\RequirePackage{luatex85}
\usepackage[utf8]{inputenc}
\usepackage{amsmath, amssymb, amsfonts, accents}
-\usetikzlibrary{graphdrawing, graphs, arrows, shapes, automata, calc}
+\usetikzlibrary{graphdrawing, graphs, arrows, shapes, automata, calc, decorations}
\usegdlibrary{trees, layered}
\usepackage{stix}
\node[state, accepting, right of = b2] (c) {$y$};
\path
- (b2) edge node {$1 / \epsilon$} (c)
+ (b2) edge node {$2 / \epsilon$} (c)
;
- \draw (b2) .. controls ($ (b2) + (1, 1.5) $) and ($ (b1) + (-1, 1.5) $) .. node [above] {$2 / \epsilon$} (b1);
+ \draw (b2) .. controls ($ (b2) + (0.7, 1.5) $) and ($ (b1) + (-0.7, 1.5) $) .. node [above] {$1 / \epsilon$} (b1);
\node [label={[label distance=0.2in, below left]270:\large{(i)}}] (a) {};
\node [label={[label distance=0.2in, below right]270:
$\begin{aligned}
, rounded corners=4
, inner sep = 2pt
, outer sep = 0pt
- , node distance = 0.35in]
+ , node distance = 0.37in]
\newcommand{\zz}{0.06in}
-\newcommand{\ww}{1pt}
-\begin{scope}[xshift=-0.5in, yshift=-8.3in]
- %\footnotesize
- \scriptsize
+\begin{scope}[xshift=-0.8in, yshift=-8.5in]
+ \footnotesize
+ %\scriptsize
% ((epsilon|a*)((a|epsilon){0,3}))
\node[state, right of = z0] (x15) {$4$};
\node[state, above right of = x15] (x16) {$5$};
- \node[state, above right of = x16, xshift = \zz, yshift = -\zz] (x17) {$6$};
+ \node[state, fill=lightgray, above right of = x16, xshift = \zz, yshift = -\zz] (x17) {$6$};
\node[state, below right of = x16, xshift = \zz, yshift = +\zz] (x18) {$8$};
\node[state, right of = x17] (x19) {$7$};
\node[state, right of = x18] (x20) {$9$};
\node[state, right of = x22] (y15) {$12$};
\node[state, above right of = y15] (y16) {$13$};
- \node[state, above right of = y16, xshift = \zz, yshift = -\zz] (y17) {$14$};
+ \node[state, fill=lightgray, above right of = y16, xshift = \zz, yshift = -\zz] (y17) {$14$};
\node[state, below right of = y16, xshift = \zz, yshift = +\zz] (y18) {$16$};
\node[state, right of = y17] (y19) {$15$};
\node[state, right of = y18] (y20) {$17$};
\node[state, right of = y22] (z15) {$20$};
\node[state, above right of = z15] (z16) {$21$};
- \node[state, above right of = z16, xshift = \zz, yshift = -\zz] (z17) {$22$};
+ \node[state, fill=lightgray, above right of = z16, xshift = \zz, yshift = -\zz] (z17) {$22$};
\node[state, below right of = z16, xshift = \zz, yshift = +\zz] (z18) {$24$};
\node[state, right of = z17] (z19) {$23$};
\node[state, right of = z18] (z20) {$25$};
\node[state, below right of = z19, xshift = \zz, yshift = +\zz] (z21) {$26$};
\node[state, below right of = z21] (z22) {$27$};
- \node[state, right of = z22] (z23) {$28$};
- \node[state, below right of = z23] (x23) {$29$};
+ \node[state, below right of = z22] (x23) {$28$};
- \node[state, above right of = x23] (x2) {$30$};
- \node[state, above right of = x2, xshift = \zz, yshift = -\zz] (x4) {$31$};
- \node[state, below right of = x2, xshift = \zz, yshift = +\zz, draw=none] (x3) {$$};
- \node[state, right of = x3] (x3X) {$35$};
- \node[state, right of = x4] (x5) {$32$};
+ \node[state, above right of = x23] (x2) {$29$};
+ \node[state, above right of = x2, xshift = \zz, yshift = -\zz] (x4X) {$30$};
+ \node[state, above right of = x4X] (x4) {$31$};
+ \node[state, below right of = x2, xshift = \zz, yshift = +\zz, draw=none] (x3) {};
+ \node[state, right of = x3] (x3Y) {$36$};
+ \node[state, above right of = x3Y] (x3X) {$37$};
+ \node[state, fill=lightgray, right of = x4] (x5) {$32$};
\node[state, right of = x5] (x6) {$33$};
\node[state, right of = x6] (x7) {$34$};
