mirror of
https://github.com/kuhyx/WUT_Computer_Science.git
synced 2026-07-04 14:43:08 +02:00
Finishing first two tasks
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|
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|
||||
Package: placeins 2005/04/18 v 2.2
|
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|
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File: tikzlibraryautomata.code.tex 2020/12/27 v3.1.8b (3.1.8b)
|
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(/usr/share/texlive/texmf-dist/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibraryshapes.multipart.code.tex
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@ -1,6 +1,7 @@
|
||||
\documentclass{report}
|
||||
\usepackage{amsmath}
|
||||
\usepackage{tikz}
|
||||
\usepackage[section]{placeins}
|
||||
\usetikzlibrary{automata, arrows.meta, positioning}
|
||||
|
||||
|
||||
@ -29,7 +30,7 @@ We are given following regular expression:
|
||||
\end{enumerate}
|
||||
|
||||
\section{Building NFA using Thompson construction algorithm}
|
||||
\begin{figure}
|
||||
\begin{figure}[!htb]
|
||||
\centering
|
||||
\begin{tikzpicture} [node distance = 2cm, on grid, auto]
|
||||
|
||||
@ -42,7 +43,7 @@ We are given following regular expression:
|
||||
\caption{Operator 'a'} \label{fig:operatorA}
|
||||
\end{figure}
|
||||
|
||||
\begin{figure}
|
||||
\begin{figure}[!htb]
|
||||
\centering
|
||||
\begin{tikzpicture} [node distance = 2cm, on grid, auto]
|
||||
|
||||
@ -55,7 +56,7 @@ We are given following regular expression:
|
||||
\caption{Operator 'b'} \label{fig:operatorB}
|
||||
\end{figure}
|
||||
|
||||
\begin{figure}
|
||||
\begin{figure}[!htb]
|
||||
\centering
|
||||
\begin{tikzpicture} [node distance = 2cm, on grid, auto]
|
||||
|
||||
@ -78,11 +79,11 @@ We are given following regular expression:
|
||||
\caption{Operator '$a^*$'} \label{fig:operatorAstar}
|
||||
\end{figure}
|
||||
|
||||
\begin{figure}
|
||||
\begin{figure}[!htb]
|
||||
\centering
|
||||
\begin{tikzpicture} [node distance = 2cm, on grid, auto]
|
||||
|
||||
\node (q6) [state, initial, initial text = {}] {$q_6$};
|
||||
\node (q6) [state, initial, initial text = {}] {$q_2$};
|
||||
\node (q0) [state, right = of q6] {$q_4$};
|
||||
\node (q1) [state, right = of q0] {$q_0$};
|
||||
\node (q2) [state, right = of q1] {$q_1$};
|
||||
@ -104,7 +105,7 @@ We are given following regular expression:
|
||||
\caption{Operator '$ba^*$'} \label{fig:operatorbastar}
|
||||
\end{figure}
|
||||
|
||||
\begin{figure}
|
||||
\begin{figure}[!htb]
|
||||
\centering
|
||||
\begin{tikzpicture} [node distance = 2cm, on grid, auto]
|
||||
|
||||
@ -134,13 +135,13 @@ We are given following regular expression:
|
||||
\caption{Operator '$ba^*b$'} \label{fig:operatorbastarb}
|
||||
\end{figure}
|
||||
|
||||
\begin{figure}
|
||||
\begin{figure}[!htb]
|
||||
\centering
|
||||
\begin{tikzpicture} [node distance = 2cm, on grid, auto]
|
||||
|
||||
