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kajigorkajigor
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Better pictures in GLR
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‎tex/FormalLanguageConstrainedReachabilityLectureNotes.pdf‎

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‎tex/FormalLanguageConstrainedReachabilityLectureNotes.tex‎

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Original file line numberDiff line numberDiff line change
@@ -105,6 +105,8 @@
105105

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\tikzstyle{r_state} = [shape=rectangle, draw, minimum size=0.2cm]
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\tikzstyle{num_state} = [draw=none, fill=none, anchor=south west, red]
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\tikzstyle{prod_node} = [shape=rectangle, draw, align=center]
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\tikzset{
@@ -147,28 +149,28 @@
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\tableofcontents
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\newpage
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150-
\input{GLR-based_CFPQ}
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% \input{List_of_contributors}
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% \input{Introduction}
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% %\input{LinearAlgebra}
155-
% \input{GraphTheoryIntro}
156-
% \input{FormalLanguageTheoryIntro}
157-
% \input{FLPQ}
158-
% %\input{RegularLanguages}
159-
% \input{Context-Free_Languages}
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% \input{CYK_for_CFPQ}
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% \input{Matrix-based_CFPQ}
162-
% \input{TensorProduct}
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% \input{SPPF}
164-
% \input{GLL-based_CFPQ}
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% \input{GLR-based_CFPQ}
166-
% %\input{CombinatorsForCFPQ}
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% %\input{DerivativesForCFPQ}
168-
% %\input{CFPQ_to_Datalog}
169-
% %\input{Multiple_Context-Free_Languages}
170-
% %\input{ConjunctiveAndBooleanLanguages}
171-
% %\input{Conclusion}
153+
154+
\input{List_of_contributors}
155+
\input{Introduction}
156+
%\input{LinearAlgebra}
157+
\input{GraphTheoryIntro}
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\input{FormalLanguageTheoryIntro}
159+
\input{FLPQ}
160+
%\input{RegularLanguages}
161+
\input{Context-Free_Languages}
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\input{CYK_for_CFPQ}
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\input{Matrix-based_CFPQ}
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\input{TensorProduct}
165+
\input{SPPF}
166+
\input{GLL-based_CFPQ}
167+
\input{GLR-based_CFPQ}
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%\input{CombinatorsForCFPQ}
169+
%\input{DerivativesForCFPQ}
170+
%\input{CFPQ_to_Datalog}
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%\input{Multiple_Context-Free_Languages}
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%\input{ConjunctiveAndBooleanLanguages}
173+
%\input{Conclusion}
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\bibliographystyle{abbrv}
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\bibliography{FormalLanguageConstrainedReachabilityLectureNotes}

‎tex/GLR-based_CFPQ.tex‎

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@@ -18,7 +18,7 @@ \section{Восходящий синтаксический анализ}
1818

1919
\begin{center}
2020
\begin{tabular}{c||c|c|c|c|c||c|c|c|c}
21-
States & $t_0$ &$\dots$ & $t_a$ & $\dots$ & \$ & $N_0$ &$\dots$ & $N_b$ & $\dots$ \\ \hline
21+
States & $t_0$ &$\dots$ & $t_a$ & $\dots$ & \$ & $N_0$ &$\dots$ & $N_b$ & $\dots$ \\ \hline \hline
2222
$\dots$ & $\dots$ &$\dots$ & $\dots$ & $\dots$ & $\dots$ & $\dots$ &$\dots$ & $\dots$ & $\dots$ \\ \hline
2323
$10$ & $\dots$ &$\dots$ & $s_i$ & $\dots$ & $r_k$ & $\dots$ &$\dots$ & $j$ & $\dots$ \\ \hline
2424
$\dots$ & $\dots$ &$\dots$ & $\dots$ & $\dots$ & $acc$ & $\dots$ &$\dots$ & $\dots$ & $\dots$
@@ -211,16 +211,16 @@ \subsection{Примеры}
211211
\begin{example}
212212
Пример управляющей LR(0) таблицы.
213213

