From 3c276be550fb14fbb8108de310e3eab069ce716e Mon Sep 17 00:00:00 2001 From: breandan Date: Tue, 27 Feb 2024 16:36:35 -0500 Subject: [PATCH] color code levenshtein automaton --- latex/splash2024/nfa_cfg.tex | 205 +++++++++++++++++------------------ latex/splash2024/splash.pdf | Bin 558174 -> 558977 bytes latex/splash2024/splash.tex | 10 +- 3 files changed, 102 insertions(+), 113 deletions(-) diff --git a/latex/splash2024/nfa_cfg.tex b/latex/splash2024/nfa_cfg.tex index c3486386..70863781 100644 --- a/latex/splash2024/nfa_cfg.tex +++ b/latex/splash2024/nfa_cfg.tex @@ -8,134 +8,123 @@ ] \node[state, initial] (00) {$q_{0,0}$}; \node[state, right of=00] (10) {$q_{1,0}$}; - \node[state, right of=10] (20) {$q_{2,0}$}; - \node[state, right of=20] (30) {$q_{3,0}$}; - \node[right of=30] (40) {$\vphantom{\vdots}\cdots$}; - \node[accepting, state, right of=40] (n0) {$q_{n,0}$}; - - \node[state, above of=00, shift={(-0.7cm,-0.0cm)}] (01) {$q_{0,1}$}; - \node[state, right of=01] (11) {$q_{1,1}$}; - \node[state, right of=11] (21) {$q_{2,1}$}; - \node[state, right of=21] (31) {$q_{3,1}$}; - \node[right of=31] (41) {$\vphantom{\vdots}\cdots$}; - \node[accepting, state, right of=41] (n1) {$q_{n,1}$}; - -\node[above of=01, shift={(-0.7cm,-0.0cm)}] (0j) {$\mathmakebox[\widthof{$\cdots$}]{\vdots}$}; -\node[right of=0j] (1j) {$\mathmakebox[\widthof{$\cdots$}]{\vdots}$}; -\node[right of=1j] (2j) {$\mathmakebox[\widthof{$\cdots$}]{\vdots}$}; -\node[right of=2j] (3j) {$\mathmakebox[\widthof{$\cdots$}]{\vdots}$}; -\node[right of=3j] (4j) {$\iddots$}; -\node[accepting, right of=4j] (nj) {$\mathmakebox[\widthof{$\cdots$}]{\vdots}$}; - -\node[state, above of=0j, shift={(-0.7cm,0.0cm)}] (0k) {$q_{0,k}$}; -\node[state, right of=0k] (1k) {$q_{1,k}$}; -\node[state, right of=1k] (2k) {$q_{2,k}$}; -\node[state, right of=2k] (3k) {$q_{3,k}$}; -\node[right of=3k] (4k) {$\vphantom{\vdots}\cdots$}; -\node[accepting, state, right of=4k] (nk) {$q_{n,k}$}; + \node[accepting, state, right of=10] (20) {$q_{2,0}$}; + \node[accepting, state, right of=20] (30) {$q_{3,0}$}; + \node[accepting, state, right of=30] (40) {$q_{4,0}$}; + \node[accepting, state, right of=40] (50) {$q_{5,0}$}; + + \node[state, above of=00, shift={(-1.5cm,-0.0cm)}] (01) {$q_{0,1}$}; + \node[state, right of=01] (11) {$q_{1,1}$}; + \node[state, right of=11] (21) {$q_{2,1}$}; + \node[accepting, state, right of=21] (31) {$q_{3,1}$}; + \node[accepting, state, right of=31] (41) {$q_{4,1}$}; + \node[accepting, state, right of=41] (51) {$q_{5,1}$}; + +\node[state, above of=01, shift={(-1.5cm,-0.0cm)}] (0j) {$q_{0,2}$}; +\node[state, right of=0j] (1j) {$q_{1,2}$}; +\node[state, right of=1j] (2j) {$q_{2,2}$}; +\node[state, right of=2j] (3j) {$q_{3,2}$}; +\node[accepting, state, right of=3j] (4j) {$q_{4,2}$}; +\node[accepting, state, right