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\author{Lizzy Hunt}
\date{\today}
\title{Assignment Three}
\hypersetup{
 pdfauthor={Lizzy Hunt},
 pdftitle={Assignment Three},
 pdfkeywords={},
 pdfsubject={},
 pdfcreator={Emacs 28.2 (Org mode 9.6.1)}, 
 pdflang={English}}
\begin{document}

\maketitle
\setlength\parindent{0pt}

\section{Question One}
\label{sec:org48bca57}
\subsection{a}
\label{sec:orgede0650}
\begin{center}
\includegraphics[width=250px]{./1a.excalidraw.png}
\end{center}
\subsection{b}
\label{sec:org59deb20}
\begin{center}
\includegraphics[width=250px]{./1b.excalidraw.png}
\end{center}
\subsection{c}
\label{sec:orgfdb1a94}
\begin{center}
\includegraphics[width=250px]{./1c.excalidraw.png}
\end{center}
\subsection{d}
\label{sec:org48223e7}
\begin{center}
\includegraphics[width=250px]{./1d.excalidraw.png}
\end{center}
\subsection{e}
\label{sec:orga20ed32}
\begin{center}
\includegraphics[width=250px]{./1e.excalidraw.png}
\end{center}
\subsection{f}
\label{sec:org14bd212}
\begin{center}
\includegraphics[width=200px]{./1f.excalidraw.png}
\end{center}

\section{Question Two}
\label{sec:org576a7f2}
\begin{center}
\begin{tabular}{rlll}
State & a & b & e\\[0pt]
0 & \(\phi\) & \(\phi\) & \{1, 3\}\\[0pt]
1 & \{2, 4\} & \{4\} & \(\phi\)\\[0pt]
2 & \{2\} & \(\phi\) & \(\phi\)\\[0pt]
3 & \(\phi\) & \{4\} & \(\phi\)\\[0pt]
4 & \(\phi\) & \{4\} & \(\phi\)\\[0pt]
\end{tabular}
\end{center}

\section{Question Three}
\label{sec:org998bd71}
\begin{center}
\begin{tabular}{rrr}
State & a & b\\[0pt]
0 & 1 & 0\\[0pt]
1 & 1 & 2\\[0pt]
2 & 1 & 3\\[0pt]
3 & 1 & 0\\[0pt]
\end{tabular}
\end{center}

\section{Question Four}
\label{sec:org7c30c40}
\subsection{a}
\label{sec:org487ab26}
\begin{center}
\includegraphics[width=350px]{./4a.excalidraw.png}
\end{center}
\subsection{b}
\label{sec:org41a1b03}
\begin{center}
\begin{tabular}{lllll}
DFA State & NFA States & a & b & c\\[0pt]
d\textsubscript{0} & \{s\textsubscript{0}, s\textsubscript{1}, s\textsubscript{2}, s\textsubscript{5}, s\textsubscript{9}\} & \{s\textsubscript{3}, s\textsubscript{6}\} (d\textsubscript{1}) & s\textsubscript{e} & s\textsubscript{e}\\[0pt]
d\textsubscript{1} & \{s\textsubscript{3}, s\textsubscript{6}\} & s\textsubscript{e} & \{s\textsubscript{4}, s\textsubscript{8}, s\textsubscript{9}, s\textsubscript{1}, s\textsubscript{2}, s\textsubscript{5}\} (d\textsubscript{2}) & \{s\textsubscript{7}, s\textsubscript{8}, s\textsubscript{9}, s\textsubscript{1}, s\textsubscript{2}, s\textsubscript{5}\} (d\textsubscript{3})\\[0pt]
d\textsubscript{2} & \{s\textsubscript{4}, s\textsubscript{8}, s\textsubscript{9}, s\textsubscript{1}, s\textsubscript{2}, s\textsubscript{5}\} & \{s\textsubscript{3}, s\textsubscript{6}\} (d\textsubscript{1}) & s\textsubscript{e} & s\textsubscript{e}\\[0pt]
d\textsubscript{3} & \{s\textsubscript{7}, s\textsubscript{8}, s\textsubscript{9}, s\textsubscript{1}, s\textsubscript{2}, s\textsubscript{5}\} & \{s\textsubscript{3}, s\textsubscript{6}\} (d\textsubscript{1}) & s\textsubscript{e} & s\textsubscript{e}\\[0pt]
\end{tabular}
\end{center}

\begin{center}
\includegraphics[width=200px]{./4b.excalidraw.png}
\end{center}
\subsection{c}
\label{sec:orgf8b74f7}
\begin{center}
\begin{tabular}{llll}
partition & a & b & c\\[0pt]
\{d\textsubscript{1}\}, \{d\textsubscript{0}, d\textsubscript{2}, d\textsubscript{3}\} & \{d\textsubscript{0}, d\textsubscript{2}, d\textsubscript{3}\} \(\Rightarrow\) \{d\textsubscript{1}, d\textsubscript{0}, d\textsubscript{0}\} & \{d\textsubscript{0}, d\textsubscript{2}, d\textsubscript{3}\} \(\Rightarrow\) \{-, -, -\} & \{d\textsubscript{0}, d\textsubscript{2}, d\textsubscript{3}\} \(\Rightarrow\) \{-, -, -\}\\[0pt]
\{d\textsubscript{1}\}, \{d\textsubscript{0}\}, \{d\textsubscript{2}, d\textsubscript{3}\} & \{d\textsubscript{2}, d\textsubscript{3}\} \(\Rightarrow\) \{d\textsubscript{0}, d\textsubscript{0}\} & \{d\textsubscript{2}, d\textsubscript{3}\} \(\Rightarrow\) \{-, -\} & \{d\textsubscript{2}, d\textsubscript{3}\} \(\Rightarrow\) \{-, -\}\\[0pt]
\end{tabular}
\end{center}

