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project.aux
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\relax
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project.fdb_latexmk
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(/usr/share/texlive/texmf-dist/tex/generic/pgf/modules/pgfmodulematrix.code.tex
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File: pgfmodulematrix.code.tex 2020/12/27 v3.1.8b (3.1.8b)
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)
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(/usr/share/texlive/texmf-dist/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibrarytopaths.code.tex
|
||||
File: tikzlibrarytopaths.code.tex 2020/12/27 v3.1.8b (3.1.8b)
|
||||
))) (/usr/share/texlive/texmf-dist/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibraryautomata.code.tex
|
||||
File: tikzlibraryautomata.code.tex 2020/12/27 v3.1.8b (3.1.8b)
|
||||
(/usr/share/texlive/texmf-dist/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibraryshapes.multipart.code.tex
|
||||
File: tikzlibraryshapes.multipart.code.tex 2020/12/27 v3.1.8b (3.1.8b)
|
||||
(/usr/share/texlive/texmf-dist/tex/generic/pgf/libraries/shapes/pgflibraryshapes.multipart.code.tex
|
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File: pgflibraryshapes.multipart.code.tex 2020/12/27 v3.1.8b (3.1.8b)
|
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|
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|
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))) (/usr/share/texlive/texmf-dist/tex/generic/pgf/libraries/pgflibraryarrows.meta.code.tex
|
||||
File: pgflibraryarrows.meta.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/tikzlibrarypositioning.code.tex
|
||||
File: tikzlibrarypositioning.code.tex 2020/12/27 v3.1.8b (3.1.8b)
|
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) (/usr/share/texlive/texmf-dist/tex/latex/l3backend/l3backend-pdftex.def
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File: l3backend-pdftex.def 2020-01-29 L3 backend support: PDF output (pdfTeX)
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\l__color_backend_stack_int=\count285
|
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\l__pdf_internal_box=\box80
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) (./project.aux)
|
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\openout1 = `project.aux'.
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\everyMPtoPDFconversion=\toks34
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) (/usr/share/texlive/texmf-dist/tex/latex/epstopdf-pkg/epstopdf-base.sty
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Package: epstopdf-base 2020-01-24 v2.11 Base part for package epstopdf
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Package epstopdf-base Info: Redefining graphics rule for `.eps' on input line 485.
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File: epstopdf-sys.cfg 2010/07/13 v1.3 Configuration of (r)epstopdf for TeX Live
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[]
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[1] [2] [3] (./project.aux) )
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Output written on project.pdf (4 pages, 86781 bytes).
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BIN
project.pdf
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project.pdf
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project.synctex.gz
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@ -0,0 +1,329 @@
|
||||
\documentclass{report}
|
||||
\usepackage{amsmath}
|
||||
\usepackage{tikz}
|
||||
\usetikzlibrary{automata, arrows.meta, positioning}
|
||||
|
||||
|
||||
|
||||
\setcounter{chapter}{+1}
|
||||
|
||||
\title{Language and Automata, Assignment 1}
|
||||
\author{Krzysztof Rudnicki\\ Student number: 307585}
|
||||
\date{\today}
|
||||
|
||||
|
||||
\begin{document}
|
||||
\maketitle
|
||||
|
||||
\section{Regular expression}
|
||||
We are given following regular expression:
|
||||
\[ a^* + ba^*b + bba^*\]
|
||||
|
||||
\section{Examples of accepted strings}
|
||||
\begin{enumerate}
|
||||
\item $ \varepsilon $
|
||||
\item a
|
||||
\item bab
|
||||
\item bba
|
||||
\item bb
|
||||
\end{enumerate}
|
||||
|
||||
\section{Building NFA using Thompson construction algorithm}
|
||||
\begin{figure}
|
||||
\centering
|
||||
\begin{tikzpicture} [node distance = 2cm, on grid, auto]
|
||||
|
||||
\node (q0) [state, initial, initial text = {}] {$q_0$};
|
||||
\node (q1) [state, accepting, right = of q0] {$q_1$};
|
||||
|
||||
\path [-stealth, thick]
|
||||
(q0) edge node {$\varepsilon$} (q1);
|
||||
\end{tikzpicture}
|
||||
\caption{Operator 'a'} \label{fig:operatorA}
|
||||
\end{figure}
|
||||
|
||||
\begin{figure}
|
||||
\centering
|
||||
\begin{tikzpicture} [node distance = 2cm, on grid, auto]
|
||||
|
||||
