8 0.00004
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
115 |
9 0.00007
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
116 |
10 0.00013
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
117 |
11 0.00026
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
118 |
12 0.00055
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
119 |
13 0.00106
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
120 |
14 0.00196
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
121 |
15 0.00378
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
122 |
16 0.00764
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
123 |
17 0.01606
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
124 |
18 0.03094
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
125 |
19 0.06508
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
126 |
20 0.12420
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
127 |
21 0.25393
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
128 |
22 0.51449
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
129 |
23 1.02174
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
130 |
24 2.05998
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
131 |
25 4.22514
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
132 |
26 8.42479
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
133 |
27 16.88678
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
134 |
28 34.79653
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
135 |
\end{filecontents}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
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|
136 |
|
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Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
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|
137 |
\begin{filecontents}{re1.data}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
138 |
1 0.00179
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
139 |
2 0.00011
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
140 |
3 0.00014
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
141 |
4 0.00026
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
142 |
5 0.00050
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
143 |
6 0.00095
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
144 |
7 0.00190
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
145 |
8 0.00287
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
146 |
9 0.00779
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
147 |
10 0.01399
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
148 |
11 0.01894
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
149 |
12 0.03666
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
150 |
13 0.07994
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
151 |
14 0.08944
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
152 |
15 0.02377
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
153 |
16 0.07392
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
154 |
17 0.22798
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
155 |
18 0.65310
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
156 |
19 2.11360
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
157 |
20 6.31606
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
158 |
21 21.46013
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
159 |
\end{filecontents}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
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|
160 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
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|
161 |
\begin{filecontents}{re2a.data}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
162 |
1 0.00227
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
163 |
5 0.00027
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
164 |
10 0.00075
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
165 |
15 0.00178
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
166 |
20 0.00102
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
167 |
25 0.00028
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
168 |
30 0.00040
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
169 |
35 0.00052
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
170 |
40 0.00075
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
171 |
45 0.00125
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
172 |
50 0.00112
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
173 |
55 0.00099
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
174 |
60 0.00113
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
175 |
65 0.00137
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
176 |
70 0.00170
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
177 |
\end{filecontents}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
178 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
179 |
\begin{filecontents}{re2b.data}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
180 |
1 0.00020
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
181 |
51 0.00080
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
182 |
101 0.00678
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
183 |
151 0.01792
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
184 |
201 0.04815
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
185 |
251 0.09648
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
186 |
301 0.23195
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
187 |
351 0.52646
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
188 |
401 0.96277
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
189 |
451 1.57726
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
190 |
501 2.00166
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
191 |
551 2.98341
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
192 |
601 4.81181
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
193 |
651 6.57054
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
194 |
701 9.73973
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
195 |
751 14.25762
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
196 |
801 14.80760
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
197 |
851 19.60958
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
198 |
901 25.43550
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
199 |
951 31.96038
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
200 |
\end{filecontents}
|
117
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
201 |
|
121
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
202 |
\begin{filecontents}{re3.data}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
203 |
1 0.001605
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
204 |
501 0.131066
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
205 |
1001 0.057885
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
206 |
1501 0.136875
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
207 |
2001 0.176238
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
208 |
2501 0.254363
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
209 |
3001 0.37262
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
210 |
3501 0.500946
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
211 |
4001 0.638384
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
212 |
4501 0.816605
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
213 |
5001 1.00491
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
214 |
5501 1.232505
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
215 |
6001 1.525672
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
216 |
6501 1.757502
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
217 |
7001 2.092784
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
218 |
7501 2.429224
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
219 |
8001 2.803037
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
220 |
8501 3.463045
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
221 |
9001 3.609
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
222 |
9501 4.081504
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
223 |
10001 4.54569
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
224 |
10501 6.17789
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
225 |
11001 6.77242
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
226 |
11501 7.95864
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
227 |
\end{filecontents}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
228 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
229 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
230 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
231 |
|
7
|
232 |
\begin{document}
|
|
233 |
|
|
234 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
235 |
\mode<presentation>{
|
|
236 |
\begin{frame}<1>[t]
|
|
237 |
\frametitle{%
|
|
238 |
\begin{tabular}{@ {}c@ {}}
|
|
239 |
\\[-3mm]
|
|
240 |
\LARGE Automata and \\[-2mm]
|
16
|
241 |
\LARGE Formal Languages (2)\\[3mm]
|
7
|
242 |
\end{tabular}}
|
|
243 |
|
16
|
244 |
%\begin{center}
|
|
245 |
%\includegraphics[scale=0.3]{pics/ante1.jpg}\hspace{5mm}
|
|
246 |
%\includegraphics[scale=0.31]{pics/ante2.jpg}\\
|
|
247 |
%\footnotesize\textcolor{gray}{Antikythera automaton, 100 BC (Archimedes?)}
|
|
248 |
%\end{center}
|
7
|
249 |
|
|
250 |
\normalsize
|
|
251 |
\begin{center}
|
|
252 |
\begin{tabular}{ll}
|
|
253 |
Email: & christian.urban at kcl.ac.uk\\
|
117
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
254 |
Office: & S1.27 (1st floor Strand Building)\\
|
16
|
255 |
Slides: & KEATS
|
7
|
256 |
\end{tabular}
|
|
257 |
\end{center}
|
|
258 |
|
|
259 |
|
|
260 |
\end{frame}}
|
|
261 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
262 |
|
|
263 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
264 |
\mode<presentation>{
|
16
|
265 |
\begin{frame}[c]
|
|
266 |
\frametitle{\begin{tabular}{c}Languages\end{tabular}}
|
|
267 |
|
|
268 |
A \alert{language} is a set of strings.\bigskip
|
|
269 |
|
117
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
270 |
A \alert{regular expression} specifies a set of strings, or language.
