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\centerline{\bf CMSC 452 Project -- Part 1. Morally Due April 8}

\centerline{\bf LEO is in charge of the Project. Any Questions Go To Him} 

\section{Intro}

{\bf Point Of This Assignment} To learn about DFA Minimization and help prepare for Part 2 of the Project. 

\begin{enumerate}
\item Two DFA's are 'equivalent' if they recognize the same language.
\item Given a DFA, we want to know if we can somehow construct another DFA that recognizes the same language, with the minimum possible number of states.
\end{enumerate}
{\bf Can we do this?}
Yes! Through a process known as DFA minimization.\\ \\
{\bf Your task:}
\begin{itemize}
    \item Research DFA minimization. Here are some resources to get you started:
    \begin{itemize}
        \item Wikipedia: \url{https://en.wikipedia.org/wiki/DFA_minimization}
        \item G4G: \url{https://www.geeksforgeeks.org/minimization-of-dfa/}
        \item UC Davis: \url{https://www.cs.ucdavis.edu/~rogaway/classes/120/winter12/minimization.pdf}
    \end{itemize}
    These should suffice for the assignment, but feel free to use other resources as well.
    \item Answer the prompts under the {\bf{Assignment}} section based on your research.
\end{itemize}

\section{Assignment}
\begin{enumerate}
    \item Let $M = (Q, \Sigma, s, \delta, F)$ be a DFA,
    \begin{enumerate}
        \item Let $q$ and $q'$ be states in $Q$. In the context of DFA Minimization, what does it mean for $q$ to be non-distinguishable from $q'$?
        \item Suppose that we begin partitioning $Q$ by grouping together non-distinguishable states. Let $P_k$ be a partition of $Q$ and $\sigma \in \Sigma$. If $q$ and $q'$ belong to the same block in $P$ and $\delta(q, \sigma) \neq \delta(q', \sigma)$, will they still be in the same block in the next partition? Why or why not?
    \end{enumerate}
    \newpage
    \item Give pseudo-code that outputs the partition of non-distinguishable states from a DFA $M = (Q, \Sigma, s, \delta, F) $, i.e outputs the states for the minimized DFA: 
    \begin{verbatim}
        new_states(M=(Q, Sigma, s, delta, F)):
    \end{verbatim}
    \newpage
    \item  Give pseudo-code that outputs the new transition function for the minimized DFA of $M$ with new states $P$:
    \begin{verbatim}
        new_delta(M=(Q, Sigma, s, delta, F), P):
    \end{verbatim}
\end{enumerate}


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