86
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
1 |
\documentclass[dvipsnames,14pt,t]{beamer}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
2 |
\usepackage{beamerthemeplainculight}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
3 |
\usepackage[T1]{fontenc}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
4 |
\usepackage[latin1]{inputenc}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
5 |
\usepackage{mathpartir}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
6 |
\usepackage[absolute,overlay]{textpos}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
7 |
\usepackage{ifthen}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
8 |
\usepackage{tikz}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
9 |
\usepackage{pgf}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
10 |
\usepackage{calc}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
11 |
\usepackage{ulem}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
12 |
\usepackage{courier}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
13 |
\usepackage{listings}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
14 |
\renewcommand{\uline}[1]{#1}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
15 |
\usetikzlibrary{arrows}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
16 |
\usetikzlibrary{automata}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
17 |
\usetikzlibrary{shapes}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
18 |
\usetikzlibrary{shadows}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
19 |
\usetikzlibrary{positioning}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
20 |
\usetikzlibrary{calc}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
21 |
\usetikzlibrary{plotmarks}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
22 |
\usepackage{graphicx}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
23 |
\usepackage{pgfplots}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
24 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
25 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
26 |
\definecolor{javared}{rgb}{0.6,0,0} % for strings
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
27 |
\definecolor{javagreen}{rgb}{0.25,0.5,0.35} % comments
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
28 |
\definecolor{javapurple}{rgb}{0.5,0,0.35} % keywords
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
29 |
\definecolor{javadocblue}{rgb}{0.25,0.35,0.75} % javadoc
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
30 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
31 |
\lstset{language=Java,
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
32 |
basicstyle=\ttfamily,
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
33 |
keywordstyle=\color{javapurple}\bfseries,
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
34 |
stringstyle=\color{javagreen},
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
35 |
commentstyle=\color{javagreen},
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
36 |
morecomment=[s][\color{javadocblue}]{/**}{*/},
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
37 |
numbers=left,
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
38 |
numberstyle=\tiny\color{black},
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
39 |
stepnumber=1,
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
40 |
numbersep=10pt,
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
41 |
tabsize=2,
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
42 |
showspaces=false,
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
43 |
showstringspaces=false}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
44 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
45 |
\lstdefinelanguage{scala}{
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
46 |
morekeywords={abstract,case,catch,class,def,%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
47 |
do,else,extends,false,final,finally,%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
48 |
for,if,implicit,import,match,mixin,%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
49 |
new,null,object,override,package,%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
50 |
private,protected,requires,return,sealed,%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
51 |
super,this,throw,trait,true,try,%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
52 |
type,val,var,while,with,yield},
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
53 |
otherkeywords={=>,<-,<\%,<:,>:,\#,@},
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
54 |
sensitive=true,
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
55 |
morecomment=[l]{//},
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
56 |
morecomment=[n]{/*}{*/},
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
57 |
morestring=[b]",
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
58 |
morestring=[b]',
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
59 |
morestring=[b]"""
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
60 |
}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
61 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
62 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
63 |
\lstset{language=Scala,
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
64 |
basicstyle=\ttfamily,
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
65 |
keywordstyle=\color{javapurple}\bfseries,
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
66 |
stringstyle=\color{javagreen},
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
67 |
commentstyle=\color{javagreen},
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
68 |
morecomment=[s][\color{javadocblue}]{/**}{*/},
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
69 |
numbers=left,
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
70 |
numberstyle=\tiny\color{black},
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
71 |
stepnumber=1,
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
72 |
numbersep=10pt,
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
73 |
tabsize=2,
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
74 |
showspaces=false,
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
75 |
showstringspaces=false}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
76 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
77 |
\lstdefinelanguage{while}{
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
78 |
morekeywords={if,then,else,while,do,true,false,write},
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
79 |
otherkeywords={=,!=,:=,<,>,;},
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
80 |
sensitive=true,
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
81 |
morecomment=[n]{/*}{*/},
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
82 |
}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
83 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
84 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
85 |
\lstset{language=While,
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
86 |
basicstyle=\ttfamily,
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
87 |
keywordstyle=\color{javapurple}\bfseries,
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
88 |
stringstyle=\color{javagreen},
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
89 |
commentstyle=\color{javagreen},
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
90 |
morecomment=[s][\color{javadocblue}]{/**}{*/},
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
91 |
numbers=left,
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
92 |
numberstyle=\tiny\color{black},
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
93 |
stepnumber=1,
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
94 |
numbersep=10pt,
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
95 |
tabsize=2,
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
96 |
showspaces=false,
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
97 |
showstringspaces=false}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
98 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
99 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
100 |
% beamer stuff
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
101 |
\renewcommand{\slidecaption}{AFL 10, King's College London, 5.~December 2012}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
102 |
\newcommand{\bl}[1]{\textcolor{blue}{#1}}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
103 |
\newcommand{\dn}{\stackrel{\mbox{\scriptsize def}}{=}}% for definitions
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
104 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
105 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
106 |
% The data files, written on the first run.