|
16
|
271 |
|
|
272 |
\end{frame}}
|
|
273 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
274 |
|
|
275 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
276 |
\mode<presentation>{
|
15
|
277 |
\begin{frame}[t]
|
117
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
278 |
\frametitle{\begin{tabular}{c}Strings\end{tabular}}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
279 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
280 |
Different ways of writing strings:
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
281 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
282 |
\begin{center}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
283 |
\begin{tabular}{ccc}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
284 |
\bl{\consolas"$hello$"}\quad{} & \bl{$[h, e, l, l, o]$} & \quad\bl{$h\!::\!e\!::\!l\!::\!l\!::\!o\!::\!N\!il$}\bigskip\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
285 |
\bl{\consolas ""} & \bl{$[]$} & \bl{$N$\!$il$}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
286 |
\end{tabular}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
287 |
\end{center}\pause
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
288 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
289 |
The concatenation operation on strings and sets of strings:
|
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{center}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
292 |
\begin{tabular}{l}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
293 |
\bl{{\consolas"$f\!oo$"}$\;@\;${\consolas"$bar$"}$\;=\;${\consolas"$f\!oobar$"}}\medskip\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
294 |
\bl{$A \;@\; B \dn \{ s_1 @ s_2 \mid s_1 \in A \wedge s_2 \in B\}$}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
295 |
\end{tabular}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
296 |
\end{center}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
297 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
298 |
\end{frame}}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
299 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
300 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
301 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
302 |
|
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 |
\mode<presentation>{
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
305 |
\begin{frame}[t]
|
7
|
306 |
\frametitle{\begin{tabular}{c}Regular Expressions\end{tabular}}
|
|
307 |
|
15
|
308 |
Their inductive definition:
|
|
309 |
|
|
310 |
|
117
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
311 |
\begin{textblock}{6}(2,6.5)
|
7
|
312 |
\begin{tabular}{@ {}rrl@ {\hspace{13mm}}l}
|
119
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
313 |
\bl{$r$} & \bl{$::=$} & \bl{$\varnothing$} & null\\
|
117
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
314 |
& \bl{$\mid$} & \bl{$\epsilon$} & empty string / {\consolas""} / $[]$\\
|
119
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
315 |
& \bl{$\mid$} & \bl{$c$} & character\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
316 |
& \bl{$\mid$} & \bl{$r_1 \cdot r_2$} & sequence\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
317 |
& \bl{$\mid$} & \bl{$r_1 + r_2$} & alternative / choice\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
318 |
& \bl{$\mid$} & \bl{$r^*$} & star (zero or more)\\
|
7
|
319 |
\end{tabular}
|
|
320 |
\end{textblock}
|
|
321 |
|
117
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 |
\only<2->{
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
324 |
\begin{textblock}{9}(4,0.5)
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
325 |
\begin{tikzpicture}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
326 |
\draw (0,0) node[inner sep=2mm,fill=cream, ultra thick, draw=red, rounded corners=2mm]
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
327 |
{\normalsize\color{darkgray}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
328 |
\begin{minipage}{9cm}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
329 |
\hspace{5mm}\mbox{{\lstset{language=Scala}\fontsize{8}{10}\selectfont
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
330 |
\texttt{\lstinputlisting{../progs/app51.scala}}}}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
331 |
\end{minipage}};
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
332 |
\end{tikzpicture}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
333 |
\end{textblock}}
|
16
|
334 |
|
|
335 |
\end{frame}}
|
|
336 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
337 |
|
|
338 |
|
|
339 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
340 |
\mode<presentation>{
|
7
|
341 |
\begin{frame}[c]
|
|
342 |
\frametitle{\begin{tabular}{c}The Meaning of a\\[-2mm] Regular Expression\end{tabular}}
|
|
343 |
|
|
344 |
\begin{textblock}{15}(1,4)
|
|
345 |
\begin{tabular}{@ {}rcl}
|
117
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
346 |
\bl{$L(\varnothing)$} & \bl{$\dn$} & \bl{$\varnothing$}\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
347 |
\bl{$L(\epsilon)$} & \bl{$\dn$} & \bl{$\{$""$\}$}\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
348 |
\bl{$L(c)$} & \bl{$\dn$} & \bl{$\{"c"\}$}\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
349 |
\bl{$L(r_1 + r_2)$} & \bl{$\dn$} & \bl{$L(r_1) \cup L(r_2)$}\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
350 |
\bl{$L(r_1 \cdot r_2)$} & \bl{$\dn$} & \bl{$L(r_1) \,@\, L(r_2)$}\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
351 |
\bl{$L(r^*)$} & \bl{$\dn$} & \bl{$\bigcup_{n \ge 0} L(r)^n$}\\
|
7
|
352 |
\end{tabular}\bigskip
|
|
353 |
|
117
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
354 |
\only<2->{
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
355 |
\hspace{5mm}\textcolor{blue}{$L(r)^0 \;\dn\; \{""\}$}\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
356 |
\textcolor{blue}{$L(r)^{n+1} \;\dn\; L(r) \,@\, L(r)^n$}}
|
11
|
357 |
\end{textblock}
|
7
|
358 |
|
117
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
359 |
|
16
|
360 |
|
117
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
361 |
\only<1->{
|
16
|
362 |
\begin{textblock}{6}(9,12)\small
|
|
363 |
\bl{$L$} is a function from regular expressions to sets of strings\\
|
117
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
364 |
\bl{$L$ : Rexp $\Rightarrow$ Set$[$String$]$}
|
16
|
365 |
\end{textblock}}
|
|
366 |
|
|
367 |
|
7
|
368 |
\end{frame}}
|
|
369 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
370 |
|
16
|
371 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
372 |
\mode<presentation>{
|
|
373 |
\begin{frame}[c]
|
|
374 |
|
|
375 |
\large
|
|
376 |
\begin{center}
|
117
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
377 |
What is \bl{$L(a^*)$}?