- \node[state, below right of = x7, xshift = \zz, yshift = +\zz] (x12) {$37$};
- \node[state, below left of = x12, xshift = -\zz, yshift = +\zz, draw=none] (x13) {$$};
- \node[state, left of = x13] (x13X) {$36$};
- \node[state, below right of = x12] (x14) {$38$};
+ \node[state, below right of = x7] (x7X) {$35$};
+ \node[state, below right of = x7X, xshift = \zz, yshift = +\zz] (x12) {$40$};
+ \node[state, below left of = x12, xshift = -\zz, yshift = +\zz, draw=none] (x13) {};
+ \node[state, left of = x13] (x13X) {$39$};
+ \node[state, above left of = x13X] (x13Y) {$38$};
+ \node[state, below right of = x12] (x14) {$41$};
- \node[state, accepting, below right of = x14] (x24) {$39$};
+ \node[state, fill=lightgray, accepting, below right of = x14] (x24) {$42$};
\path
(x0) edge node [above left] {$1/1$} (x1)
(x15) edge node [above left] {$1/5$} (x16)
(x16) edge [bend left] node [above] {$1/\epsilon$} (x17)
(x16) edge [bend right] node [above, near end] {$2/\epsilon$} (x18)
- (x17) edge [line width=\ww] node {$a/\epsilon$} (x19)
+ (x17) edge node {$a/\epsilon$} (x19)
(x18) edge node {$1/\epsilon$} (x20)
(x19) edge [bend left] node [above] {$1/\epsilon$} (x21)
(x20) edge [bend right] node [above, near start] {$1/\epsilon$} (x21)
(y15) edge node [above left] {$1/5$} (y16)
(y16) edge [bend left] node [above] {$1/\epsilon$} (y17)
(y16) edge [bend right] node [above, near end] {$2/\epsilon$} (y18)
- (y17) edge [line width=\ww] node {$a/\epsilon$} (y19)
+ (y17) edge node {$a/\epsilon$} (y19)
(y18) edge node {$1/\epsilon$} (y20)
(y19) edge [bend left] node [above] {$1/\epsilon$} (y21)
(y20) edge [bend right] node [above, near start] {$1/\epsilon$} (y21)
(z15) edge node [above left] {$1/5$} (z16)
(z16) edge [bend left] node [above] {$1/\epsilon$} (z17)
(z16) edge [bend right] node [above, near end] {$2/\epsilon$} (z18)
- (z17) edge [line width=\ww] node {$a/\epsilon$} (z19)
+ (z17) edge node {$a/\epsilon$} (z19)
(z18) edge node {$1/\epsilon$} (z20)
(z19) edge [bend left] node [above] {$1/\epsilon$} (z21)
(z20) edge [bend right] node [above, near start] {$1/\epsilon$} (z21)
(z21) edge node [above right] {$1/6$} (z22)
- (z22) edge node [above] {$1/\epsilon$} (z23)
- (z23) edge node [above right] {$1/4$} (x23)
+ (z22) edge node [above right] {$1/4$} (x23)
(x23) edge node [below right] {$1/7$} (x2)
- (x2) edge [bend left] node [above] {$1/\epsilon$} (x4)
- (x2) edge [bend right = 20] node [above] {$2/\epsilon$} (x3X)
+ (x2) edge [bend left] node [above] {$1/\epsilon$} (x4X)
+ (x2) edge [bend right = 20] node [above] {$2/-\!\!9$} (x3Y)
+ (x4X) edge node {$1/9$} (x4)
(x4) edge node [above] {$1/\epsilon$} (x5)
- (x5) edge [line width=\ww] node [above] {$a/\epsilon$} (x6)
- (x6) edge node [above] {$1/\epsilon$} (x7)
- (x7) edge [bend left] node [above] {$1/\epsilon$} (x12)
- (x3X) edge node [above] {$1/\epsilon$} (x13X)
+ (x5) edge node [above] {$a/\epsilon$} (x6)
+ (x6) edge node [above] {$2/\epsilon$} (x7)
+ (x7) edge node {$1/10$} (x7X)
+ (x7X) edge [bend left] node {$1/-\!\!11$} (x12)
+ (x3Y) edge node {$1/11$} (x3X)
+ (x3X) edge node [above] {$1/\epsilon$} (x13Y)
+ (x13Y) edge node {$1/12$} (x13X)
(x13X) edge [bend right = 20] node [above] {$1/\epsilon$} (x12)
(x12) edge node [above right] {$1/8$} (x14)
(x14) edge node [above right] {$1/2$} (x24)
;
- \draw (y22) .. controls ($ (y22) + (0.5, -0.5) $) and ($ (z22) + (-0.5, -0.5) $) .. node [above] {$1/\epsilon$} (z22);
+ \draw (y22) .. controls ($ (y22) + (0.5, -0.6) $) and ($ (z22) + (-0.5, -0.6) $) .. node [above] {$1/\epsilon$} (z22);
