Changeset 170 for docs/trunk

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• docs/trunk/omega-test-slides/omega-test.tex

  r169	r170
  734	734	\section{Formulating Problems}
  735	735
  736	\begin{frame}[fragile]
  737	\frametitle{Replication}
  738	\begin{lstlisting}
  739	PAR i = 0 FOR 10
  740	a[i] := a[i+1]
  741	\end{lstlisting}
  742	\begin{itemize}
  743	\item For parallel replication (e.g. 0 FOR 10), we introduce a ghost variable $i'$: 0ドル \leq i < i' \leq 9$
  744	\item Effectively checking for any two arbitrary (non-equal) indices
  745	\item Must check both ways!
  746	\begin{itemize}
  747	\item \lstinline|a[i] := a[i+1]| is `safe' for $i = i' + 1,ドル but not $i + 1 = i'$
  748	\end{itemize}
  749	\end{itemize}
  736	\begin{frame}
  737	\frametitle{Turning Code into Equations}
  750	738	\end{frame}
  751	739
  …	…
  770	758	\item They may cancel out anyway:
  771	759	\begin{lstlisting}
  772	PAR i = 0 FOR 10
  773	scr[width*y + i] := 255
  760	scr[width*y + 3], scr[width*y + 4] := 255,255
  774	761	\end{lstlisting}
  775	\item Set $\sigma = $ \lstinline|width*y|: $\sigma + (削除) i = \sigma + i' \implies i = i' (削除ここまで)$
  762	\item Set $\sigma = $ \lstinline|width*y|: $\sigma + (追記) 3 = \sigma + 4 \implies 3 = 4 (追記ここまで)$
  776	763	\end{itemize}
  777	764	\end{frame}
  …	…
  878	865	%TODO try Adam's problem from the last presentation
  879	866
  880	%TODO we could probably cover all four x,y +- combinations:
  881	%For negative y, use -y
  882	%For negative x, change the sign of a (I think?)
  883	%Even though four problems are generated, three are likely to be falsifiable quickly
  867	\begin{frame}[fragile]
  868	\frametitle{Replication}
  869	\begin{lstlisting}
  870	PAR i = 0 FOR 10
  871	a[i] := a[i+1]
  872	\end{lstlisting}
  873	\begin{itemize}
  874	\item For parallel replication (e.g. 0 FOR 10), we introduce a ghost variable $i'$: 0ドル \leq i < i' \leq 9$
  875	\item Effectively checking for any two arbitrary (non-equal) indices
  876	\item Must check both ways!
  877	\begin{itemize}
  878	\item \lstinline|a[i] := a[i+1]| is `safe' for $i = i' + 1,ドル but not $i + 1 = i'$
  879	\end{itemize}
  880	\end{itemize}
  881	\end{frame}
  884	882
  885	883	%replicated 0 FOR n. i + 1 REM n and j + 1 REM n, 0 <= i <= j - 1 <= n - 2

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