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\title[Free Project]{Sequence Complexity}
\author{Axel Schumacher}
\institute{Télécom Paristech}
\date{July $4^{th}$, 2011}


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\begin{document}

\begin{frame}
  \titlepage
\end{frame}

\begin{frame}{Presentation}
  \begin{itemize}
    \item{1 2 3 4 ... ?}
    \item{9 9 9 ... ?}
    \item{1 2 2 3 3 3 ... ?}
    \item{1 2 2 3 3 4 ... ?}
    \item{1 1 2 1 2 3 1 1 2 1 2 3 1 2 3 4 ... ?}
    \item{1 1 1 1 2 2 ... ? }
  \end{itemize}
  \begin{center}
  Completing those sequences: easy for a human being\\
  (trivial notions in math)\\
  What about computers?
  \end{center}
\end{frame}

\begin{frame}{Constraints}
  \begin{itemize}
    \item{
      Two operators
      \begin{itemize}
        \item{Copy: C}
        \item{Increment: I}
      \end{itemize}}
    \item{No combinatory explosion}
    \item{Work and think in a "human" way}
  \end{itemize}
\end{frame}

\begin{frame}{Implementation}
  Suffixed notation, close to Factor:\\
  \begin{itemize}
    \item{
      Copy:\\
      \textit{What Times C}\\
      Examples:
      \begin{itemize}
        \item{5 5 5 5 $\rightarrow$ 5 4 \textit{C}}
        \item{1 2 1 2 1 2 $\rightarrow$ \{1 2\} 3 \textit{C}}
      \end{itemize}}
    \item{
      Increment:\\
      \textit{What Where Times I}\\
      Examples:
      \begin{itemize}
        \item{1 2 3 4 $\rightarrow$ 1 0 4 \textit{I}}
        \item{1 1 1 2 1 2 3 1 3 $\rightarrow$ \{1 1 1\} \{0 2\} 3 \textit{I}}
      \end{itemize}}
  \end{itemize}
\end{frame}

\begin{frame}{Extend a sequence}
  \begin{center}
    If we can compress a sequence to one operator and its arguments,\\
    we just have to increment its \textit{Times} field and decompress
  \end{center}
\end{frame}

\begin{frame}{Search order}
  We try:
  \begin{itemize}
    \item{to remove from 0 up to (length - 2) elements}
    \item{an operator}
    \item{a tested size}
  \end{itemize}
  With all those choices, we try to compress the whole sequence.\\
  We try another one if complexity is too high.
\end{frame}

\begin{frame}{Possible improvements}
  \begin{center}
    \begin{itemize}
    \item{Solve "once applied operators" problem}
    \item{Find a Kantian model}
    \item{Respect "human" memory use}
  \end{itemize}
   
  \end{center}
\end{frame}

\begin{frame}{Conclusion}
  \begin{center}
  Subject not that easy\\
  Factor is a powerful language\\
  Very enlightening project
  \end{center}
\end{frame}
 
\end{document}