Changeset 169

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

  r168	r169
  35	35	\subject{Talks}
  36	36
  37	\date{(削除) 24 (削除ここまで) January 2008}
  37	\date{(追記) 31 (追記ここまで) January 2008}
  38	38
  39	39	\begin{document}
  …	…
  149	149	\item General aim is to eliminate variables (reduce dimensions)
  150	150	\item Deal with equalities first (easiest) then inequalities
  151	\item Integer division is not reversible (and requires rational numbers), so is avoided.
  151	\item Inexact integer division requires rational numbers, so is avoided.
  152	\begin{itemize}
  153	\item Division is only used to remove common factors in coefficients
  154	\end{itemize}
  152	155	\end{itemize}
  153	156	\end{frame}
  …	…
  738	741	\end{lstlisting}
  739	742	\begin{itemize}
  740	\item For parallel replication (e.g. 0 FOR 10), we introduce a ghost variable $i'$: 0ドル \leq i (削除) \leq i' - 1,ドル $ (削除ここまで)i' \leq 9$
  743	\item For parallel replication (e.g. 0 FOR 10), we introduce a ghost variable $i'$: 0ドル \leq i (追記) < (追記ここまで)i' \leq 9$
  741	744	\item Effectively checking for any two arbitrary (non-equal) indices
  742	745	\item Must check both ways!
  …	…
  748	751
  749	752	\begin{frame}
  750	\frametitle{Flattening (削除) (削除ここまで)Expressions}
  753	\frametitle{Flattening (追記) occam (追記ここまで)Expressions}
  751	754	\begin{itemize}
  752	755	\item \lstinline|3*(7-i)| becomes 21ドル + (-3)i$
  753	\item Addition is left alone, subtraction is turned into addition(削除) (削除ここまで)
  756	\item Addition is left alone, subtraction is turned into addition(追記) ($x - y$ becomes $x + (-y)$) (追記ここまで)
  754	757	\item Multiplied expressions are multiplied out
  755	758	\item Division and modulo are special \ldots
  …	…
  763	766	\begin{itemize}
  764	767	\item We can't express anything useful about them
  765	\end{itemize}
  766	\item They often cancel out anyway:
  768	\item Can get false alarms (e.g. \lstinline|a[x*x],a[x+1] := 0,0| treated as $y = x+1$)
  769	\end{itemize}
  770	\item They may cancel out anyway:
  767	771	\begin{lstlisting}
  768	772	PAR i = 0 FOR 10
  …	…
  1108	1112	\frametitle{Questions?}
  1109	1113	\begin{itemize}
  1110	%TODO put references here (the Pugh Omega Test paper, occam 2.1 manual, and maybe the Kessler paper
  1111	\item Blah
  1114	\item TODO put references here (the Pugh Omega Test paper, occam 2.1 manual, and maybe the Kessler paper
  1112	1115	\end{itemize}
  1113	1116	\end{frame}

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