|
16
|
378 |
\end{center}
|
|
379 |
|
|
380 |
\end{frame}}
|
|
381 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
382 |
|
|
383 |
|
|
384 |
|
11
|
385 |
\newcommand{\YES}{\textcolor{gray}{yes}}
|
|
386 |
\newcommand{\NO}{\textcolor{gray}{no}}
|
|
387 |
\newcommand{\FORALLR}{\textcolor{gray}{$\forall$ r.}}
|
7
|
388 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
389 |
\mode<presentation>{
|
|
390 |
\begin{frame}[c]
|
11
|
391 |
\frametitle{\begin{tabular}{c}Reg Exp Equivalences\end{tabular}}
|
7
|
392 |
|
|
393 |
\begin{center}
|
16
|
394 |
\begin{tabular}{l@ {\hspace{7mm}}rcl@ {\hspace{7mm}}l}
|
117
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
395 |
&\bl{$(a + b) + c$} & \bl{$\equiv^?$} & \bl{$a + (b + c)$} & \onslide<2->{\YES}\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
396 |
&\bl{$a + a$} & \bl{$\equiv^?$} & \bl{$a$} & \onslide<3->{\YES}\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
397 |
&\bl{$(a \cdot b) \cdot c$} & \bl{$\equiv^?$} & \bl{$a \cdot (b \cdot c)$} & \onslide<4->{\YES}\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
398 |
&\bl{$a \cdot a$} & \bl{$\equiv^?$} & \bl{$a$} & \onslide<5->{\NO}\\
|
11
|
399 |
&\bl{$\epsilon^*$} & \bl{$\equiv^?$} & \bl{$\epsilon$} & \onslide<6->{\YES}\\
|
|
400 |
&\bl{$\varnothing^*$} & \bl{$\equiv^?$} & \bl{$\varnothing$} & \onslide<7->{\NO}\\
|
117
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
401 |
\FORALLR &\bl{$r \cdot \epsilon$} & \bl{$\equiv^?$} & \bl{$r$} & \onslide<8->{\YES}\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
402 |
\FORALLR &\bl{$r + \epsilon$} & \bl{$\equiv^?$} & \bl{$r$} & \onslide<9->{\NO}\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
403 |
\FORALLR &\bl{$r + \varnothing$} & \bl{$\equiv^?$} & \bl{$r$} & \onslide<10->{\YES}\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
404 |
\FORALLR &\bl{$r \cdot \varnothing$} & \bl{$\equiv^?$} & \bl{$r$} & \onslide<11->{\NO}\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
405 |
&\bl{$c \cdot (a + b)$} & \bl{$\equiv^?$} & \bl{$(c \cdot a) + (c \cdot b)$} & \onslide<12->{\YES}\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
406 |
&\bl{$a^*$} & \bl{$\equiv^?$} & \bl{$\epsilon + (a \cdot a^*)$} & \onslide<13->{\YES}
|
11
|
407 |
\end{tabular}
|
7
|
408 |
\end{center}
|
|
409 |
|
|
410 |
\end{frame}}
|
|
411 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
412 |
|
|
413 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
414 |
\mode<presentation>{
|
|
415 |
\begin{frame}[c]
|
119
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
416 |
\frametitle{\begin{tabular}{c}The Specification\\[-1mm] for Matching\end{tabular}}
|
11
|
417 |
|
|
418 |
\large
|
119
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
419 |
a regular expression \bl{$r$} matches a string \bl{$s$}\\ if and only if
|
11
|
420 |
|
|
421 |
\begin{center}
|
119
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
422 |
\bl{$s \in L(r)$}\\
|
11
|
423 |
\end{center}\bigskip\bigskip\pause
|
|
424 |
|
117
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
425 |
\end{frame}}
|
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 |
|
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 |
\mode<presentation>{
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
430 |
\begin{frame}[t]
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
431 |
\frametitle{\begin{tabular}{c}\bl{$(a?\{n\}) \cdot a\{n\}$}\end{tabular}}
|
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 |
\mbox{}\\[-13mm]
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
434 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
435 |
\begin{tikzpicture}[y=.2cm, x=.3cm]
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
436 |
%axis
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
437 |
\draw (0,0) -- coordinate (x axis mid) (30,0);
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
438 |
\draw (0,0) -- coordinate (y axis mid) (0,30);
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
439 |
%ticks
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
440 |
\foreach \x in {0,5,...,30}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
441 |
\draw (\x,1pt) -- (\x,-3pt)
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
442 |
node[anchor=north] {\x};
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
443 |
\foreach \y in {0,5,...,30}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
444 |
\draw (1pt,\y) -- (-3pt,\y)
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
445 |
node[anchor=east] {\y};
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
446 |
%labels
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
447 |
\node[below=0.6cm] at (x axis mid) {\bl{a}s};
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
448 |
\node[rotate=90, left=1.2cm] at (y axis mid) {secs};
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
449 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
450 |
%plots
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
451 |
\draw[color=blue] plot[mark=*, mark options={fill=white}]
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
452 |
file {re-python.data};
|
119
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
453 |
\draw[color=brown] plot[mark=pentagon*, mark options={fill=white} ]
|
117
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
454 |
file {re-ruby.data};
|
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 |
%legend
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
457 |
\begin{scope}[shift={(4,20)}]
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
458 |
\draw[color=blue] (0,0) --
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
459 |
plot[mark=*, mark options={fill=white}] (0.25,0) -- (0.5,0)
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
460 |
node[right]{\small Python};
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
461 |
\draw[yshift=-\baselineskip, color=brown] (0,0) --
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
462 |
plot[mark=pentagon*, mark options={fill=white}] (0.25,0) -- (0.5,0)
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
463 |
node[right]{\small Ruby};
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
464 |
\end{scope}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
465 |
\end{tikzpicture}
|
11
|
466 |
|
|
467 |
\end{frame}}
|
|
468 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
469 |
|
|
470 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
471 |
\mode<presentation>{
|
118
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
472 |
\begin{frame}[c]
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
473 |
\frametitle{\begin{tabular}{c}Evil Regular Expressions\end{tabular}}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
474 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
475 |
\begin{itemize}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
476 |
\item \alert{R}egular \alert{e}xpression \alert{D}enial \alert{o}f \alert{S}ervice (ReDoS)\bigskip
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