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
107 |
\begin{filecontents}{compiled.data}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
108 |
%1 0.234146
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
109 |
%5000 0.227539
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
110 |
%10000 0.280748
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
111 |
50000 1.087897
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
112 |
100000 3.713165
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
113 |
250000 21.6624545
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
114 |
500000 85.872613
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
115 |
750000 203.6408015
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
116 |
1000000 345.736574
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
117 |
\end{filecontents}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
118 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
119 |
\begin{filecontents}{interpreted.data}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
120 |
%1 0.00503
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
121 |
200 1.005863
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
122 |
400 7.8296765
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
123 |
500 15.43106
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
124 |
600 27.2321885
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
125 |
800 65.249271
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
126 |
1000 135.4493445
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
127 |
1200 232.134097
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
128 |
1400 382.527227
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
129 |
\end{filecontents}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
130 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
131 |
\begin{filecontents}{interpreted2.data}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
132 |
%1 0.00503
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
133 |
200 1.005863
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
134 |
400 7.8296765
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
135 |
600 27.2321885
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
136 |
800 65.249271
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
137 |
1000 135.4493445
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
138 |
1200 232.134097
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
139 |
1400 382.527227
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
140 |
\end{filecontents}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
141 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
142 |
\begin{filecontents}{compiled2.data}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
143 |
200 0.222058
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
144 |
400 0.215204
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
145 |
600 0.202031
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
146 |
800 0.21986
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
147 |
1000 0.205934
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
148 |
1200 0.1981615
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
149 |
1400 0.207116
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
150 |
\end{filecontents}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
151 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
152 |
\begin{document}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
153 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
154 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
155 |
\mode<presentation>{
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
156 |
\begin{frame}<1>[t]
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
157 |
\frametitle{%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
158 |
\begin{tabular}{@ {}c@ {}}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
159 |
\\[-3mm]
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
160 |
\LARGE Automata and \\[-2mm]
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
161 |
\LARGE Formal Languages (10)\\[3mm]
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
162 |
\end{tabular}}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
163 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
164 |
\normalsize
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
165 |
\begin{center}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
166 |
\begin{tabular}{ll}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
167 |
Email: & christian.urban at kcl.ac.uk\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
168 |
Of$\!$fice: & S1.27 (1st floor Strand Building)\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
169 |
Slides: & KEATS (also home work is there)\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
170 |
\end{tabular}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
171 |
\end{center}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
172 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
173 |
\end{frame}}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
174 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
175 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
176 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
177 |
\mode<presentation>{
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
178 |
\begin{frame}[c]
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
179 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
180 |
\Large\bf
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
181 |
There are more problems, than there are programs.\bigskip\bigskip\pause\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
182 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
183 |
There must be a problem for which there is no program.
