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http://github.com/Rekamux/Free-Project
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  1\documentclass{beamer}
  2
  3\usepackage[T1]{fontenc} 
  4\usepackage[utf8]{inputenc}
  5\usepackage[english]{babel}
  6%% \usepackage{pslatex}
  7%% \usepackage{colortbl} 
  8%% \usepackage{calc} 
  9
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 30    \begin{beamercolorbox}[wd=.3\paperwidth,ht=2.25ex,dp=1ex,center]{title in head/foot}%
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 47  \vskip0pt%
 48}
 49
 50
 51\title[Free Project]{Sequence Complexity}
 52\author{Axel Schumacher}
 53\institute{Télécom Paristech}
 54\date{July $4^{th}$, 2011}
 55
 56
 57%---------------------------------------
 58%---------------------------------------
 59
 60
 61\begin{document}
 62
 63\begin{frame}
 64  \titlepage
 65\end{frame}
 66
 67\begin{frame}{Presentation}
 68  \begin{itemize}
 69    \item{1 2 3 4 ... ?}
 70    \item{9 9 9 ... ?}
 71    \item{1 2 2 3 3 3 ... ?}
 72    \item{1 2 2 3 3 4 ... ?}
 73    \item{1 1 2 1 2 3 1 1 2 1 2 3 1 2 3 4 ... ?}
 74    \item{1 1 1 1 2 2 ... ? }
 75  \end{itemize}
 76  \begin{center}
 77  Completing those sequences: easy for a human being\\
 78  (trivial notions in math)\\
 79  What about computers?
 80  \end{center}
 81\end{frame}
 82
 83\begin{frame}{Constraints}
 84  \begin{itemize}
 85    \item{
 86      Two operators
 87      \begin{itemize}
 88        \item{Copy: C}
 89        \item{Increment: I}
 90      \end{itemize}}
 91    \item{No combinatory explosion}
 92    \item{Work and think in a "human" way}
 93  \end{itemize}
 94\end{frame}
 95
 96\begin{frame}{Implementation}
 97  Suffixed notation, close to Factor:\\
 98  \begin{itemize}
 99    \item{
100      Copy:\\
101      \textit{What Times C}\\
102      Examples:
103      \begin{itemize}
104        \item{5 5 5 5 $\rightarrow$ 5 4 \textit{C}}
105        \item{1 2 1 2 1 2 $\rightarrow$ \{1 2\} 3 \textit{C}}
106      \end{itemize}}
107    \item{
108      Increment:\\
109      \textit{What Where Times I}\\
110      Examples:
111      \begin{itemize}
112        \item{1 2 3 4 $\rightarrow$ 1 0 4 \textit{I}}
113        \item{1 1 1 2 1 2 3 1 3 $\rightarrow$ \{1 1 1\} \{0 2\} 3 \textit{I}}
114      \end{itemize}}
115  \end{itemize}
116\end{frame}
117
118\begin{frame}{Extend a sequence}
119  \begin{center}
120    If we can compress a sequence to one operator and its arguments,\\
121    we just have to increment its \textit{Times} field and decompress
122  \end{center}
123\end{frame}
124
125\begin{frame}{Search order}
126  We try:
127  \begin{itemize}
128    \item{to remove from 0 up to (length - 2) elements}
129    \item{an operator}
130    \item{a tested size}
131  \end{itemize}
132  With all those choices, we try to compress the whole sequence.\\
133  We try another one if complexity is too high.
134\end{frame}
135
136\begin{frame}{Possible improvements}
137  \begin{center}
138    \begin{itemize}
139    \item{Solve "once applied operators" problem}
140    \item{Find a Kantian model}
141    \item{Respect "human" memory use}
142  \end{itemize}
143   
144  \end{center}
145\end{frame}
146
147\begin{frame}{Conclusion}
148  \begin{center}
149  Subject not that easy\\
150  Factor is a powerful language\\
151  Very enlightening project
152  \end{center}
153\end{frame}
154 
155\end{document}