\draw (x22) .. controls ($ (x22) + (0.8, -0.8) $) and ($ (z22) + (-0.8, -0.8) $) .. node [above, near start] {$1/\epsilon$} (z22);
- \draw (z0) .. controls ($ (z0) + (1.0, -1.0) $) and ($ (z23) + (-1.0, -1.0) $) .. node [above, near start] {$2/-\!\!5$} (z23);
- \draw (x6) .. controls ($ (x6) + (0.4, 0.8) $) and ($ (x5) + (-0.4, 0.8) $) .. node [above] {$2/\epsilon$} (x5);
+ \draw (z0) .. controls ($ (z0) + (1.0, -1.0) $) and ($ (z22) + (-1.0, -1.0) $) .. node [above, near start] {$2/-\!\!5$} (z22);
+ \draw (x6) .. controls ($ (x6) + (0.3, 0.8) $) and ($ (x5) + (-0.3, 0.8) $) .. node [above] {$1/\epsilon$} (x5);
\draw (x4) .. controls ($ (x4) + (0.6, -0.6) $) and ($ (x7) + (-0.6, -0.6) $) .. node [above] {$2/\epsilon$} (x7);
- \path (x0) edge [draw=none] node [below=0.1in, midway] {\large{(k)} -- TNFA for RE $(a|\epsilon)^{0,3}(a^{0,\infty}|\epsilon)$} (x24);
+ \path (x0) edge [draw=none] node [below=0.1in, midway] {\large{(k)} -- TNFA for RE $(a|\epsilon)^{0,3}((a^{0,\infty})|(\epsilon))$} (x24);
+
+\end{scope}
+
+\iffalse
+\tikzstyle{every node}=[draw=none, rectangle, rounded corners, node distance = 0.2in];
+\begin{scope}[xshift=-0.5in, yshift=-9in]
+ %\footnotesize
+ \scriptsize
+
+ \node (n1) {$1$};
+ \node [right of = n1] (n2) {$2$};
+ \node [right of = n2] (n3) {$3$};
+ \node [right of = n3] (n4) {$4$};
+ \node [right of = n4] (n5) {$5$};
+ \node [right of = n5, draw] (n6) {$6$};
+
+ \node [below of = n6] (n8) {$8$};
+ \node [right of = n8] (n9) {$9$};
+ \node [right of = n9] (n10) {$10$};
+ \node [right of = n10] (n11) {$11$};
+ \node [right of = n11] (n27) {$27$};
+ \node [right of = n27] (n29) {$28$};
+ \node [right of = n29] (n30) {$29$};
+ \node [right of = n30] (n31) {$30$};
+ \node [right of = n31, draw] (n32) {$31$};
+
+ \node [below of = n32] (n34) {$33$};
+ \node [right of = n34] (n37) {$36$};
+ \node [right of = n37] (n38) {$37$};
+ \node [right of = n38, draw] (n39) {$38$};
+
+ \node [below of = n31] (n31X) {};
+ \node [below of = n34] (n35X) {$34$};
+ \node [right of = n35X] (n36X) {$35$};
+ \node [right of = n36X, draw, cross out] (n37X) {$36$};
+
+ \node [below of = n30] (n28Y) {};
+ \node [below of = n28Y] (n28YY) {};
+ \node [below of = n28YY] (n12Y) {$12$};
+ \node [right of = n12Y] (n13Y) {$13$};
+ \node [right of = n13Y, draw] (n14Y) {$14$};
+
+ \node [below of = n14Y] (n16Z) {$16$};
+ \node [right of = n16Z] (n17Z) {$17$};
+ \node [right of = n17Z] (n18Z) {$18$};
+ \node [right of = n18Z] (n19Z) {$19$};
+ \node [right of = n19Z, draw, cross out] (n27Z) {$27$};
+
+ \node [below of = n27Z] (n20W) {$20$};
+ \node [right of = n20W] (n21W) {$21$};
+ \node [right of = n21W, draw] (n22W) {$22$};
+
+ \node [below of = n27] (n27U) {};
+ \node [below of = n27U] (n27UU) {};
+ \node [below of = n27UU] (n27UUU) {};
+ \node [below of = n27UUU] (n27UUUU) {};
+ \node [below of = n27UUUU] (n27UUUUU) {};
+ \node [below of = n27UUUUU, draw, cross out] (n27UUUUU) {$27$};
+
+ \draw [-] (n1) -- (n2) -- (n3) -- (n4) -- (n5) -- (n6);
+ \draw [-] (n5) -- (n8) -- (n9) -- (n10) -- (n11) -- (n27) -- (n29) -- (n30) -- (n31) -- (n32);
+ \draw [-] (n31) -- (n34) -- (n37) -- (n38) -- (n39);
+ \draw [-] (n30) -- (n35X) -- (n36X) -- (n37X);
+ \draw [-] (n11) -- (n12Y) -- (n13Y) -- (n14Y);
+ \draw [-] (n13Y) --(n16Z) -- (n17Z) -- (n18Z) -- (n19Z) -- (n27Z);
+ \draw [-] (n19Z) -- (n20W) -- (n21W) -- (n22W);
+ \draw [-] (n3) -- (n27UUUUU);
+
+MATCH a.
+THIS ALLOWS TO SHOW ALL RULES OF COMPARISON (some on the 1st epsilon-closure, some on second).
+
\end{scope}
+\fi
\end{tikzpicture}