477 |
\item Evil regular expressions\medskip
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
478 |
\begin{itemize}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
479 |
\item \bl{$(a?\{n\}) \cdot a\{n\}$}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
480 |
\item \bl{$(a^+)^+$}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
481 |
\item \bl{$([a$\,-\,$z]^+)^*$}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
482 |
\item \bl{$(a + a \cdot a)^+$}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
483 |
\item \bl{$(a + a?)^+$}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
484 |
\end{itemize}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
485 |
\end{itemize}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
486 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
487 |
\end{frame}}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
488 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
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 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
491 |
\mode<presentation>{
|
11
|
492 |
\begin{frame}[t]
|
|
493 |
\frametitle{\begin{tabular}{c}A Matching Algorithm\end{tabular}}
|
|
494 |
|
117
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
495 |
\small
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
496 |
\ldots{}whether a regular expression can match the empty string:
|
11
|
497 |
\begin{center}
|
117
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
498 |
\begin{tabular}{@ {}l@ {\hspace{2mm}}c@ {\hspace{2mm}}l@ {}}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
499 |
\bl{$nullable(\varnothing)$} & \bl{$\dn$} & \bl{$f\!\/alse$}\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
500 |
\bl{$nullable(\epsilon)$} & \bl{$\dn$} & \bl{$true$}\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
501 |
\bl{$nullable (c)$} & \bl{$\dn$} & \bl{$f\!alse$}\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
502 |
\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
|
503 |
\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
|
504 |
\bl{$nullable (r^*)$} & \bl{$\dn$} & \bl{$true$} \\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
505 |
\end{tabular}
|
16
|
506 |
\end{center}
|
|
507 |
|
117
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
508 |
\only<2->{
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
509 |
\begin{textblock}{9}(3.4,10)
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
510 |
\begin{tikzpicture}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
511 |
\draw (0,0) node[inner sep=2mm,fill=cream, ultra thick, draw=red, rounded corners=2mm]
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
512 |
{\normalsize\color{darkgray}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
513 |
\begin{minipage}{9cm}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
514 |
\hspace{5mm}\mbox{{\lstset{language=Scala}\fontsize{8}{10}\selectfont
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
515 |
\texttt{\lstinputlisting{../progs/app5.scala}}}}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
516 |
\end{minipage}};
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
517 |
\end{tikzpicture}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
518 |
\end{textblock}}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
519 |
|
11
|
520 |
\end{frame}}
|
|
521 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
522 |
|
|
523 |
|
|
524 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
525 |
\mode<presentation>{
|
|
526 |
\begin{frame}[c]
|
15
|
527 |
\frametitle{\begin{tabular}{c}The Derivative of a Rexp\end{tabular}}
|
7
|
528 |
|
|
529 |
\large
|
119
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
530 |
If \bl{$r$} matches the string \bl{$c\!::\!s$}, what is a regular expression that matches \bl{$s$}?\bigskip\bigskip\bigskip\bigskip
|
7
|
531 |
|
|
532 |
\small
|
117
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
533 |
\bl{$der\,c\,r$} gives the answer
|
7
|
534 |
\end{frame}}
|
|
535 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
536 |
|
|
537 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
538 |
\mode<presentation>{
|
|
539 |
\begin{frame}[c]
|
19
|
540 |
\frametitle{\begin{tabular}{c}The Derivative of a Rexp (2)\end{tabular}}
|
7
|
541 |
|
|
542 |
\begin{center}
|
|
543 |
\begin{tabular}{@ {}l@ {\hspace{2mm}}c@ {\hspace{2mm}}l@ {\hspace{-10mm}}l@ {}}
|
117
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
544 |
\bl{$der\, c\, (\varnothing)$} & \bl{$\dn$} & \bl{$\varnothing$} & \\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
545 |
\bl{$der\, c\, (\epsilon)$} & \bl{$\dn$} & \bl{$\varnothing$} & \\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
546 |
\bl{$der\, c\, (d)$} & \bl{$\dn$} & \bl{if $c = d$ then $\epsilon$ else $\varnothing$} & \\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
547 |
\bl{$der\, c\, (r_1 + r_2)$} & \bl{$\dn$} & \bl{$der\, c\, r_1 + der\, c\, r_2$} & \\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
548 |
\bl{$der\, c\, (r_1 \cdot r_2)$} & \bl{$\dn$} & \bl{if $nullable (r_1)$}\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
549 |
& & \bl{then $(der\,c\,r_1) \cdot r_2 + der\, c\, r_2$}\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
550 |
& & \bl{else $(der\, c\, r_1) \cdot r_2$}\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
551 |
\bl{$der\, c\, (r^*)$} & \bl{$\dn$} & \bl{$(der\,c\,r) \cdot (r^*)$} &\smallskip\\\pause
|
7
|
552 |
|
119
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
553 |
\bl{$der\!s\, []\, r$} & \bl{$\dn$} & \bl{$r$} & \\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
554 |
\bl{$der\!s\, (c\!::\!s)\, r$} & \bl{$\dn$} & \bl{$der\!s\,s\,(der\,c\,r)$} & \\
|
7
|
555 |
\end{tabular}
|
|
556 |
\end{center}
|
|
557 |
|
117
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
558 |
\only<3->{
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
559 |
\begin{textblock}{10.5}(2,5)
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
560 |
\begin{tikzpicture}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
561 |
\draw (0,0) node[inner sep=2mm,fill=cream, ultra thick, draw=red, rounded corners=2mm]
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
562 |
{\normalsize\color{darkgray}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
563 |
\begin{minipage}{10.5cm}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
564 |
\hspace{5mm}\mbox{{\lstset{language=Scala}\fontsize{8}{10}\selectfont
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
565 |
\texttt{\lstinputlisting{../progs/app6.scala}}}}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
566 |
\end{minipage}};
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
567 |
\end{tikzpicture}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
568 |
\end{textblock}}
|
7
|
569 |
|
|
570 |
\end{frame}}
|
|
571 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
572 |
|
|
573 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
574 |
