\documentclass[11pt]{article}
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\title{\vspace{-3ex}\bf Pushdown Automata\\[2ex]
\rm\normalsize CS 311, Fall 2015}
\date{}
\author{}

\begin{document}
\maketitle

\paragraph{Exercise 1}
\begin{enumerate}[a)]
    \item Describe in english the language generated by the following Grammar
        \begin{align*}
            S &\rightarrow aSb \;|\; bY \;|\; Ya \\
            Y &\rightarrow bY \;|\; Ya \:|\; \varepsilon
        \end{align*}
    \vspace{\stretch{1}}
    \item Draw a state diagram for a PDA that recognizes the language generated by the grammar in part $a$. 
        (You may use the simplified machine that pushes multiple symbols to the stack at a time.)
    \vspace{\stretch{3}}
\end{enumerate}

\newpage
\paragraph{Exercise 2}
\begin{enumerate}[a)]
    \item Describe in english the language generated by the following Grammar
        \begin{align*}
            A &\rightarrow BA \;|\; \varepsilon \\
            B &\rightarrow aBb \;|\; \varepsilon
        \end{align*}
    \vspace{\stretch{1}}
    \item Draw a state diagram for a PDA that recognizes the language generated by the grammar in part $a$. 
        (You may use the simplified machine that pushes multiple symbols to the stack at a time.)
    \vspace{\stretch{3}}
\end{enumerate}

\end{document}