\node (q8) [state, initial, initial text = {}] {$q_8$};
|
||||
\node (q9) [state, right = of q8] {$q_9$};
|
||||
\node (q4) [state, right = of q9] {$q_{4}$};
|
||||
\node (q8) [state, initial, initial text = {}] {$q_2$};
|
||||
\node (q9) [state, right = of q8] {$q_3$};
|
||||
\node (q4) [state, accepting, right = of q9] {$q_{4}$};
|
||||
|
||||
\path [-stealth, thick]
|
||||
(q8) edge node {$b$} (q9);
|
||||
@ -152,12 +153,12 @@ We are given following regular expression:
|
||||
\caption{Operator '$bb$'} \label{fig:operatorbb}
|
||||
\end{figure}
|
||||
|
||||
\begin{figure}
|
||||
\begin{figure}[!htb]
|
||||
\centering
|
||||
\begin{tikzpicture} [node distance = 2cm, on grid, auto]
|
||||
|
||||
\node (q8) [state, initial, initial text = {}] {$q_8$};
|
||||
\node (q9) [state, right = of q8] {$q_9$};
|
||||
\node (q8) [state, initial, initial text = {}] {$q_2$};
|
||||
\node (q9) [state, right = of q8] {$q_3$};
|
||||
\node (q0) [state, right = of q9] {$q_4$};
|
||||
\node (q1) [state, right = of q0] {$q_0$};
|
||||
\node (q2) [state, right = of q1] {$q_1$};
|
||||
@ -182,7 +183,7 @@ We are given following regular expression:
|
||||
\caption{Operator '$bba^*$'} \label{fig:operatorbbastar}
|
||||
\end{figure}
|
||||
|
||||
\begin{figure}
|
||||
\begin{figure}[!htb]
|
||||
\centering
|
||||
\begin{tikzpicture} [node distance = 2cm, on grid, auto]
|
||||
|
||||
@ -195,16 +196,14 @@ We are given following regular expression:
|
||||
\node (q3) [state, right = of q2] {$q_5$};
|
||||
% ba*b
|
||||
\node (q4) [state, below right = of q10] {$q_6$};
|
||||
\node (q5) [state, right = of q4] {$q_4$};
|
||||
\node (q6) [state, right = of q5] {$q_0$};
|
||||
\node (q7) [state, right = of q6] {$q_1$};
|
||||
\node (q8) [state, right = of q7] {$q_5$};
|
||||
\node (q5) [state, right = of q4] {$q_8$};
|
||||
\node (q6) [state, right = of q5] {$q_9$};
|
||||
\node (q7) [state, right = of q6] {$q_{12}$};
|
||||
\node (q8) [state, right = of q7] {$q_{13}$};
|
||||
\node (q9) [state, right = of q8] {$q_7$};
|
||||
|
||||
\node (q11) [state, accepting, above right = of q9] {$q_{11}$};
|
||||
|
||||
|
||||
|
||||
\path [-stealth, thick]
|
||||
(q10) edge node {$\varepsilon$} (q0);
|
||||
|
||||
@ -246,7 +245,7 @@ We are given following regular expression:
|
||||
\caption{Operator '$a^*+ba^*b$'} \label{fig:operatorastarOrbastarb}
|
||||
\end{figure}
|
||||
|
||||
\begin{figure}
|
||||
\begin{figure}[!htb]
|
||||
\begin{tikzpicture} [node distance = 1.5cm, on grid, auto]
|
||||
|
||||
\node (q12) [state, initial, initial text = {}] {$q_{12}$};
|
||||
@ -260,16 +259,43 @@ We are given following regular expression:
|
||||
\node (q3) [state, right = of q2] {$q_5$};
|
||||
% ba*b
|
||||
\node (q4) [state, below right = of q10] {$q_6$};
|
||||
\node (q5) [state, right = of q4] {$q_4$};
|
||||
\node (q6) [state, right = of q5] {$q_0$};
|
||||
\node (q7) [state, right = of q6] {$q_1$};
|
||||
\node (q8) [state, right = of q7] {$q_5$};
|
||||