214-
\begin{tabular}{|c|c|c|c||c|}
215-
\hline & a & b & \$ & S \\ [0.5ex]
214+
\begin{tabular}{c||c|c|c||c}
215+
& a & b & \$ & S \\ \hline
216216
\hline 0 & $s_3$, $r_1$ & $r_1$ & $r_1$ & 1 \\
217217
\hline 1 & & & acc & \\
218218
\hline 2 & $r_2$ & $r_2$ & $r_2$ & \\
219219
\hline 3 & $s_3$, $r_1$ & $r_1$ & $r_1$ & 4 \\
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\hline 4 & & $s_5$ & & \\
221221
\hline 5 & $s_3, r_1$ & $r_1$ & $r_1$ & 6 \\
222-
\hline 6 & $r_0$ & $r_0$ & $r_0$ & \\ [1ex]
223-
\hline
222+
\hline 6 & $r_0$ & $r_0$ & $r_0$ &
223+
224224
\end{tabular}
225225

226226
Как видим, в данном случае в таблице присутствуют shift-reduce конфликты. В случае, когда не удаётся построить таблицу без конфликтов, говорят, что грамматика не LR(0).
@@ -236,16 +236,15 @@ \subsection{Примеры}
236236
\textit{FOLLOW}_1(S) = \{b, \$\}
237237
$$
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\begin{tabular}{|c|c|c|c||c|}
240-
\hline & a & b & \$ & S \\ [0.5ex]
239+
\begin{tabular}{c||c|c|c||c}
240+
& a & b & \$ & S \\ \hline
241241
\hline 0 & $s_3$ & $r_1$ & $r_1$ & 1 \\
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\hline 1 & & & acc & \\
243243
\hline 2 & & & & \\
244244
\hline 3 & $s_3$ & $r_1$ & $r_1$ & 4 \\
245245
\hline 4 & & $s_5$ & & \\
246246
\hline 5 & $s_3$ & $r_1$ & $r_1$ & 6 \\
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\hline 6 & & $r_0$ & $r_0$ & \\ [1ex]
248-
\hline
249248
\end{tabular}
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В данном случае в таблице отсутствуют shift-reduce конфликты. То есть наша грамматика SLR(1), но не LR(0).
@@ -421,138 +420,22 @@ \subsection{Классический GLR алгоритм}
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Построим для данной грамматики LR автомат:
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426-
427-
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% Text Node
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430-
\draw (60.5,61) node [color={rgb, 255:red, 62; green, 45; blue, 45 } ,opacity=1 ] {$ \begin{array}{l}
431-
S'\rightarrow .S\$\\
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S\rightarrow .abC\\
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S\rightarrow .aBC
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\end{array}$};
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% Text Node
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437-
\draw (60.5,148.5) node {$S'\rightarrow S.\$$};
438-
% Text Node
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440-
% Text Node
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% Text Node
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% Text Node
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% Text Node
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448-
% Text Node
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450-
% Text Node
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452-
\draw (180.5,61) node [color={rgb, 255:red, 62; green, 45; blue, 45 } ,opacity=1 ] {$ \begin{array}{l}
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S\rightarrow a.BC\\
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S\rightarrow a.bC\\
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B\rightarrow .b
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\end{array}$};
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% Text Node
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459-
% Text Node
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461-
\draw (299.5,61) node [color={rgb, 255:red, 62; green, 45; blue, 45 } ,opacity=1 ] {$ \begin{array}{l}
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S\rightarrow ab.C\\
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B\rightarrow b.\\
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C\rightarrow .c
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\end{array}$};
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% Text Node
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\draw (25,209) .. controls (25,206.24) and (27.24,204) .. (30,204) -- (91,204) .. controls (93.76,204) and (96,206.24) .. (96,209) -- (96,224) .. controls (96,226.76) and (93.76,229) .. (91,229) -- (30,229) .. controls (27.24,229) and (25,226.76) .. (25,224) -- cycle ;
468-
\draw (60.5,216.5) node {$S'\rightarrow S\$.$};
469-
% Text Node
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\draw (69,111) node [scale=0.9,color={rgb, 255:red, 0; green, 0; blue, 0 } ,opacity=1 ] {$S$};