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
184 |
\end{frame}}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
185 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
186 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
187 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
188 |
\mode<presentation>{
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
189 |
\begin{frame}[c]
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
190 |
\frametitle{Revision: Proofs}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
191 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
192 |
\begin{center}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
193 |
\includegraphics[scale=0.4]{river-stones.jpg}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
194 |
\end{center}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
195 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
196 |
\end{frame}}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
197 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
198 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
199 |
\mode<presentation>{
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
200 |
\begin{frame}[c]
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
201 |
\frametitle{Subsets}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
202 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
203 |
\Large
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
204 |
\bl{$A \subseteq B$}\bigskip\bigskip\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
205 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
206 |
\bl{$\forall e.\; e \in A \Rightarrow e \in B$}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
207 |
\end{frame}}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
208 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
209 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
210 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
211 |
\mode<presentation>{
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
212 |
\begin{frame}[c]
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
213 |
\frametitle{Subsets}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
214 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
215 |
\Large
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
216 |
\bl{$A \subseteq B$} and \bl{$B \subseteq A$}\bigskip
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
217 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
218 |
then \bl{$A = B$}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
219 |
\end{frame}}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
220 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
221 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
222 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
223 |
\mode<presentation>{
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
224 |
\begin{frame}[c]
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
225 |
\frametitle{Injective Function}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
226 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
227 |
\Large
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
228 |
\bl{f} is an injective function iff \bigskip
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
229 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
230 |
\bl{$\forall x y.\; f(x) = f(y) \Rightarrow x = y$}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
231 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
232 |
\end{frame}}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
233 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
234 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
235 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
236 |
\mode<presentation>{
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
237 |
\begin{frame}[c]
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
238 |
\frametitle{Cardinality}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
239 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
240 |
\Large
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
241 |
\bl{$|A|$} $\dn$ ``how many elements''\bigskip\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
242 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
243 |
\bl{$A \subseteq B \Rightarrow |A| \leq |B|$}\bigskip\\\pause
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
244 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
245 |
if there is an injective function \bl{$f: A \rightarrow B$} then \bl{$|A| \leq |B|$}\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
246 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
247 |
\end{frame}}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
248 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
249 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
250 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
251 |
\mode<presentation>{
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
252 |
\begin{frame}[c]
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
253 |
\frametitle{Natural Numbers}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
254 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
255 |
\Large
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
256 |
\bl{$\mathbb{N}$} \bl{$\dn$} \bl{$\{0, 1, 2, 3, .......\}$}\bigskip\pause
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
257 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
258 |
\bl{$A$} is \alert{countable} iff \bl{$|A| \leq |\mathbb{N}|$}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
259 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
260 |
\end{frame}}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
261 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
262 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
263 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
264 |
\mode<presentation>{
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
265 |
\begin{frame}[c]
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
266 |
\frametitle{First Question}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
267 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
268 |
\Large
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
269 |
\bl{$|\mathbb{N} - \{0\}| \;\;\;\alert{?}\;\;\; |\mathbb{N}| $}\bigskip\bigskip
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
270 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
271 |
\normalsize
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
272 |
\bl{$\geq$} or \bl{$\leq$} or \bl{$=$}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
273 |
\end{frame}}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
274 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
275 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
276 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
277 |
\mode<presentation>{
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
278 |
\begin{frame}[c]
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
279 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
280 |
\Large
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
281 |
\bl{$|\mathbb{N} - \{0, 1\}| \;\;\;\alert{?}\;\;\; |\mathbb{N}| $}\bigskip\pause
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
282 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
283 |
\bl{$|\mathbb{N} - \mathbb{O}| \;\;\;\alert{?}\;\;\; |\mathbb{N}| $}\bigskip\bigskip
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
284 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
285 |
\normalsize
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
286 |
\bl{$\mathbb{O}$} $\dn$ odd numbers\quad \bl{$\{1,3,5......\}$}\\ \pause
