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% Created 2023-10-07 Sat 14:51
% Intended LaTeX compiler: pdflatex
\documentclass[11pt]{article}
\usepackage[utf8]{inputenc}
\usepackage[T1]{fontenc}
\usepackage{graphicx}
\usepackage{longtable}
\usepackage{wrapfig}
\usepackage{rotating}
\usepackage[normalem]{ulem}
\usepackage{amsmath}
\usepackage{amssymb}
\usepackage{capt-of}
\usepackage{hyperref}
\notindent \notag \usepackage{amsmath} \usepackage[a4paper,margin=1in,portrait]{geometry}
\author{Elizabeth Hunt}
\date{\today}
\title{HW 02}
\hypersetup{
pdfauthor={Elizabeth Hunt},
pdftitle={HW 02},
pdfkeywords={},
pdfsubject={},
pdfcreator={Emacs 28.2 (Org mode 9.7-pre)},
pdflang={English}}
\begin{document}
\maketitle
\setlength\parindent{0pt}
\section{Problem 1}
\label{sec:org41ad199}
\subsection{Part 1}
\label{sec:orgabe730c}
\(L(M) = \{ x | x \in \{ a \}^{*} \} \cup \{ x | x \in \{ b \}^{*} \} \cup \{ x | x \in \{ c \}^{*} \}\)
\subsection{Part 2}
\label{sec:orgb60fdea}
\begin{center}
\includegraphics[width=300px]{./img/p01_02.png}
\end{center}
\(Q = {q_0, q_1, q_2, q_3}\)
\(\Sigma = {a, b, c}\)
\(F = {q_1, q_2, q_3}\)
\(\delta(q_0, a) = {q_1}, \delta(q_1, a) = {q_1}, \delta(q_0, b) = {q_2}, \delta(q_2, b) = {q_2}, \delta(q_0, c) = {q_3}, \delta(q_3, c) = c\)
\section{Problem 2}
\label{sec:org9cf81d0}
\subsection{Work}
\label{sec:org2daff9f}
\begin{center}
\begin{tabular}{lll}
subset & 0 & 1\\[0pt]
\{q\textsubscript{0}\} & \{q\textsubscript{0}, q\textsubscript{1}\} & \{q\textsubscript{1}\}\\[0pt]
\{q\textsubscript{1}\} & \{q\textsubscript{2}\} & \{q\textsubscript{2}\}\\[0pt]
\{q\textsubscript{2}\} & \{q\textsubscript{2}\} & \{q\textsubscript{2}\}\\[0pt]
\{q\textsubscript{0}, q\textsubscript{1}\} & \{q\textsubscript{0}, q\textsubscript{1}\} \(\cup\) \{q\textsubscript{2}\} & \{q\textsubscript{1}\} \(\cup\) \{q\textsubscript{2}\}\\[0pt]
\{q\textsubscript{0}, q\textsubscript{1}, q\textsubscript{2}\} & \{q\textsubscript{0}, q\textsubscript{1}\} \(\cup\) \{q\textsubscript{2}\} \(\cup\) \{q\textsubscript{2}\} & \{q\textsubscript{1}\} \(\cup\) \{q\textsubscript{2}\} \(\cup\) \{q\textsubscript{2}\}\\[0pt]
\{q\textsubscript{1}, q\textsubscript{2}\} & \{q\textsubscript{2}\} \(\cup\) \{q\textsubscript{2}\} & \{q\textsubscript{2}\} \(\cup\) \{q\textsubscript{2}\}\\[0pt]
\end{tabular}
\end{center}
\subsection{Solution}
\label{sec:org7701586}
\begin{center}
\includegraphics[width=300px]{./img/p02.png}
\end{center}
\(Q_D = \{q_0, q_1, q_2, q_3, q_4, q_5\}\)
\(\Sigma = \{0, 1\}\)
\(F_D = \{q_1, q_2, q_4, q_5\}\)
\(\delta_D(q_0, 0) = q_1\)
\(\delta_D(q_0, 1) = q_2\)
\(\delta_D(q_1, 0) = q_5\)
\(\delta_D(q_1, q) = q_4\)
\(\delta_D(q_2, 0) = \delta_D(q_2, 1) = q_3\)
\(\delta_D(q_3, 0) = \delta_D(q_3, 1) = q_3\)
\(\delta_D(q_4, 0) = \delta_D(q_4, 1) = q_4\)
\(\delta_D(q_5, 0) = q_5\)
\(\delta_D(q_5, 1} = q_4\)
\section{Problem 3}
\label{sec:orge1c9402}
See attached python
\end{document}
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