# HG changeset patch # User Masataka Kohagura # Date 1455039700 -32400 # Node ID 73dd8d6a66b92d25662bd4066b2b5177f73d4e89 # Parent b2e4ac4e08f24e73921c660a8e09791a161eb187 add some images diff -r b2e4ac4e08f2 -r 73dd8d6a66b9 c4.tex --- a/c4.tex Tue Feb 09 19:46:46 2016 +0900 +++ b/c4.tex Wed Feb 10 02:41:40 2016 +0900 @@ -304,7 +304,7 @@ 次に正規表現木から非決定性有限オートマトン(NFA)、決定性有限オートマトン(DFA)を生成する。 オートマトンは、入力に対して状態に対応した処理を行ない結果を出力する仮想的な自動機械である。 -正規表現はオートマトンで表現することができるので、状態と入力(ここでは正規表現)が判れば次はどのような状態になるのか示すことができる。 +正規表現はオートマトンで表現することができるので、状態と入力(ここでは正規表現)が判れば次はどのような状態になるのか決定される。 \begin{figure}[htpb] \begin{center} @@ -435,6 +435,7 @@ これにより、正規表現木に状態の割り振りを行ない、入力を行なったら状態が遷移するようにできた。 現在の状態(current state)と入力(input)によって次の状態(next state)が一意に決まっており、それをテーブル化して正規表現をファイルにかける。(図\ref{fig:dfaregex}) +このように、ある状態にある入力を与えると次の状態の遷移先が一意に決まるオートマトンのとこを決定性オートマトンという。 \begin{figure}[htpb] \begin{center} @@ -445,10 +446,56 @@ \end{figure} しかし、生成された正規表現木によっては、現在の状態と入力による次の状態が一意に決まらない場合もある。 -図\ref{fig:nfaregex} +図\ref{fig:nfaex}はある状態にある文字を入力すると遷移先が複数存在する場合である。状態 4 に `b' が入力されると状態 2 か状態 4 に遷移する。 +このように 1 つの入力に対して遷移先が複数存在すると、どの状態に遷移をしたらよいのかわからくなる。 +このようなオートマトンを非決定性オートマトンという。 + +これを解決する方法として Subset Construction を適用する。 + +\begin{figure}[htpb] + \begin{center} + \includegraphics[scale=0.2]{images/regex/nfaex.pdf} + \end{center} + \caption{1 入力に対して遷移先が複数存在する(NFA)} + \label{fig:nfaex} +\end{figure} + +\subsection{Subset Construction による NFA から DFA の変換} +Subset Construction は、ある状態から 1 つの入力に対して複数の状態遷移先がある場合、それらの状態 1 つの新しい状態としてまとめ、その新しい状態から新しい遷移先を構成しそれを繰り返す手法である。 + +\begin{figure}[htpb] + \begin{center} + \includegraphics[scale=0.2]{images/regex/nfa.pdf} + \end{center} + \caption{NFA の例} + \label{fig:nfa} +\end{figure} -\subsection{Subset Construction による NFA から DFA の変換} +\begin{figure}[htpb] + \begin{center} + \includegraphics[scale=0.2]{images/regex/dfa.pdf} + \end{center} + \caption{NFA を Subset Construction によって DFA に変換} + \label{fig:dfa} +\end{figure} + +\begin{figure}[htpb] + \begin{center} + \includegraphics[scale=0.2]{images/regex/subset.pdf} + \end{center} + \caption{Subset Construction によって新しく生成された状態の状態遷移の生成} + \label{fig:subset} +\end{figure} + +\begin{figure}[htpb] + \begin{center} + \includegraphics[scale=0.2]{images/regex/subsetauto.pdf} + \end{center} + \caption{Subset Construction 後のオートマトンの変化} + \label{fig:subsetauto} +\end{figure} + on the fly subset construction で使わない状態は生成しないで済む @@ -457,23 +504,6 @@ \subsection{(Word をノードに含める話)} IBM stream processing - -\begin{figure}[htpb] - \begin{center} - \includegraphics[scale=0.2]{images/regex/dfa.pdf} - \end{center} - \caption{dfa} - \label{fig:dfa} -\end{figure} - -\begin{figure}[htpb] - \begin{center} - \includegraphics[scale=0.2]{images/regex/nfa.pdf} - \end{center} - \caption{nfa} - \label{fig:nfa} -\end{figure} - \begin{figure}[htpb] \begin{center} \includegraphics[scale=0.2]{images/regex/transitiontable.pdf} diff -r b2e4ac4e08f2 -r 73dd8d6a66b9 images/image.graffle --- a/images/image.graffle Tue Feb 09 19:46:46 2016 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- {210.76799439792558, 310.17252335224578} - - Style - - shadow - - Draws - NO - - stroke - - HeadArrow - FilledArrow - Legacy - - LineType - 1 - TailArrow - 0 - - - - - Bounds - {{48.188976815178634, 72.283465222767958}, {126.55484330832485, 30}} + Bounds + {{51.009341643316688, 89.291339392830992}, {126.55484330832485, 30}} Class ShapedGraphic FitText @@ -54609,7 +59363,7 @@ \deftab720 \pard\pardeftab720\partightenfactor0 -\f0\fs32 \cf0 ( c | [a-z]* ) b} +\f0\fs32 \cf0 ( a | a[a-z]* ) b} @@ -54680,7 +59434,7 @@ キャンバス 7 Frame - {{463, 191}, {1198, 966}} + {{-283, 211}, {1198, 966}} ShowInfo ShowRuler @@ -54692,9 +59446,9 @@ TopSlabHeight 682 VisibleRegion - {{0, -12}, {684, 808}} + {{351.85185185185185, 0.92592592592592593}, {633.33333333333337, 748.14814814814804}} Zoom - 1 + 1.0800000000000001 ZoomValues @@ -54774,8 +59528,8 @@ NFA - 1 - 1 + 1.0800000000000001 + 1.0900000000000001 diff -r b2e4ac4e08f2 -r 73dd8d6a66b9 images/regex/dfa.bb --- a/images/regex/dfa.bb Tue Feb 09 19:46:46 2016 +0900 +++ b/images/regex/dfa.bb Wed Feb 10 02:41:40 2016 +0900 @@ -1,5 +1,5 @@ %%Title: images/regex/dfa.pdf %%Creator: extractbb 20150315 -%%BoundingBox: 0 0 1614 900 -%%CreationDate: Mon Feb 8 11:22:40 2016 +%%BoundingBox: 0 0 1266 570 +%%CreationDate: Wed Feb 10 02:35:50 2016 diff -r b2e4ac4e08f2 -r 73dd8d6a66b9 images/regex/dfa.pdf Binary file images/regex/dfa.pdf has changed diff -r b2e4ac4e08f2 -r 73dd8d6a66b9 images/regex/dfaregex.pdf Binary file images/regex/dfaregex.pdf has changed diff -r b2e4ac4e08f2 -r 73dd8d6a66b9 images/regex/nfa.bb --- a/images/regex/nfa.bb Tue Feb 09 19:46:46 2016 +0900 +++ b/images/regex/nfa.bb Wed Feb 10 02:41:40 2016 +0900 @@ -1,5 +1,5 @@ %%Title: images/regex/nfa.pdf %%Creator: extractbb 20150315 -%%BoundingBox: 0 0 1440 615 -%%CreationDate: Mon Feb 8 11:22:40 2016 +%%BoundingBox: 0 0 639 636 +%%CreationDate: Wed Feb 10 02:35:45 2016 diff -r b2e4ac4e08f2 -r 73dd8d6a66b9 images/regex/nfa.pdf Binary file images/regex/nfa.pdf has changed diff -r b2e4ac4e08f2 -r 73dd8d6a66b9 images/regex/nfaex.bb --- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/images/regex/nfaex.bb Wed Feb 10 02:41:40 2016 +0900 @@ -0,0 +1,5 @@ +%%Title: images/regex/nfaex.pdf +%%Creator: extractbb 20150315 +%%BoundingBox: 0 0 1371 2034 +%%CreationDate: Wed Feb 10 01:40:47 2016 + diff -r b2e4ac4e08f2 -r 73dd8d6a66b9 images/regex/nfaex.pdf Binary file images/regex/nfaex.pdf has changed diff -r b2e4ac4e08f2 -r 73dd8d6a66b9 images/regex/setstate.bb --- a/images/regex/setstate.bb Tue Feb 09 19:46:46 2016 +0900 +++ b/images/regex/setstate.bb Wed Feb 10 02:41:40 2016 +0900 @@ -1,5 +1,5 @@ %%Title: images/regex/setstate.pdf %%Creator: extractbb 20150315 -%%BoundingBox: 0 0 1719 1962 -%%CreationDate: Mon Feb 8 14:57:30 2016 +%%BoundingBox: 0 0 1719 2067 +%%CreationDate: Wed Feb 10 02:00:00 2016 diff -r b2e4ac4e08f2 -r 73dd8d6a66b9 images/regex/setstate.pdf Binary file images/regex/setstate.pdf has changed diff -r b2e4ac4e08f2 -r 73dd8d6a66b9 images/regex/subset.bb --- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/images/regex/subset.bb Wed Feb 10 02:41:40 2016 +0900 @@ -0,0 +1,5 @@ +%%Title: images/regex/subset.pdf +%%Creator: extractbb 20150315 +%%BoundingBox: 0 0 1323 1056 +%%CreationDate: Wed Feb 10 02:36:26 2016 + diff -r b2e4ac4e08f2 -r 73dd8d6a66b9 images/regex/subset.pdf Binary file images/regex/subset.pdf has changed diff -r b2e4ac4e08f2 -r 73dd8d6a66b9 images/regex/subsetauto.bb --- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/images/regex/subsetauto.bb Wed Feb 10 02:41:40 2016 +0900 @@ -0,0 +1,5 @@ +%%Title: images/regex/subsetauto.pdf +%%Creator: extractbb 20150315 +%%BoundingBox: 0 0 915 927 +%%CreationDate: Wed Feb 10 02:36:26 2016 + diff -r b2e4ac4e08f2 -r 73dd8d6a66b9 images/regex/subsetauto.pdf Binary file images/regex/subsetauto.pdf has changed diff -r b2e4ac4e08f2 -r 73dd8d6a66b9 master_paper.pdf Binary file master_paper.pdf has changed