\node (q5) [state, right = of q4] {$q_8$};
|
||||
\node (q6) [state, right = of q5] {$q_9$};
|
||||
\node (q7) [state, right = of q6] {$q_{12}$};
|
||||
\node (q8) [state, right = of q7] {$q_{13}$};
|
||||
\node (q9) [state, right = of q8] {$q_7$};
|
||||
|
||||
\node (q11) [state, above right = of q9] {$q_{11}$};
|
||||
|
||||
\node (q13) [state, accepting, below right = of q11] {$q_{13}$};
|
||||
|
||||
% bba*
|
||||
\node (q14) [state, below right = of q12] {$q_{14}$};
|
||||
\node (q15) [state, right = of q14] {$q_{15}$};
|
||||
\node (q16) [state, right = of q15] {$q_{16}$};
|
||||
\node (q17) [state, right = of q16] {$q_{17}$};
|
||||
\node (q18) [state, right = of q17] {$q_{18}$};
|
||||
\node (q19) [state, right = of q18] {$q_{19}$};
|
||||
|
||||
\path [-stealth, thick]
|
||||
(q12) edge node {$b$} (q14);
|
||||
|
||||
\path [-stealth, thick]
|
||||
(q14) edge node {$b$} (q15);
|
||||
\path [-stealth, thick]
|
||||
(q15) edge node {$b$} (q16);
|
||||
\path [-stealth, thick]
|
||||
(q16) edge node {$\varepsilon$} (q17);
|
||||
\path [-stealth, thick]
|
||||
(q16) edge [bend right] node[below left] {$\varepsilon$} (q19);
|
||||
\path [-stealth, thick]
|
||||
(q17) edge node {$a$} (q18);
|
||||
\path [-stealth, thick]
|
||||
(q18) edge node {$\varepsilon$} (q19);
|
||||
\path [-stealth, thick]
|
||||
(q18) [bend left] edge node {$\varepsilon$} (q17);
|
||||
\path [-stealth, thick]
|
||||
(q19) edge [bend right] node {$b$} (q13);
|
||||
|
||||
\path [-stealth, thick]
|
||||
(q12) edge node {$\varepsilon$} (q10);
|
||||
@ -300,7 +326,7 @@ We are given following regular expression:
|
||||
\path [-stealth, thick]
|
||||
(q5) edge node {$\varepsilon$} (q6);
|
||||
\path [-stealth, thick]
|
||||
(q5) edge [bend right] node[below left] {$\varepsilon$} (q8);
|
||||
(q5) edge [bend left] node[below left] {$\varepsilon$} (q8);
|
||||
\path [-stealth, thick]
|
||||
(q6) edge node {a} (q7);
|
||||
\path [-stealth, thick]
|
||||
@ -320,6 +346,106 @@ We are given following regular expression:
|
||||
\caption{Operator '$a^*+ba^*b + bba^*$'} \label{fig:final}
|
||||
\end{figure}
|
||||
|
||||
\begin{figure}[!htb]
|
||||
\begin{tikzpicture} [node distance = 1.5cm, on grid, auto]
|
||||
|
||||
\node (q12) [state, initial, initial text = {}] {$q_{0}$};
|
||||
|
||||
\node (q10) [state, above right = of q12] {$q_{1}$};
|
||||
% a*
|
||||
|
||||
\node (q0) [state, above right = of q10] {$q_3$};
|
||||
\node (q1) [state, right = of q0] {$q_6$};
|
||||
\node (q2) [state, right = of q1] {$q_9$};
|
||||
\node (q3) [state, right = of q2] {$q_{12}$};
|
||||
% ba*b
|
||||
\node (q4) [state, below right = of q10] {$q_4$};
|
||||
\node (q5) [state, right = of q4] {$q_7$};
|
||||
\node (q6) [state, right = of q5] {$q_{10}$};
|
||||
\node (q7) [state, right = of q6] {$q_{13}$};
|
||||
\node (q8) [state, right = of q7] {$q_{15}$};
|
||||
\node (q9) [state, right = of q8] {$q_{17}$};
|
||||
|
||||
\node (q11) [state, above right = of q9] {$q_{18}$};