\mode<presentation>{
|
|
575 |
\begin{frame}[c]
|
119
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
576 |
\frametitle{\begin{tabular}{c}Examples\end{tabular}}
|
7
|
577 |
|
119
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
578 |
Given \bl{$r \dn ((a \cdot b) + b)^*$} what is
|
7
|
579 |
|
119
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
580 |
\begin{center}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
581 |
\begin{tabular}{l}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
582 |
\bl{$der\,a\,r$}\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
583 |
\bl{$der\,b\,r$}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
584 |
\end{tabular}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
585 |
\end{center}
|
7
|
586 |
|
|
587 |
|
|
588 |
\end{frame}}
|
|
589 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
590 |
|
17
|
591 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
592 |
\mode<presentation>{
|
|
593 |
\begin{frame}[t]
|
119
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
594 |
\frametitle{\begin{tabular}{c}\bl{$(a?\{n\}) \cdot a\{n\}$}\end{tabular}}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
595 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
596 |
\mbox{}\\[-13mm]
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
597 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
598 |
\begin{tikzpicture}[y=.2cm, x=.3cm]
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
599 |
%axis
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
600 |
\draw (0,0) -- coordinate (x axis mid) (30,0);
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
601 |
\draw (0,0) -- coordinate (y axis mid) (0,30);
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
602 |
%ticks
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
603 |
\foreach \x in {0,5,...,30}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
604 |
\draw (\x,1pt) -- (\x,-3pt)
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
605 |
node[anchor=north] {\x};
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
606 |
\foreach \y in {0,5,...,30}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
607 |
\draw (1pt,\y) -- (-3pt,\y)
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
608 |
node[anchor=east] {\y};
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
609 |
%labels
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
610 |
\node[below=0.6cm] at (x axis mid) {\bl{a}s};
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
611 |
\node[rotate=90, left=1.2cm] at (y axis mid) {secs};
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
612 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
613 |
%plots
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
614 |
\draw[color=blue] plot[mark=*, mark options={fill=white}]
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
615 |
file {re-python.data};
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
616 |
\draw[color=red] plot[mark=triangle*, mark options={fill=white} ]
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
617 |
file {re1.data};
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
618 |
\draw[color=brown] plot[mark=pentagon*, mark options={fill=white} ]
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
619 |
file {re-ruby.data};
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
620 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
621 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
622 |
%legend
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
623 |
\begin{scope}[shift={(4,20)}]
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
624 |
\draw[color=blue] (0,0) --
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
625 |
plot[mark=*, mark options={fill=white}] (0.25,0) -- (0.5,0)
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
626 |
node[right]{\small Python};
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
627 |
\draw[yshift=-\baselineskip, color=brown] (0,0) --
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
628 |
plot[mark=pentagon*, mark options={fill=white}] (0.25,0) -- (0.5,0)
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
629 |
node[right]{\small Ruby};
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
630 |
\draw[yshift=\baselineskip, color=red] (0,0) --
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
631 |
plot[mark=triangle*, mark options={fill=white}] (0.25,0) -- (0.5,0)
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
632 |
node[right]{\small Scala V1};
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
633 |
\end{scope}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
634 |
\end{tikzpicture}
|
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 |
\mode<presentation>{
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
641 |
\begin{frame}[t]
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
642 |
\frametitle{\begin{tabular}{c}Proofs about Rexps\end{tabular}}
|
17
|
643 |
|
|
644 |
Remember their inductive definition:\\[5cm]
|
|
645 |
|
|
646 |
\begin{textblock}{6}(5,5)
|
|
647 |
\begin{tabular}{@ {}rrl}
|
119
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
648 |
\bl{$r$} & \bl{$::=$} & \bl{$\varnothing$}\\
|
17
|
649 |
& \bl{$\mid$} & \bl{$\epsilon$} \\
|
119
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
650 |
& \bl{$\mid$} & \bl{$c$} \\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
651 |
& \bl{$\mid$} & \bl{$r_1 \cdot r_2$}\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
652 |
& \bl{$\mid$} & \bl{$r_1 + r_2$} \\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
653 |
& \bl{$\mid$} & \bl{$r^*$} \\
|
17
|
654 |
\end{tabular}
|
|
655 |
\end{textblock}
|
|
656 |
|
119
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
657 |
If we want to prove something, say a property \bl{$P(r)$}, for all regular expressions \bl{$r$} then \ldots
|
17
|
658 |
|
|
659 |
\end{frame}}
|
|
660 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
661 |
|
|
662 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
663 |
\mode<presentation>{
|
|
664 |
\begin{frame}[c]
|
|
665 |
\frametitle{\begin{tabular}{c}Proofs about Rexp (2)\end{tabular}}
|
|
666 |
|
|
667 |
\begin{itemize}
|
|
668 |
\item \bl{$P$} holds for \bl{$\varnothing$}, \bl{$\epsilon$} and \bl{c}\bigskip
|
119
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
669 |
\item \bl{$P$} holds for \bl{$r_1 + r_2$} under the assumption that \bl{$P$} already
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
670 |
holds for \bl{$r_1$} and \bl{$r_2$}.\bigskip
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
671 |
\item \bl{$P$} holds for \bl{$r_1 \cdot r_2$} under the assumption that \bl{$P$} already
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
672 |
holds for \bl{$r_1$} and \bl{$r_2$}.\bigskip
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
673 |
\item \bl{$P$} holds for \bl{$r^*$} under the assumption that \bl{$P$} already
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
674 |
holds for \bl{$r$}.
