Changeset 141

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

  r140	r141
  451	451	\end{frame}
  452	452
  453	\begin{frame}(削除) (削除ここまで)[fragile]
  453	\begin{frame}(追記) <1> (追記ここまで)[fragile]
  454	454	\frametitle{Shadows}
  455	455	\begin{itemize}
  456	\item Set of constraints $C_R$ ($a\beta \leq b\alpha$ for all pairs) is real shadow of constraints $C$.
  457	%\item If ($L,ドル$U$) are the number of (lower,upper) bounds on eliminated variable, the real shadow introduces $L.U$ new equations.
  458	\item We at least know: $\lnot \operatorname{hasIntSol}(C_R) \implies \lnot \operatorname{hasIntSol}(C)$
  459	\end{itemize}
  460	$\operatorname{hasIntSol}(C_R) \land \lnot \operatorname{hasIntSol}(C) \implies (\lnot \exists x: a\beta \leq abx \leq b\alpha)$
  456	\item Set of constraints $C_R$ ($a\beta \leq b\alpha$ for all pairs) is real shadow of constraints $C$
  457
  458	%New slide:
  459	\item No integer solution to $C_R$ $\implies$ no integer solution to $C$
  460	\item Integer solution to $C_R$ $\land$ no integer solution to $C$ $\implies$ $(\lnot \exists x: a\beta \leq abx \leq b\alpha)$
  461	\item $\therefore$ Integer solution to $C_R$ $\land (\exists x: a\beta \leq abx \leq b\alpha) \implies $ integer solution to $C$
  462	\end{itemize}
  463
  464
  465	%Old slide:
  466	%%\item If ($L,ドル$U$) are the number of (lower,upper) bounds on eliminated variable, the real shadow introduces $L.U$ new equations.
  467	%\item We at least know: $\lnot \operatorname{hasIntSol}(C_R) \implies \lnot \operatorname{hasIntSol}(C)$
  468	%\end{itemize}
  469	%$\operatorname{hasIntSol}(C_R) \land \lnot \operatorname{hasIntSol}(C) \implies (\lnot \exists x: a\beta \leq abx \leq b\alpha)$
  461	470	\note{Using:
  462	471
  …	…
  473	482	$(A \land \lnot C) \implies B$ (by definition)
  474	483	}
  475	$\operatorname{hasIntSol}(C_R) \land (\exists x: a\beta \leq abx \leq b\alpha) \implies \operatorname{hasIntSol}(C)$
  484	%$\operatorname{hasIntSol}(C_R) \land (\exists x: a\beta \leq abx \leq b\alpha) \implies \operatorname{hasIntSol}(C)$
  485
  486
  476	487	\end{frame}
  477	488

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