of=4j] (5j) {$q_{5,2}$}; + +\node[state, above of=0j, shift={(-1.5cm,0.0cm)}] (0k) {$q_{0,3}$}; +\node[state, right of=0k] (1k) {$q_{1,3}$}; +\node[state, right of=1k] (2k) {$q_{2,3}$}; +\node[state, right of=2k] (3k) {$q_{3,3}$}; +\node[state, right of=3k] (4k) {$q_{4,3}$}; +\node[accepting, state, right of=4k] (5k) {$q_{5,3}$}; \draw [->] (00) edge[below] node{$\sigma_1$} (10); \draw [->] (10) edge[below] node{$\sigma_2$} (20); \draw [->] (20) edge[below] node{$\sigma_3$} (30); \draw [->] (30) edge[below] node{$\sigma_4$} (40); -\draw [->] (40) edge[below] node{$\sigma_n$} (n0); +\draw [->] (40) edge[below] node{$\sigma_5$} (50); \draw [->] (01) edge[below] node{$\sigma_1$} (11); \draw [->] (11) edge[below] node{$\sigma_2$} (21); \draw [->] (21) edge[below] node{$\sigma_3$} (31); \draw [->] (31) edge[below] node{$\sigma_4$} (41); -\draw [->] (41) edge[below] node{$\sigma_n$} (n1); +\draw [->] (41) edge[below] node{$\sigma_5$} (51); \draw [->] (0j) edge[below] node{$\sigma_1$} (1j); \draw [->] (1j) edge[below] node{$\sigma_2$} (2j); \draw [->] (2j) edge[below] node{$\sigma_3$} (3j); \draw [->] (3j) edge[below] node{$\sigma_4$} (4j); -\draw [->] (4j) edge[below] node{$\sigma_n$} (nj); +\draw [->] (4j) edge[below] node{$\sigma_5$} (5j); \draw [->] (0k) edge[below] node{$\sigma_1$} (1k); \draw [->] (1k) edge[below] node{$\sigma_2$} (2k); \draw [->] (2k) edge[below] node{$\sigma_3$} (3k); \draw [->] (3k) edge[below] node{$\sigma_4$} (4k); -\draw [->] (4k) edge[below] node{$\sigma_n$} (nk); - -\draw [->] (00) edge[left] node{$\cdot$} (11); -\draw [->] (10) edge[left] node{$\cdot$} (21); -\draw [->] (20) edge[left] node{$\cdot$} (31); -\draw [->] (30) edge[left] node{$\cdot$} (41); -\draw [->, blue] (30) edge[bend right, below] node{$\color{blue}\sigma_5$} (41); -\draw [->] (40) edge[ right] node{$\sigma_n$} (n1); -\draw [->] (40) edge[bend right, left] node{$\cdot$} (n1); - -\draw [->, red] (00) edge[bend left=2] node[east, shift={(-0.5cm,-0.8cm)}]{$\color{red}\sigma_3$} (3j); -\draw [->, red] (10) edge[bend left=2] node[east, shift={(-0.5cm,-0.8cm)}]{$\color{red}\sigma_4$} (4j); -%\draw [->, red] (20) edge[bend left=7] node[east, shift={(-0.7cm,-0.8cm)}]{$\color{red}\sigma_5$} (3j); -%\draw [->, red] (30) edge[bend left=7] node[east, shift={(-0.7cm,-0.8cm)}]{$\color{red}\sigma_6$} (4j); - -\draw [->] (01) edge[left] node{$\cdot$} (1j); -\draw [->] (11) edge[left] node{$\cdot$} (2j); -\draw [->] (21) edge[left] node{$\cdot$} (3j); -\draw [->] (31) edge[left] node{$\cdot$} (4j); -\draw [->, blue] (31) edge[bend right, below] node{$\color{blue}\sigma_5$} (4j); -\draw [->] (41) edge[ right] node{$\sigma_n$} (nj); -\draw [->] (41) edge[bend right, left] node{$\cdot$} (nj); - -\draw [->] (0j) edge[left] node{$\cdot$} (1k); -\draw [->] (1j) edge[left] node{$\cdot$} (2k); -\draw [->] (2j) edge[left] node{$\cdot$} (3k); -\draw [->] (3j) edge[left] node{$\cdot$} (4k); -\draw [->, blue] (3j) edge[bend right, below] node{$\color{blue}\sigma_5$} (4k); -\draw [->] (4j) edge[ right] node{$\sigma_n$} (nk); -\draw [->] (4j) edge[bend right, left] node{$\cdot$} (nk); - -\draw [->] (00) edge[bend left, left] node{$\cdot$} (01); -\draw [->] (10) edge[bend left, left] node{$\cdot$} (11); -\draw [->] (20) edge[bend left, left] node{$\cdot$} (21); -\draw [->] (30) edge[bend left, left] node{$\cdot$} (31); -\draw [->] (40) edge[right] node{$\cdot$} (41); -\draw [->] (n0) edge[bend right, right] node{$\cdot$} (n1); - -\draw [->] (01) edge[bend left, left] node{$\cdot$} (0j); -\draw [->] (11) edge[bend left, left] node{$\cdot$} (1j); -\draw [->] (21) edge[bend left, left] node{$\cdot$} (2j); -\draw [->] (31) edge[bend left, left] node{$\cdot$} (3j); -\draw [->] (41) edge[right] node{$\cdot$} (4j); -\draw [->] (n1) edge[bend right, right] node{$\cdot$} (nj); - -\draw [->] (0j) edge[bend left, left] node{$\cdot$} (0k); -\draw [->] (1j) edge[bend left, left] node{$\cdot$} (1k); -\draw [->] (2j) edge[bend left, left] node{$\cdot$} (2k); -\draw [->] (3j) edge[bend left, left] node{$\cdot$} (3k); -\draw [->] (4j) edge[right] node{$\cdot$} (4k); -\draw [->] (nj) edge[bend right, right] node{$\cdot$} (nk); - -\draw [->, blue] (00) edge[below] node[shift={(-0.7cm,-0.5cm)}]{$\color{blue}\sigma_2$} (21); -\draw [->, blue] (10) edge[below] node[shift={(-0.7cm,-0.5cm)}]{$\color{blue}\sigma_3$} (31); -\draw [->, blue] (20) edge[below] node[shift={(-0.7cm,-0.5cm)}]{$\color{blue}\sigma_4$} (41); - -\draw [->, blue] (01) edge[below] node[shift={(-0.7cm,-0.5cm)}]{$\color{blue}\sigma_2$} (2j); -\draw [->, blue] (11) edge[below] node[shift={(-0.7cm,-0.5cm)}]{$\color{blue}\sigma_3$} (3j); -\draw [->, blue] (21) edge[below] node[shift={(-0.7cm,-0.5cm)}]{$\color{blue}\sigma_4$} (4j); - -\draw [->, blue] (0j) edge[below] node[shift={(-0.7cm,-0.5cm)}]{$\color{blue}\sigma_2$} (2k); -\draw [->, blue] (1j) edge[below] node[shift={(-0.7cm,-0.5cm)}]{$\color{blue}\sigma_3$} (3k); -\draw [->, blue] (2j) edge[below] node[shift={(-0.7cm,-0.5cm)}]{$\color{blue}\sigma_4$} (4k); +\draw [->] (4k) edge[below] node{$\sigma_5$} (5k); + +\draw [->] (00) edge[left] node{$\phantom{\cdot}$} (11); +\draw [->] (10) edge[left] node{$\phantom{\cdot}$} (21); +\draw [->] (20) edge[left] node{$\phantom{\cdot}$} (31); +\draw [->] (30) edge[left] node{$\phantom{\cdot}$} (41); +\draw [->] (40) edge[left] node{$\phantom{\cdot}$} (51); + +% Super-knight arcs +\draw [->, red] (00) edge[bend left=3] node[east, shift={(-0.3cm,-0.65cm)}]{$\color{red}\sigma_3$} (3j); +\draw [->, red] (10) edge[bend left=3] node[east, shift={(-0.3cm,-0.65cm)}]{$\color{red}\sigma_4$} (4j); +\draw [->, red] (20) edge[bend left=3] node[east, shift={(-0.3cm,-0.65cm)}]{$\color{red}\sigma_5$} (5j); +\draw [->, red] (01) edge[bend left=3] node[east, shift={(-0.3cm,-0.65cm)}]{$\color{red}\sigma_3$} (3k); +\draw [->, red] (11) edge[bend left=3] node[east, shift={(-0.3cm,-0.65cm)}]{$\color{red}\sigma_4$} (4k); +\draw [->, red] (21) edge[bend left=3] node[east, shift={(-0.3cm,-0.65cm)}]{$\color{red}\sigma_5$} (5k); + +\draw [->, violet] (00) edge[bend right=1] node[east, shift={(0cm,0.35cm)}]{$\color{violet}\sigma_4$} (4k); +\draw [->, violet] (10) edge[bend right=1] node[east, shift={(0cm,0.35cm)}]{$\color{violet}\sigma_5$} (5k); + +\draw [->] (01) edge[left] node{$\phantom{\cdot}$} (1j); +\draw [->] (11) edge[left] node{$\phantom{\cdot}$} (2j); +\draw [->] (21) edge[left] node{$\phantom{\cdot}$} (3j); +\draw [->] (31) edge[left] node{$\phantom{\cdot}$} (4j); +\draw [->] (41) edge[left] node{$\phantom{\cdot}$} (5j); + +\draw [->] (0j) edge[left] node{$\phantom{\cdot}$} (1k); +\draw [->] (1j) edge[left] node{$\phantom{\cdot}$} (2k); +\draw [->] (2j) edge[left] node{$\phantom{\cdot}$} (3k); +\draw [->] (3j) edge[left] node{$\phantom{\cdot}$} (4k); +\draw [->] (4j) edge[left] node{$\phantom{\cdot}$} (5k); + +\draw [->] (00) edge[bend left=10, left] node{$\phantom{\cdot}$} (01); +\draw [->] (10) edge[bend left=10, left] node{$\phantom{\cdot}$} (11); +\draw [->] (20) edge[bend left=10, left] node{$\phantom{\cdot}$} (21); +\draw [->] (30) edge[bend left=10, left] node{$\phantom{\cdot}$} (31); +\draw [->] (40) edge[bend left=10, left] node{$\phantom{\cdot}$} (41); +\draw [->] (50) edge[bend left=10, left] node{$\phantom{\cdot}$} (51); + +\draw [->] (01) edge[bend left=10, left] node{$\phantom{\cdot}$} (0j); +\draw [->] (11) edge[bend left=10, left] node{$\phantom{\cdot}$} (1j); +\draw [->] (21) edge[bend left=10, left] node{$\phantom{\cdot}$} (2j); +\draw [->] (31) edge[bend left=10, left] node{$\phantom{\cdot}$} (3j); +\draw [->] (41) edge[bend left=10, left] node{$\phantom{\cdot}$} (4j); +\draw [->] (51) edge[bend left=10, left] node{$\phantom{\cdot}$} (5j); + +\draw [->] (0j) edge[bend left=10, left] node{$\phantom{\cdot}$} (0k); +\draw [->] (1j) edge[bend left=10, left] node{$\phantom{\cdot}$} (1k); +\draw [->] (2j) edge[bend left=10, left] node{$\phantom{\cdot}$} (2k); +\draw [->] (3j) edge[bend left=10, left] node{$\phantom{\cdot}$} (3k); +\draw [->] (4j) edge[bend left=10, left] node{$\phantom{\cdot}$} (4k); +\draw [->] (5j) edge[bend left=10, left] node{$\phantom{\cdot}$} (5k); + +\draw [->, blue] (00) edge[bend left=2,below] node[shift={(-0.7cm,-0.5cm)}]{$\color{blue}\sigma_2$} (21); +\draw [->, blue] (10) edge[bend left=2,below] node[shift={(-0.7cm,-0.5cm)}]{$\color{blue}\sigma_3$} (31); +\draw [->, blue] (20) edge[bend