|
17
|
675 |
\end{itemize}
|
|
676 |
|
|
677 |
\end{frame}}
|
|
678 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
679 |
|
|
680 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
681 |
\mode<presentation>{
|
|
682 |
\begin{frame}[c]
|
|
683 |
\frametitle{\begin{tabular}{c}Proofs about Rexp (3)\end{tabular}}
|
|
684 |
|
|
685 |
Assume \bl{$P(r)$} is the property:
|
|
686 |
|
|
687 |
\begin{center}
|
119
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
688 |
\bl{$nullable(r)$} if and only if \bl{$"" \in L(r)$}
|
17
|
689 |
\end{center}
|
|
690 |
|
|
691 |
\end{frame}}
|
|
692 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
693 |
|
|
694 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
695 |
\mode<presentation>{
|
|
696 |
\begin{frame}[c]
|
119
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
697 |
\frametitle{\begin{tabular}{c}Proofs about Rexp (4)\end{tabular}}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
698 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
699 |
Let \bl{$Der\,c\,A$} be the set defined as
|
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 |
\bl{$Der\,c\,A \dn \{ s \;|\; c\!::\!s \in A\}$ }
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
703 |
\end{center}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
704 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
705 |
We can prove
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
706 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
707 |
\begin{center}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
708 |
\bl{$L(der\,c\,r) = Der\,c\,(L(r))$}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
709 |
\end{center}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
710 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
711 |
by induction on \bl{$r$}.
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
712 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
713 |
\end{frame}}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
714 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
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 |
|
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 |
\mode<presentation>{
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
719 |
\begin{frame}[c]
|
17
|
720 |
\frametitle{\begin{tabular}{c}Proofs about Strings\end{tabular}}
|
|
721 |
|
119
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
722 |
If we want to prove something, say a property \bl{$P(s)$}, for all strings \bl{$s$} then \ldots\bigskip
|
17
|
723 |
|
|
724 |
\begin{itemize}
|
|
725 |
\item \bl{$P$} holds for the empty string, and\medskip
|
119
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
726 |
\item \bl{$P$} holds for the string \bl{$c\!::\!s$} under the assumption that \bl{$P$}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
727 |
already holds for \bl{$s$}
|
17
|
728 |
\end{itemize}
|
|
729 |
\end{frame}}
|
|
730 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
731 |
|
19
|
732 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
733 |
\mode<presentation>{
|
|
734 |
\begin{frame}[c]
|
|
735 |
\frametitle{\begin{tabular}{c}Proofs about Strings (2)\end{tabular}}
|
|
736 |
|
119
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
737 |
We can finally prove
|
19
|
738 |
|
|
739 |
\begin{center}
|
119
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
740 |
\bl{$matcher(r, s)$} if and only if \bl{$s \in L(r)$}
|
19
|
741 |
\end{center}
|
|
742 |
|
|
743 |
|
|
744 |
\end{frame}}
|
|
745 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
17
|
746 |
|
|
747 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
748 |
\mode<presentation>{
|
119
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
749 |
\begin{frame}[t]
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
750 |
\frametitle{\begin{tabular}{c}\bl{$(a?\{n\}) \cdot a\{n\}$}\end{tabular}}
|
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 |
\mbox{}\\[-13mm]
|
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 |
\begin{tikzpicture}[y=.2cm, x=.3cm]
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
755 |
%axis
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
756 |
\draw (0,0) -- coordinate (x axis mid) (30,0);
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
757 |
\draw (0,0) -- coordinate (y axis mid) (0,30);
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
758 |
%ticks
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
759 |
\foreach \x in {0,5,...,30}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
760 |
\draw (\x,1pt) -- (\x,-3pt)
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
761 |
node[anchor=north] {\x};
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
762 |
\foreach \y in {0,5,...,30}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
763 |
\draw (1pt,\y) -- (-3pt,\y)
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
764 |
node[anchor=east] {\y};
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
765 |
%labels
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
766 |
\node[below=0.6cm] at (x axis mid) {\bl{a}s};
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
767 |
\node[rotate=90, left=1.2cm] at (y axis mid) {secs};
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
768 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
769 |
%plots
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
770 |
\draw[color=blue] plot[mark=*, mark options={fill=white}]
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
771 |
file {re-python.data};
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
772 |
\draw[color=red] plot[mark=triangle*, mark options={fill=white} ]
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
773 |
file {re1.data};
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
774 |
\draw[color=brown] plot[mark=pentagon*, mark options={fill=white} ]
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
775 |
file {re-ruby.data};
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
776 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
777 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
778 |
%legend
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
779 |
\begin{scope}[shift={(4,20)}]
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
780 |
\draw[color=blue] (0,0) --
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
781 |
plot[mark=*, mark options={fill=white}] (0.25,0) -- (0.5,0)
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
782 |
node[right]{\small Python};
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
783 |
\draw[yshift=-\baselineskip, color=brown] (0,0) --
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
784 |
plot[mark=pentagon*, mark options={fill=white}] (0.25,0) -- (0.5,0)
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
785 |
node[right]{\small Ruby};
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
786 |
\draw[yshift=\baselineskip, color=red] (0,0) --
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
787 |
plot[mark=triangle*, mark options={fill=white}] (0.25,0) -- (0.5,0)
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
788 |
node[right]{\small Scala V1};
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
789 |
\end{scope}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
790 |
\end{tikzpicture}
|
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 |
\end{frame}}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
793 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
794 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
795 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
796 |
\mode<presentation>{
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
797 |
\begin{frame}[c]
|
120
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
798 |
\frametitle{\begin{tabular}{c}A Problem\end{tabular}}
|
119
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
799 |
|
120
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
800 |
We represented the ``n-times'' \bl{$a\{n\}$} as a sequence regular expression:
|
119
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
801 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
802 |
\begin{center}
|
120
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
803 |
\begin{tabular}{rl}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
804 |
1: & \bl{$a$}\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
805 |
2: & \bl{$a\cdot a$}\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
806 |
3: & \bl{$a\cdot a\cdot a$}\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
807 |
& \ldots\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
808 |
13: & \bl{$a\cdot a\cdot a\cdot a\cdot a\cdot a\cdot a\cdot a\cdot a\cdot a\cdot a\cdot a\cdot a$}\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
809 |
& \ldots\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
810 |
20:
|
119
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
811 |
\end{tabular}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
812 |
\end{center}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
813 |
|
120
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
814 |
This problem is aggravated with \bl{$a?$} being represented as \bl{$\epsilon + a$}.
