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+% Created 2023-09-20 Wed 15:58
+% 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{Question One}
+\label{sec:org859695d}
+\subsection{Partition Refinement}
+\label{sec:org55dda6e}
+\{ \{q\textsubscript{0}, q\textsubscript{1}, q\textsubscript{3}\}, \{q\textsubscript{2}, q\textsubscript{4}\} \}
+
+S\textsubscript{1} = \{(q\textsubscript{0}, q\textsubscript{1}), (q\textsubscript{0}, q\textsubscript{3}), (q\textsubscript{1}, q\textsubscript{3})\}
+S\textsubscript{2} = \{(q\textsubscript{2}, q\textsubscript{4})\}
+
+\(\delta\)(q\textsubscript{0}, 1) = q\textsubscript{3} \(\in\) S\textsubscript{1}
+\(\delta\)(q\textsubscript{1}, 1) = q\textsubscript{4} \(\in\) S\textsubscript{2}
+
+(q\textsubscript{0}, q\textsubscript{1}) need to be split
+
+\(\delta\)(q\textsubscript{0}, 0) = q\textsubscript{1} \(\in\) S\textsubscript{1}
+\(\delta\)(q\textsubscript{3}, 0) = q\textsubscript{2} \(\in\) S\textsubscript{2}
+
+(q\textsubscript{1}, q\textsubscript{2}) need to be split
+
+\(\forall\) x \(\in\) \(\Sigma\), \(\delta\)(q\textsubscript{1}, x) = \(\delta\)(q\textsubscript{3}, x)
+so \{q\textsubscript{1}, q\textsubscript{3}\} does not need to be split
+
+In S\textsubscript{2}, \(\delta\)(q\textsubscript{2}, 0) \(\in\) S\textsubscript{1} and \(\delta\)(q\textsubscript{4}, 0) \(\in\) S\textsubscript{2}, thus need to be split
+
+Finally, the refined partitions are \{\{q\textsubscript{0}\}, \{q\textsubscript{1}, q\textsubscript{3}\}, \{q\textsubscript{2}\}, \{q\textsubscript{4}\}\}
+
+\subsection{Minimization}
+\label{sec:org870d4d3}
+\begin{center}
+\begin{tabular}{rllll}
+a \(\in\) \(\Sigma\) & \{q\textsubscript{0}\} & \{q\textsubscript{1}, q\textsubscript{3}\} & \{q\textsubscript{2}\} & \{q\textsubscript{4}\}\\[0pt]
+0 & \{q\textsubscript{1}, q\textsubscript{3}\} & \{q\textsubscript{2}\} & \{q\textsubscript{1}, q\textsubscript{3}\} & \{q\textsubscript{4}\}\\[0pt]
+1 & \{q\textsubscript{1}, q\textsubscript{3}\} & \{q\textsubscript{4}\} & \{q\textsubscript{4}\} & \{q\textsubscript{4}\}\\[0pt]
+\end{tabular}
+\end{center}
+
+with d\textsubscript{0} = \{q\textsubscript{0}\}, d\textsubscript{1} = \{q\textsubscript{1}, q\textsubscript{3}\}, d\textsubscript{2} = \{q\textsubscript{2}\} and d\textsubscript{3} = \{q\textsubscript{4}\}
+
+\begin{center}
+\includegraphics[width=350px]{./img/min_dfa.png}
+\end{center}
+
+\section{Question Two}
+\label{sec:orga1d2018}
+See attached python
+\end{document}
+\ No newline at end of file