\begin{center}
\includegraphics[width=200px]{./4c.excalidraw.png}
\end{center}

\section{Question Five}
\label{sec:org8639475}
\subsection{regex 1}
\label{sec:org6ec41c1}
\subsubsection{NFA}
\label{sec:org4702761}
\begin{center}
\includegraphics[width=350px]{./51a.excalidraw.png}
\end{center}

\subsubsection{DFA}
\label{sec:org1f48afb}
\begin{center}
\begin{tabular}{llll}
DFA State & NFA States & 1 & 0\\[0pt]
d\textsubscript{0} & \{s\textsubscript{0}, s\textsubscript{1}, s\textsubscript{2}, s\textsubscript{4}, s\textsubscript{7}\} & \{s\textsubscript{1}, s\textsubscript{2}, s\textsubscript{3}, s\textsubscript{4}, s\textsubscript{6}, s\textsubscript{7}\} (d\textsubscript{1}) & \{s\textsubscript{1}, s\textsubscript{2}, s\textsubscript{4}, s\textsubscript{5}, s\textsubscript{6}, s\textsubscript{7}\} (d\textsubscript{2})\\[0pt]
d\textsubscript{1} & \{s\textsubscript{1}, s\textsubscript{2}, s\textsubscript{3}, s\textsubscript{4}, s\textsubscript{6}, s\textsubscript{7}\} & d\textsubscript{1} & d\textsubscript{2}\\[0pt]
d\textsubscript{2} & \{s\textsubscript{1}, s\textsubscript{2}, s\textsubscript{4}, s\textsubscript{5}, s\textsubscript{6}, s\textsubscript{7}\} & d\textsubscript{1} & d\textsubscript{2}\\[0pt]
\end{tabular}
\end{center}

\begin{center}
\includegraphics[width=200px]{./51b.excalidraw.png}
\end{center}

\subsubsection{Minimization}
\label{sec:orgbd13a9a}
\begin{center}
\begin{tabular}{lrr}
partition & 1 & 0\\[0pt]
\{d\textsubscript{0}, d\textsubscript{1}, d\textsubscript{2}\} & \{d\textsubscript{0}, d\textsubscript{1}, d\textsubscript{2}\} \(\Rightarrow\) \{d\textsubscript{1}, d\textsubscript{1}, d\textsubscript{1}\} & \{d\textsubscript{0}, d\textsubscript{1}, d\textsubscript{2}\} \(\Rightarrow\) \{d\textsubscript{2}, d\textsubscript{2}, d\textsubscript{2}\}\\[0pt]
\end{tabular}
\end{center}

\begin{center}
\includegraphics[width=75px]{./51c.excalidraw.png}
\end{center}

\subsection{regex 2}
\label{sec:org65aa1cc}
\subsubsection{NFA}
\label{sec:org0a8dd3a}
\begin{center}
\includegraphics[width=350px]{./52a.excalidraw.png}
\end{center}
\subsubsection{DFA}
\label{sec:orgbf87fa0}
\begin{center}
\begin{tabular}{llll}
DFA State & NFA States & 1 & 0\\[0pt]
d\textsubscript{0} & \{s\textsubscript{0}, s\textsubscript{1}, s\textsubscript{2}, s\textsubscript{3}, s\textsubscript{5}, s\textsubscript{11}, s\textsubscript{6}, s\textsubscript{12} \} & \{s\textsubscript{1}, s\textsubscript{2}, s\textsubscript{3}, s\textsubscript{5}, s\textsubscript{6}, s\textsubscript{7}, s\textsubscript{8}, s\textsubscript{10}, s\textsubscript{11}, s\textsubscript{12}\} (d\textsubscript{1}) & \{s\textsubscript{1}, s\textsubscript{2}, s\textsubscript{3}, s\textsubscript{4}, s\textsubscript{5}, s\textsubscript{11}, s\textsubscript{6}, s\textsubscript{12}\} (d\textsubscript{2})\\[0pt]
d\textsubscript{1} & \{s\textsubscript{1}, s\textsubscript{2}, s\textsubscript{3}, s\textsubscript{5}, s\textsubscript{6}, s\textsubscript{7}, s\textsubscript{8}, s\textsubscript{10}, s\textsubscript{11}, s\textsubscript{12}\} & d\textsubscript{1} & \{s\textsubscript{1}, s\textsubscript{2}, s\textsubscript{3}, s\textsubscript{4}, s\textsubscript{5}, s\textsubscript{9}, s\textsubscript{11}, s\textsubscript{6}, s\textsubscript{12}\} (d\textsubscript{3})\\[0pt]
d\textsubscript{2} & \{s\textsubscript{1}, s\textsubscript{2}, s\textsubscript{3}, s\textsubscript{4}, s\textsubscript{5}, s\textsubscript{11}, s\textsubscript{6}\} & d\textsubscript{1} & d\textsubscript{2}\\[0pt]
d\textsubscript{3} & \{s\textsubscript{1}, s\textsubscript{2}, s\textsubscript{3}, s\textsubscript{4}, s\textsubscript{5}, s\textsubscript{9}, s\textsubscript{11}, s\textsubscript{6}, s\textsubscript{12}\} & d\textsubscript{1} & d\textsubscript{2}\\[0pt]
\end{tabular}
\end{center}