|
119
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
815 |
\end{frame}}
|
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 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
819 |
\mode<presentation>{
|
120
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
820 |
\begin{frame}[c]
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
821 |
\frametitle{\begin{tabular}{c}Solving the Problem\end{tabular}}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
822 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
823 |
What happens if we extend our regular expressions
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
824 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
825 |
\begin{center}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
826 |
\begin{tabular}{rcl}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
827 |
\bl{$r$} & \bl{$::=$} & \bl{\ldots}\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
828 |
& \bl{$\mid$} & \bl{$r\{n\}$}\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
829 |
& \bl{$\mid$} & \bl{$r?$}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
830 |
\end{tabular}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
831 |
\end{center}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
832 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
833 |
What is their meaning? What are the cases for \bl{$nullable$} and \bl{$der$}?
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
834 |
\end{frame}}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
835 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
836 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
837 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
838 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
839 |
\mode<presentation>{
|
119
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
840 |
\begin{frame}[t]
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
841 |
\frametitle{\begin{tabular}{c}\bl{$(a?\{n\}) \cdot a\{n\}$}\end{tabular}}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
842 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
843 |
\mbox{}\\[-13mm]
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
844 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
845 |
\begin{tikzpicture}[y=.2cm, x=.12cm]
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
846 |
%axis
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
847 |
\draw (0,0) -- coordinate (x axis mid) (70,0);
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
848 |
\draw (0,0) -- coordinate (y axis mid) (0,30);
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
849 |
%ticks
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
850 |
\foreach \x in {0,10,...,70}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
851 |
\draw (\x,1pt) -- (\x,-3pt)
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
852 |
node[anchor=north] {\x};
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
853 |
\foreach \y in {0,5,...,30}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
854 |
\draw (1pt,\y) -- (-3pt,\y)
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
855 |
node[anchor=east] {\y};
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
856 |
%labels
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
857 |
\node[below=0.6cm] at (x axis mid) {\bl{a}s};
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
858 |
\node[rotate=90, left=1.2cm] at (y axis mid) {secs};
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
859 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
860 |
%plots
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
861 |
\draw[color=blue] plot[mark=*, mark options={fill=white}]
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
862 |
file {re-python.data};
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
863 |
\draw[color=red] plot[mark=triangle*, mark options={fill=white} ]
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
864 |
file {re1.data};
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
865 |
\draw[color=green] plot[mark=square*, mark options={fill=white} ]
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
866 |
file {re2a.data};
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
867 |
\draw[color=brown] plot[mark=pentagon*, mark options={fill=white} ]
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
868 |
file {re-ruby.data};
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
869 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
870 |
%legend
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
871 |
\begin{scope}[shift={(4,20)}]
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
872 |
\draw[color=blue] (0,0) --
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
873 |
plot[mark=*, mark options={fill=white}] (0.25,0) -- (0.5,0)
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
874 |
node[right]{\small Python};
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
875 |
\draw[yshift=-\baselineskip, color=brown] (0,0) --
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
876 |
plot[mark=pentagon*, mark options={fill=white}] (0.25,0) -- (0.5,0)
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
877 |
node[right]{\small Ruby};
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
878 |
\draw[yshift=\baselineskip, color=red] (0,0) --
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
879 |
plot[mark=triangle*, mark options={fill=white}] (0.25,0) -- (0.5,0)
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
880 |
node[right]{\small Scala V1};
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
881 |
\draw[yshift=2\baselineskip, color=green] (0,0) --
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
882 |
plot[mark=square*, mark options={fill=white}] (0.25,0) -- (0.5,0)
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
883 |
node[right]{\small Scala V2};
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
884 |
\end{scope}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
885 |
\end{tikzpicture}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
886 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
887 |
\end{frame}}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
888 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
889 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
890 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
891 |
\mode<presentation>{
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
892 |
\begin{frame}[t]
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
893 |
\frametitle{\begin{tabular}{c}\bl{$(a?\{n\}) \cdot a\{n\}$}\end{tabular}}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
894 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
895 |
\mbox{}\\[-13mm]
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
896 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
897 |
\begin{tabular}{@ {\hspace{-5mm}}l}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
898 |
\begin{tikzpicture}[y=.2cm, x=.01cm]
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
899 |
%axis
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
900 |
\draw (0,0) -- coordinate (x axis mid) (1000,0);
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
901 |
\draw (0,0) -- coordinate (y axis mid) (0,30);
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
902 |
%ticks
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
903 |
\foreach \x in {0,100,...,1000}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
904 |
\draw (\x,1pt) -- (\x,-3pt)
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
905 |
node[anchor=north] {\x};
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
906 |
\foreach \y in {0,5,...,30}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
907 |
\draw (1pt,\y) -- (-3pt,\y)
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
908 |
node[anchor=east] {\y};
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
909 |
%labels
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
910 |
\node[below=0.6cm] at (x axis mid) {\bl{a}s};
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
911 |
\node[rotate=90, left=1.2cm] at (y axis mid) {secs};
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
912 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
913 |
%plots
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
914 |
\draw[color=blue] plot[mark=*, mark options={fill=white}]
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
915 |
file {re-python.data};
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
916 |
\draw[color=red] plot[mark=triangle*, mark options={fill=white} ]
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
917 |
file {re1.data};
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
918 |
\draw[color=green] plot[mark=square*, mark options={fill=white} ]
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
919 |
file {re2b.data};
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
920 |
\draw[color=brown] plot[mark=pentagon*, mark options={fill=white} ]
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
921 |
file {re-ruby.data};
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
922 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
923 |
%legend
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
924 |
\begin{scope}[shift={(100,20)}]
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
925 |
\draw[color=blue] (0,0) --
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
926 |
plot[mark=*, mark options={fill=white}] (0.25,0) -- (50,0)
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
927 |
node[right]{\small Python};
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
928 |
\draw[yshift=-13, color=brown] (0,0) --
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
929 |
plot[mark=pentagon*, mark options={fill=white}] (0.25,0) -- (50,0)
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
930 |
node[right]{\small Ruby};
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
931 |
\draw[yshift=13, color=red] (0,0) --
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
932 |
plot[mark=triangle*, mark options={fill=white}] (0.25,0) -- (50,0)
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
933 |
node[right]{\small Scala V1};
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
934 |
\draw[yshift=26, color=green] (0,0) --
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
935 |
plot[mark=square*, mark options={fill=white}] (0.25,0) -- (50,0)
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
936 |
node[right]{\small Scala V2};
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
937 |
\end{scope}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
938 |
\end{tikzpicture}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
939 |
\end{tabular}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
940 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
941 |
\end{frame}}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
942 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
943 |
|
121
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
944 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
945 |
\mode<presentation>{
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
946 |
\begin{frame}[c]
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
947 |
\frametitle{\begin{tabular}{c}Examples\end{tabular}}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
948 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
949 |
Recall the example of \bl{$r \dn ((a \cdot b) + b)^*$} with
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
950 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
951 |
\begin{center}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
952 |
\begin{tabular}{l}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
953 |
\bl{$der\,a\,r = ((\epsilon \cdot b) + \varnothing) \cdot r$}\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
954 |
\bl{$der\,b\,r = ((\varnothing \cdot b) + \epsilon)\cdot r$}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
955 |
\end{tabular}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
956 |
\end{center}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
957 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
958 |
What are these regular expressions equal to?