|
||||
|
||||
\node (q13) [state, accepting, below right = of q11] {$q_{19}$};
|
||||
|
||||
% bba*
|
||||
\node (q14) [state, below right = of q12] {$q_{2}$};
|
||||
\node (q15) [state, right = of q14] {$q_{5}$};
|
||||
\node (q16) [state, right = of q15] {$q_{8}$};
|
||||
\node (q17) [state, right = of q16] {$q_{11}$};
|
||||
\node (q18) [state, right = of q17] {$q_{14}$};
|
||||
\node (q19) [state, right = of q18] {$q_{16}$};
|
||||
|
||||
\path [-stealth, thick]
|
||||
(q12) edge node {$b$} (q14);
|
||||
|
||||
\path [-stealth, thick]
|
||||
(q14) edge node {$b$} (q15);
|
||||
\path [-stealth, thick]
|
||||
(q15) edge node {$b$} (q16);
|
||||
\path [-stealth, thick]
|
||||
(q16) edge node {$\varepsilon$} (q17);
|
||||
\path [-stealth, thick]
|
||||
(q16) edge [bend right] node[below left] {$\varepsilon$} (q19);
|
||||
\path [-stealth, thick]
|
||||
(q17) edge node {$a$} (q18);
|
||||
\path [-stealth, thick]
|
||||
(q18) edge node {$\varepsilon$} (q19);
|
||||
\path [-stealth, thick]
|
||||
(q18) [bend left] edge node {$\varepsilon$} (q17);
|
||||
\path [-stealth, thick]
|
||||
(q19) edge [bend right] node {$b$} (q13);
|
||||
|
||||
\path [-stealth, thick]
|
||||
(q12) edge node {$\varepsilon$} (q10);
|
||||
|
||||
\path [-stealth, thick]
|
||||
(q10) edge node {$\varepsilon$} (q0);
|
||||
|
||||
\path [-stealth, thick]
|
||||
(q10) edge node {$\varepsilon$} (q4);
|
||||
|
||||
% a*
|
||||
\path [-stealth, thick]
|
||||
(q0) edge node {$\varepsilon$} (q1);
|
||||
\path [-stealth, thick]
|
||||
(q0) edge [bend right] node[below left] {$\varepsilon$} (q3);
|
||||
\path [-stealth, thick]
|
||||
(q1) edge node {a} (q2);
|
||||
\path [-stealth, thick]
|
||||
(q2) [bend left] edge node {$\varepsilon$} (q1);
|
||||
\path [-stealth, thick]
|
||||
(q2) edge node {$\varepsilon$} (q3);
|
||||
\path [-stealth, thick]
|
||||
(q3) edge node {$\varepsilon$} (q11);
|
||||
|
||||
% ba*b
|
||||
\path [-stealth, thick]
|
||||
(q4) edge node {$b$} (q5);
|
||||
\path [-stealth, thick]
|
||||
(q5) edge node {$\varepsilon$} (q6);
|
||||
\path [-stealth, thick]
|
||||
(q5) edge [bend left] node[below left] {$\varepsilon$} (q8);
|
||||
\path [-stealth, thick]
|
||||
(q6) edge node {a} (q7);
|
||||
\path [-stealth, thick]
|
||||
(q7) [bend left] edge node {$\varepsilon$} (q6);
|
||||
\path [-stealth, thick]
|
||||
(q7) edge node {$\varepsilon$} (q8);
|
||||
\path [-stealth, thick]
|
||||
(q8) edge node {$b$} (q9);
|
||||
\path [-stealth, thick]
|
||||
(q9) edge node {$\varepsilon$} (q11);
|
||||
\path [-stealth, thick]
|
||||
(q11) edge node {$\varepsilon$} (q13);
|
||||
|
||||
% bba*
|
||||
|
||||
\end{tikzpicture}
|
||||
\caption{Operator '$a^*+ba^*b + bba^*$' - changed names of states} \label{fig:final}
|
||||
\end{figure}
|
||||
|
||||
\section{Transforming NFA into DFA using subset algorithm}
|
||||
\section{Constructing minimal state DFA}
|
||||
|
||||
Loading…
Reference in New Issue
Block a user