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
287 |
\bl{$\mathbb{E}$} $\dn$ even numbers\quad \bl{$\{0,2,4......\}$}\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
288 |
\end{frame}}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
289 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
290 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
291 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
292 |
\mode<presentation>{
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
293 |
\begin{frame}[c]
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
294 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
295 |
\Large
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
296 |
\bl{$|\mathbb{N} \cup \mathbb{-N}| \;\;\;\alert{?}\;\;\; |\mathbb{N}| $}\bigskip\bigskip
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
297 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
298 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
299 |
\normalsize
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
300 |
\bl{$\mathbb{\phantom{-}N}$} $\dn$ positive numbers\quad \bl{$\{0,1,2,3,......\}$}\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
301 |
\bl{$\mathbb{-N}$} $\dn$ negative numbers\quad \bl{$\{0,-1,-2,-3,......\}$}\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
302 |
\end{frame}}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
303 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
304 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
305 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
306 |
\mode<presentation>{
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
307 |
\begin{frame}[c]
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
308 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
309 |
\Large
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
310 |
\bl{$A$} is \alert{countable} if there exists an injective \bl{$f : A \rightarrow \mathbb{N}$}\bigskip
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
311 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
312 |
\bl{$A$} is \alert{uncountable} if there does not exist an injective \bl{$f : A \rightarrow \mathbb{N}$}\bigskip\bigskip
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
313 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
314 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
315 |
countable: \bl{$|A| \leq |\mathbb{N}|$}\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
316 |
uncountable: \bl{$|A| > |\mathbb{N}|$}\pause\bigskip
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
317 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
318 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
319 |
Does there exist such an \bl{$A$} ?
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
320 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
321 |
\end{frame}}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
322 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
323 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
324 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
325 |
\mode<presentation>{
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
326 |
\begin{frame}[c]
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
327 |
\frametitle{Halting Problem}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
328 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
329 |
\large
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
330 |
Assume a program \bl{$H$} that decides for all programs \bl{$A$} and all
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
331 |
input data \bl{$D$} whether\bigskip
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
332 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
333 |
\begin{itemize}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
334 |
\item \bl{$H(A, D) \dn 1$} iff \bl{$A(D)$} terminates
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
335 |
\item \bl{$H(A, D) \dn 0$} otherwise
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
336 |
\end{itemize}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
337 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
338 |
\end{frame}}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
339 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
340 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
341 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
342 |
\mode<presentation>{
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
343 |
\begin{frame}[c]
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
344 |
\frametitle{Halting Problem (2)}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
345 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
346 |
\large
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
347 |
Given such a program \bl{$H$} define the following program \bl{$C$}:
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
348 |
for all programs \bl{$A$}\bigskip
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
349 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
350 |
\begin{itemize}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
351 |
\item \bl{$C(A) \dn 0$} iff \bl{$H(A, A) = 0$}
|
87
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
352 |
\item \bl{$C(A) \dn$ loops} otherwise
|
86
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
353 |
\end{itemize}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
354 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
355 |
\end{frame}}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
356 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
357 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
358 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
359 |
\mode<presentation>{
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
360 |
\begin{frame}[c]
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
361 |
\frametitle{Contradiction}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
362 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
363 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
364 |
\bl{$H(C, C)$} is either \bl{$0$} or \bl{$1$}.
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
365 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
366 |
\begin{itemize}
|
87
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
367 |
\item \bl{$H(C, C) = 1$} $\stackrel{\text{def}\,H}{\Rightarrow}$ \bl{$C(C)\downarrow$} $\stackrel{\text{def}\,C}{\Rightarrow}$ \bl{$H(C, C)=0$}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
368 |
\item \bl{$H(C, C) = 0$} $\stackrel{\text{def}\,H}{\Rightarrow}$ \bl{$C(C)$} loops $\stackrel{\text{def}\,C}{\Rightarrow}$\\
|
86
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
369 |
\hspace{7cm}\bl{$H(C, C)=1$}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
370 |
\end{itemize}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
371 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
372 |
Contradiction in both cases. So \bl{$H$} cannot exist.
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
373 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
374 |
\end{frame}}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
375 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
376 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
377 |
\end{document}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
378 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
379 |
%%% Local Variables:
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
380 |
%%% mode: latex
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
381 |
%%% TeX-master: t
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
382 |
%%% End:
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
383 |
|