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\title[Multigraphical Membrane Systems]{Continuous versus Discrete:\\
some topics with a regard\\ to membrane computing}
\author[Adam Obtu\l owicz, IMPAN, Warsaw, Poland]{Adam Obtu\l owicz\\ Institute of Mathematics, Polish Academy of Sciences\\
Warsaw, Poland}
\date{}

\begin{document}
\frame{\titlepage}

\frame{\frametitle{Discretization programs}
Fredkin--Sorkin--Wolfram \di\ programs of physics via E.~Fredkin's
digitalization, R.~D.~Sorkin's causal sets, and S.~Wolfram's cellular automata
approach give rise to a question:

}
\frame{\frametitle{Question}
Does the \di\ mean a lost (or eventually how to find counterparts) of
classical quantitative properties of \ct ly (\wrt time among others) treated
processes like

\bit
\item stability property,
\item \as\ \bh\ (i.e.\ tending of process trajectories---the solutions of
some differential equations to some possibly regular curves),
\item irregular \bh:
\bit
\item chaos$^1$,
\item perturbations.
\eit
\eit
{\small $^1$\,D. A. Hill, \ti{Chaotic Chaos}, Math. Intelligencer
22(3), 5, 2000}
}

\frame{\frametitle{Answer}
Some (partial) answer to this question is contained in:
\bit
\item characterization of irregular \bh\ of processes represented by large
graphs (like causal sets and their Hosse diagrams) in terms of \dm s like
fractal \dm,
\item the attempts of making the discrete constructs \ct\ one, like K.~Martin
and P.~Panangaden work of building back space-time manifold from Sorkin like
causal order.
\eit
}

\frame{\frametitle{Membrane computing}
Concerning \me\ computing one could:

\bit
\item \rp\ processes generated by P~\s s by causal sets like T.~Bolognesi
\rp s computational processes of various mechanisms,
\eit
then
\bit
\item approach the causal sets \rp ing processes generated by P \s s like in
the answer to the main question given above.
\eit

}
\end{document}