left=2,below] node[shift={(-0.7cm,-0.5cm)}]{$\color{blue}\sigma_4$} (41); +\draw [->, blue] (30) edge[bend left=2,below] node[shift={(-0.7cm,-0.5cm)}]{$\color{blue}\sigma_5$} (51); + +\draw [->, blue] (01) edge[bend left=2,below] node[shift={(-0.7cm,-0.5cm)}]{$\color{blue}\sigma_2$} (2j); +\draw [->, blue] (11) edge[bend left=2,below] node[shift={(-0.7cm,-0.5cm)}]{$\color{blue}\sigma_3$} (3j); +\draw [->, blue] (21) edge[bend left=2,below] node[shift={(-0.7cm,-0.5cm)}]{$\color{blue}\sigma_4$} (4j); +\draw [->, blue] (31) edge[bend left=2,below] node[shift={(-0.7cm,-0.5cm)}]{$\color{blue}\sigma_4$} (5j); + +\draw [->, blue] (0j) edge[bend left=2,below] node[shift={(-0.7cm,-0.5cm)}]{$\color{blue}\sigma_2$} (2k); +\draw [->, blue] (1j) edge[bend left=2,below] node[shift={(-0.7cm,-0.5cm)}]{$\color{blue}\sigma_3$} (3k); +\draw [->, blue] (2j) edge[bend left=2,below] node[shift={(-0.7cm,-0.5cm)}]{$\color{blue}\sigma_4$} (4k); +\draw [->, blue] (3j) edge[bend left=2,below] node[shift={(-0.7cm,-0.5cm)}]{$\color{blue}\sigma_5$} (5k); %https://tex.stackexchange.com/a/20986/139648 -\draw [decorate,decoration={brace,amplitude=10pt,raise=10pt,mirror}] (00.south west) -- (n0.south east) node[midway,yshift=-3em]{\textbf{String length}}; -\draw [decorate,decoration={brace,amplitude=10pt,raise=20pt}] (00.south west) -- (0k.north west) node[midway,xshift=-40pt,rotate=-75]{\textbf{Edit distance}}; +\draw [decorate,decoration={brace,amplitude=10pt,raise=10pt,mirror}] (00.south west) -- (50.south east) node[midway,yshift=-3em]{\textbf{String length}}; +\draw [decorate,decoration={brace,amplitude=10pt,raise=20pt}] (00.south west) -- (0k.north west) node[midway,xshift=-1.2cm,yshift=-0.6cm,rotate=-60]{\textbf{Edit distance}}; \end{tikzpicture} -} -%\end{minipage} -%\hfill -%\begin{minipage}[l]{5 cm} -%\centering -%\underline{CFG}\vspace{2pt} -%\begin{align*} -%S &\Rightarrow \{\cdot \in Q \mid \delta(\cdot, q_{n,0}) \leq k\}\\ -%+ &\Rightarrow \{\cdot \in \Sigma\}\\ -%\big\{q_{i, j} &\Rightarrow \{q_{i, j-1}+\} \mid i, j \in [0, n]\times[1, k]\big\}\\ -%\big\{q_{i, j} &\Rightarrow \{q_{i-1, j-1}+\}\mid i, j\in[1, n]\times [1, k]\big\}\\ -%\big\{q_{i, j} &\Rightarrow \{q_{i-1, j} \sigma_i \}\mid i, j \in [1, n]\times[0, k]\big\} \\ -%\big\{q_{i, j} &\Rightarrow \{q_{i-2, j-1} \sigma_i\} \mid i, j \in [2, n]\times[1, k] \big\}\\ -%\end{align*} -%\end{minipage} \ No newline at end of file +} \ No newline at end of file diff --git a/latex/splash2024/splash.pdf b/latex/splash2024/splash.pdf index 73d4cba7ac0150f13d8a64f840c3e4f3a7695b95..2c141cbd22babda41a948a16b47136cef0ef4823 100644 GIT binary patch delta 55360 zcmX6^V{o8Nv)zrov6GE$+qO2gy|I%gwr$(CZCe}L+BkRL@BTVxdb+E6y1J%LbM+Lm4XGq%YFS`Lz3qm8)IE(I|LLD_8i(8;p?AaPnv5l>m 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