\node (q0) [state, initial, initial text = {}] {$q_2$};
|
||||
\node (q1) [state, accepting, right = of q0] {$q_3$};
|
||||
|
||||
\path [-stealth, thick]
|
||||
(q0) edge node {$\varepsilon$} (q1);
|
||||
\end{tikzpicture}
|
||||
\caption{Operator 'b'} \label{fig:operatorB}
|
||||
\end{figure}
|
||||
|
||||
\begin{figure}
|
||||
\centering
|
||||
\begin{tikzpicture} [node distance = 2cm, on grid, auto]
|
||||
|
||||
\node (q0) [state, initial, initial text = {}] {$q_4$};
|
||||
\node (q1) [state, right = of q0] {$q_0$};
|
||||
\node (q2) [state, right = of q1] {$q_1$};
|
||||
\node (q3) [state, accepting, right = of q2] {$q_5$};
|
||||
|
||||
\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);
|
||||
\end{tikzpicture}
|
||||
\caption{Operator '$a^*$'} \label{fig:operatorAstar}
|
||||
\end{figure}
|
||||
|
||||
\begin{figure}
|
||||
\centering
|
||||
\begin{tikzpicture} [node distance = 2cm, on grid, auto]
|
||||
|
||||
\node (q6) [state, initial, initial text = {}] {$q_6$};
|
||||
\node (q0) [state, right = of q6] {$q_4$};
|
||||
\node (q1) [state, right = of q0] {$q_0$};
|
||||
\node (q2) [state, right = of q1] {$q_1$};
|
||||
\node (q3) [state, accepting, right = of q2] {$q_5$};
|
||||
|
||||
\path [-stealth, thick]
|
||||
(q6) edge node {$b$} (q0);
|
||||
\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);
|
||||
\end{tikzpicture}
|
||||
\caption{Operator '$ba^*$'} \label{fig:operatorbastar}
|
||||
\end{figure}
|
||||
|
||||
\begin{figure}
|
||||
\centering
|
||||
\begin{tikzpicture} [node distance = 2cm, on grid, auto]
|
||||
|
||||
\node (q6) [state, initial, initial text = {}] {$q_6$};
|
||||
\node (q0) [state, right = of q6] {$q_4$};
|
||||
\node (q1) [state, right = of q0] {$q_0$};
|
||||
\node (q2) [state, right = of q1] {$q_1$};
|
||||
\node (q3) [state, right = of q2] {$q_5$};
|
||||
\node (q7) [state, accepting, right = of q3] {$q_7$};
|
||||
|
||||
\path [-stealth, thick]
|
||||
(q6) edge node {$b$} (q0);
|
||||
\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 {$b$} (q7);
|
||||
|
||||
\end{tikzpicture}
|
||||
\caption{Operator '$ba^*b$'} \label{fig:operatorbastarb}
|
||||
\end{figure}
|
||||
|
||||
\begin{figure}
|
||||
\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] {$q_{4}$};
|
||||
|
||||
\path [-stealth, thick]
|
||||
(q8) edge node {$b$} (q9);
|
||||
\path [-stealth, thick]
|
||||
(q9) edge node {$b$} (q4);
|
||||
|
||||
|
||||
\end{tikzpicture}
|
||||
\caption{Operator '$bb$'} \label{fig:operatorbb}
|
||||
\end{figure}
|
||||
|
||||
\begin{figure}
|
||||
\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 (q0) [state, right = of q9] {$q_4$};
|
||||
\node (q1) [state, right = of q0] {$q_0$};
|
||||
\node (q2) [state, right = of q1] {$q_1$};
|
||||
\node (q3) [state, accepting, right = of q2] {$q_5$};
|
||||
|
||||
\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]
|
||||
(q8) edge node {$b$} (q9);
|
||||
\path [-stealth, thick]
|
||||
(q9) edge node {$b$} (q4);
|
||||
\end{tikzpicture}
|
||||
\caption{Operator '$bba^*$'} \label{fig:operatorbbastar}
|
||||
\end{figure}
|
||||
|
||||
\begin{figure}
|
||||
\centering
|
||||
\begin{tikzpicture} [node distance = 2cm, on grid, auto]
|
||||
|
||||
\node (q10) [state, initial, initial text = {}] {$q_{10}$};
|
||||
% a*
|
||||
|
||||
\node (q0) [state, above right = of q10] {$q_4$};
|
||||
\node (q1) [state, right = of q0] {$q_0$};
|
||||
\node (q2) [state, right = of q1] {$q_1$};
|
||||
\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 (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);
|
||||
|
||||
\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 right] 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);
|
||||
\end{tikzpicture}
|
||||
\caption{Operator '$a^*+ba^*b$'} \label{fig:operatorastarOrbastarb}
|
||||
\end{figure}
|
||||
|
||||
\begin{figure}
|
||||
\begin{tikzpicture} [node distance = 1.5cm, on grid, auto]
|
||||
|
||||
\node (q12) [state, initial, initial text = {}] {$q_{12}$};
|
||||
|
||||
\node (q10) [state, above right = of q12] {$q_{10}$};
|
||||
% a*
|
||||
|
||||
\node (q0) [state, above right = of q10] {$q_4$};
|
||||
\node (q1) [state, right = of q0] {$q_0$};
|
||||
\node (q2) [state, right = of q1] {$q_1$};
|
||||
\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 (q9) [state, right = of q8] {$q_7$};
|
||||
|
||||
\node (q11) [state, above right = of q9] {$q_{11}$};
|
||||
|
||||
\node (q13) [state, accepting, below right = of q11] {$q_{13}$};
|
||||
|
||||
|
||||
\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 right] 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 '$a^*+ba^*b + bba^*$'} \label{fig:final}
|
||||
\end{figure}
|
||||
|
||||
|
||||
\section{Transforming NFA into DFA using subset algorithm}
|
||||
\section{Constructing minimal state DFA}
|
||||
|
||||
|
||||
|
||||
\end{document}
|
||||
Loading…
Reference in New Issue
Block a user