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
959 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
960 |
\end{frame}}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
961 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
962 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
963 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
964 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
965 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
966 |
\mode<presentation>{
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
967 |
\begin{frame}[t]
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
968 |
\frametitle{\begin{tabular}{c}\bl{$(a?\{n\}) \cdot a\{n\}$}\end{tabular}}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
969 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
970 |
\mbox{}\\[-9mm]
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
971 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
972 |
\begin{tabular}{@ {\hspace{-5mm}}l}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
973 |
\begin{tikzpicture}[y=.2cm, x=.0008cm]
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
974 |
%axis
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
975 |
\draw (0,0) -- coordinate (x axis mid) (12000,0);
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
976 |
\draw (0,0) -- coordinate (y axis mid) (0,30);
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
977 |
%ticks
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
978 |
\foreach \x in {0,2000,...,12000}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
979 |
\draw (\x,1pt) -- (\x,-3pt)
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
980 |
node[anchor=north] {\x};
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
981 |
\foreach \y in {0,5,...,30}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
982 |
\draw (1pt,\y) -- (-3pt,\y)
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
983 |
node[anchor=east] {\y};
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
984 |
%labels
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
985 |
\node[below=0.6cm] at (x axis mid) {\bl{a}s};
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
986 |
\node[rotate=90, left=1.2cm] at (y axis mid) {secs};
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
987 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
988 |
%plots
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
989 |
\draw[color=red] plot[mark=triangle*, mark options={fill=white} ]
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
990 |
file {re1.data};
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
991 |
\draw[color=green] plot[mark=square*, mark options={fill=white} ]
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
992 |
file {re2b.data};
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
993 |
\draw[color=black] plot[mark=square*, mark options={fill=white} ]
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
994 |
file {re3.data};
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
995 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
996 |
%legend
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
997 |
\begin{scope}[shift={(2000,20)}]
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
998 |
\draw[color=red] (0,0) --
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
999 |
plot[mark=triangle*, mark options={fill=white}] (0.25,0) -- (50,0)
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1000 |
node[right]{\small Scala V1};
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1001 |
\draw[yshift=13, color=green] (0,0) --
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1002 |
plot[mark=square*, mark options={fill=white}] (0.25,0) -- (50,0)
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1003 |
node[right]{\small Scala V2};
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1004 |
\draw[yshift=26, color=black] (0,0) --
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1005 |
plot[mark=square*, mark options={fill=white}] (0.25,0) -- (50,0)
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1006 |
node[right]{\small Scala V3};
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1007 |
\end{scope}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1008 |
\end{tikzpicture}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1009 |
\end{tabular}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1010 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1011 |
\end{frame}}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1012 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1013 |
|
119
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1014 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1015 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1016 |
\mode<presentation>{
|
17
|
1017 |
\begin{frame}[c]
|
|
1018 |
\frametitle{\begin{tabular}{c}Regular Languages\end{tabular}}
|
|
1019 |
|
121
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1020 |
A language (a set of strings) is \alert{regular} iff there exists
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1021 |
a regular expression that recognises all its strings.\bigskip\bigskip\pause
|
17
|
1022 |
|
121
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1023 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1024 |
Do you think there are languages that are {\bf not} regular?
|
17
|
1025 |
\end{frame}}
|
|
1026 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
1027 |
|
|
1028 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
1029 |
\mode<presentation>{
|
|
1030 |
\begin{frame}[c]
|
|
1031 |
\frametitle{\begin{tabular}{c}Automata\end{tabular}}
|
|
1032 |
|
|
1033 |
A deterministic finite automaton consists of:
|
|
1034 |
|
|
1035 |
\begin{itemize}
|
|
1036 |
\item a set of states
|
|
1037 |
\item one of these states is the start state
|
|
1038 |
\item some states are accepting states, and
|
|
1039 |
\item there is transition function\medskip
|
|
1040 |
|
|
1041 |
\small
|
|
1042 |
which takes a state as argument and a character and produces a new state\smallskip\\
|
|
1043 |
this function might not always be defined
|
|
1044 |
\end{itemize}
|
|
1045 |
|
|
1046 |
\end{frame}}
|
|
1047 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
1048 |
|
7
|
1049 |
|
119
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1050 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1051 |
|
7
|
1052 |
\end{document}
|
|
1053 |
|
|
1054 |
%%% Local Variables:
|
|
1055 |
%%% mode: latex
|
|
1056 |
%%% TeX-master: t
|
|
1057 |
%%% End:
|
|
1058 |
|