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% Text Node
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\draw (69,178) node [scale=0.9,color={rgb, 255:red, 0; green, 0; blue, 0 } ,opacity=1 ] {$\$$};
473-
% Text Node
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475-
\draw (416,61) node [color={rgb, 255:red, 62; green, 45; blue, 45 } ,opacity=1 ] {$S\rightarrow abC.$};
476-
% Text Node
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\draw (240,51) node [scale=0.9,color={rgb, 255:red, 0; green, 0; blue, 0 } ,opacity=1 ] {$b$};
478-
% Text Node
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\draw (356,51) node [scale=0.9,color={rgb, 255:red, 0; green, 0; blue, 0 } ,opacity=1 ] {$C$};
480-
% Text Node
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482-
\draw (181,149.5) node [color={rgb, 255:red, 62; green, 45; blue, 45 } ,opacity=1 ] {$ \begin{array}{l}
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S\rightarrow aB.C\\
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C\rightarrow .c
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\end{array}$};
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% Text Node
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\draw (142,210) .. controls (142,207.24) and (144.24,205) .. (147,205) -- (215,205) .. controls (217.76,205) and (220,207.24) .. (220,210) -- (220,225) .. controls (220,227.76) and (217.76,230) .. (215,230) -- (147,230) .. controls (144.24,230) and (142,227.76) .. (142,225) -- cycle ;
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\draw (181,217.5) node [color={rgb, 255:red, 62; green, 45; blue, 45 } ,opacity=1 ] {$S\rightarrow aBC.$};
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% Text Node
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\draw (271,142) .. controls (271,139.24) and (273.24,137) .. (276,137) -- (324,137) .. controls (326.76,137) and (329,139.24) .. (329,142) -- (329,157) .. controls (329,159.76) and (326.76,162) .. (324,162) -- (276,162) .. controls (273.24,162) and (271,159.76) .. (271,157) -- cycle ;
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\draw (300,149.5) node [color={rgb, 255:red, 62; green, 45; blue, 45 } ,opacity=1 ] {$C\rightarrow c.$};
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% Text Node
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% Text Node
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% Text Node
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% Text Node
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% Text Node
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% Text Node
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504-
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505-
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506-
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507-
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% Connection
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511-
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% Connection
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515-
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% Connection
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518-
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519-
520-
% Connection
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522-
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523-
524-
% Connection
525-
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526-
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527-
528-
% Connection
529-
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530-
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531-
532-
% Connection
533-
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534-
\draw [shift={(299.93,137)}, rotate = 269.68] [color={rgb, 255:red, 0; green, 0; blue, 0 } ][line width=0.75] (10.93,-3.29) .. controls (6.95,-1.4) and (3.31,-0.3) .. (0,0) .. controls (3.31,0.3) and (6.95,1.4) .. (10.93,3.29) ;
535-
536-
% Connection
537-
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538-
\draw [shift={(271,149.5)}, rotate = 180] [color={rgb, 255:red, 0; green, 0; blue, 0 } ][line width=0.75] (10.93,-3.29) .. controls (6.95,-1.4) and (3.31,-0.3) .. (0,0) .. controls (3.31,0.3) and (6.95,1.4) .. (10.93,3.29) ;
539-
540-
541-
\end{tikzpicture}
423+
\begin{center}
424+
\input{figures/GLR/GLR_example.tex}
425+
\end{center}
542426