\begin{center}
\includegraphics[width=150px]{./52b.excalidraw.png}
\end{center}

\subsubsection{Minimization}
\label{sec:orgba6f5c6}
\begin{center}
\begin{tabular}{lrr}
partition & 1 & 0\\[0pt]
\{d\textsubscript{0}, d\textsubscript{1}, d\textsubscript{2}, d\textsubscript{3}\} & \{d\textsubscript{0}, d\textsubscript{1}, d\textsubscript{2}, d\textsubscript{3}\} \(\Rightarrow\) \{d\textsubscript{1}, d\textsubscript{1}, d\textsubscript{1}, d\textsubscript{1}\} & \{d\textsubscript{0}, d\textsubscript{1}, d\textsubscript{2}, d\textsubscript{3}\} \(\Rightarrow\) \{d\textsubscript{2}, d\textsubscript{3}, d\textsubscript{2}, d\textsubscript{2}\}\\[0pt]
\end{tabular}
\end{center}

\begin{center}
\includegraphics[width=100px]{./52c.excalidraw.png}
\end{center}

\section{Question Six}
\label{sec:org7b91bcb}
\subsection{a}
\label{sec:orgb412f3c}
\subsubsection{DFA}
\label{sec:org4ae1ae3}
\begin{center}
\includegraphics[width=350px]{./6a.excalidraw.png}
\end{center}

\subsubsection{catMap}
\label{sec:org443dec8}
\begin{verbatim}
{
  '-': 'sign',
  '+': 'sign',
  [0-9]: 'digit',
  'e': 'scntfc'
}
\end{verbatim}

\subsubsection{transMap}
\label{sec:org77c35dc}
\begin{verbatim}
{
  's0': {
    'sign': 's1',
    'digit': 's2',
  },
  's1': {
    'digit': 's2',
  },
  's2': {
    'digit': 's2',
    'scntfc': 's3',
  },
  's3': {
    'sign': 's4',
    'digit': 's5',
  },
  's4': {
    'digit': 's6',
  },
  's5': {
    'digit': 's6',
  },
  's6': {
    'digit': 's6',
  },
}
\end{verbatim}

\subsubsection{tokenTypes}
\label{sec:orgefb9ab0}
\begin{verbatim}
{
  's2': 'integer',
  's6': 'integer,
}
\end{verbatim}
\subsection{b}
\label{sec:org6479f00}
\subsubsection{DFA}
\label{sec:org3c2c109}
\begin{center}
\includegraphics[width=200px]{./6b.excalidraw.png}
\end{center}

\subsubsection{catMap}
\label{sec:org5fb6951}
\begin{verbatim}
{
  [a-zA-Z]: 'letter',
  '_': 'letter',
  [0-9]: 'digit',
}
\end{verbatim}

\subsubsection{transMap}
\label{sec:org51968cd}
\begin{verbatim}
{
  's1': {
    'letter': 's2'
  },
  's2': {
    'letter': 's2',
    'digit': 's2',
  },
}
\end{verbatim}

\subsection{c}
\label{sec:orgaadecbc}
\subsubsection{DFA}
\label{sec:orgbc936b3}
\begin{center}
\includegraphics[width=400px]{./6c.excalidraw.png}
\end{center}

\subsubsection{catMap}
\label{sec:org0f61017}
\begin{verbatim}
{
  [^(\n)*/]: 'nonc',
  '\n': 'newline',
  'eof': 'eof',
  '/': 'slash',
  '*': 'star'
}
\end{verbatim}
\subsubsection{transMap}
\label{sec:orge8e62ef}
\begin{verbatim}
{
  's0': {
    'slash': 's1',
  },
  's1': {
    'slash': 's2',
    'star': 's4',
  },
  's2': {
    'nonc': 's2',
    'newline': 's3',
    'eof': 's3'
  },
  's4': {
    'nonc': 's4',
    'star': 's5',
  },
  's5': {
    'nonc': 's4',
    'newline': 's4',
    'slash': 's6'
  }
}
\end{verbatim}

\subsubsection{tokenType}
\label{sec:orgb999994}
\begin{verbatim}
{
  's3': 'singleLineComment',
  's6': 'multiLineComment',
}
\end{verbatim}
\end{document}