543427
И управляющую таблицу:
544428

545-
\begin{tabular}{|c|c|c|c|c||c|c|c|}
546-
\hline & a & b & c & \$ & B & C & S \\ [0.5ex]
429+
\begin{tabular}{c||c|c|c|c||c|c|c}
430+
& a & b & c & \$ & B & C & S \\ \hline
547431
\hline 0 & $s_2$ & & & & & 1 & \\
548432
\hline 1 & & & & acc & & & \\
549433
\hline 2 & & $s_3$ & & & 4 & & \\
550434
\hline 3 & & & $s_6$, $r_3$ & & & 5 & \\
551435
\hline 4 & & & $s_6$ & & & 7 & \\
552436
\hline 5 & & & & $r_1$ & & & \\
553437
\hline 6 & & & & $r_4$ & & & \\
554-
\hline 7 & & & & $r_2$ & & & \\ [1ex]
555-
\hline
438+
\hline 7 & & & & $r_2$ & & &
556439
\end{tabular}
557440

558441
Разберем слово $w$ с помощью алгоритма GLR. Использована следующая аннотация: вершины-состояния обозначены кругами, вершины-символы --- прямоугольниками.

‎tex/figures/GLR/GLR_example.tex‎

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1+
\begin{tikzpicture}[> = stealth,node distance=1.25cm, on grid, scale=0.8, every node/.style={scale=0.8}]
2+
\node[r_state] (s_0)
3+
{
4+
$
5+
\begin{aligned}
6+
S' &\to \cdot S \$ \\
7+
S &\to \cdot a b C \\
8+
S &\to \cdot a B C
9+
\end{aligned}
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$
11+
};
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\node[r_state] (s_1) [below=2.5cm of s_0]
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{
14+
$ S' \to S \cdot \$ $
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};
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\node[r_state] (s_acc) [below=2cm of s_1]
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{
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$ S' \to S \$ \cdot $
19+
};
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\node[r_state] (s_2) [right=3cm of s_0]
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{
22+
$
23+
\begin{aligned}
24+
S &\to a \cdot B C \\
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S &\to a \cdot b C \\
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B &\to \cdot b
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\end{aligned}
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$
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};
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\node[r_state] (s_3) [right=3cm of s_2]
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{
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$
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\begin{aligned}
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S &\to a b \cdot C \\
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B &\to b \cdot \\
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C &\to \cdot c
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\end{aligned}
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$
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};
41+
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\node[r_state] (s_5) [right=3cm of s_3]
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{
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$
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\begin{aligned}
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S &\to a b C \cdot
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\end{aligned}
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$
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};
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\node[r_state] (s_4) [below=2.5cm of s_2]
52+
{
53+
$
54+
\begin{aligned}
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S &\to a B \cdot C \\
56+
C &\to \cdot c
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\end{aligned}
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$
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};
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\node[r_state] (s_6) [right=3cm of s_4]
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{
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$
64+
\begin{aligned}
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C &\to c \cdot
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\end{aligned}
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$
68+
};
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\node[r_state] (s_7) [below=2cm of s_4]
71+
{
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$
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\begin{aligned}
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S &\to a B C \cdot
75+
\end{aligned}
76+
$
77+
};
78+
79+
\node[num_state] at (s_0.north west) {0};
80+
\node[num_state] at (s_1.north west) {1};
81+
\node[num_state] at (s_2.north west) {2};
82+
\node[num_state] at (s_3.north west) {3};
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\node[num_state] at (s_4.north west) {4};
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\node[num_state] at (s_5.north west) {5};
85+
\node[num_state] at (s_6.north west) {6};
86+
\node[num_state] at (s_7.north west) {7};
87+
\node[num_state] at (s_acc.north west) {acc};
88+
89+
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\path[->]
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(s_0) edge [above] node {$a$} (s_2)
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edge [right] node {$S$} (s_1)
93+
(s_1) edge [right] node {$\$$} (s_acc)
94+
(s_2) edge [above] node {$b$} (s_3)
95+
edge [right] node {$B$} (s_4)
96+
(s_3) edge [above] node {$C$} (s_5)
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edge [right] node {$c$} (s_6)
98+
(s_4) edge [above] node {$c$} (s_6)
99+
edge [right] node {$C$} (s_7)
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;
101+
\end{tikzpicture}

‎tex/figures/GLR/LR0/complete.tex‎

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@@ -1,11 +1,4 @@
11
\begin{tikzpicture}[> = stealth,node distance=3.25cm, on grid, scale=0.8, every node/.style={scale=0.8}]
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\node[draw=none, fill=none] at (-1.4, 1.2) {0};
3-
\node[draw=none, fill=none] at (3.1, 0.55) {1};
4-
\node[draw=none, fill=none] at (7.1, 0.55) {2};
5-
\node[draw=none, fill=none] at (-1.4, -1.8) {3};
6-
\node[draw=none, fill=none] at (2.9, -2.5) {4};
7-
\node[draw=none, fill=none] at (6.7, -1.8) {5};
8-
\node[draw=none, fill=none] at (11, -2.5) {6};
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\node[r_state] (s_0)
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{
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$
@@ -53,6 +46,14 @@
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$ S \to a S b S \cdot$
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};
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49+
\node[num_state] at (s_0.north west) {0};
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\node[num_state] at (s_1.north west) {1};
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\node[num_state] at (s_2.north west) {2};
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\node[num_state] at (s_3.north west) {3};
53+
\node[num_state] at (s_4.north west) {4};
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\node[num_state] at (s_5.north west) {5};
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\node[num_state] at (s_6.north west) {6};
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\path[->]
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(s_0) edge [left] node {$a$} (s_3)
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edge [above] node {$S$} (s_1)

‎tex/figures/GLR/LR0/state0.tex‎

Lines changed: 2 additions & 1 deletion
Original file line numberDiff line numberDiff line change
@@ -1,5 +1,4 @@
11
\begin{tikzpicture}[> = stealth,node distance=3.25cm, on grid, scale=0.8, every node/.style={scale=0.8}]
2-
\node[draw=none, fill=none] at (-1.4, 1.2) {0};
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\node[r_state] (s_0)
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{
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$
@@ -10,4 +9,6 @@
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\end{aligned}
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$
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};
12+
13+
\node[num_state] at (s_0.north west) {0};
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\end{tikzpicture}

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