%
% Assignment 2e for CS3530 Computational Theory:
% Context-free Languages
% Fall 2024
%
% Problems taken from Sipser
%

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\textbf{\Large CS 3530: Assignment 2e} \\[2mm]
Fall 2024
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%% \section*{Problem 2.30a (10 points)}

%% \subsection*{Problem}

%% Use the pumping lemma to show that the following languages are not context free.

%% \begin{itemize}
%% \item [a.] $\{ 0^n1^n0^n1^n | n \ge 0 \}$

%%   \textbf{Solution}

%% \end{itemize}


\section*{Problem 2.44 (20 points)}

\subsection*{Problem}

If $A$ and $B$ are languages, define $A\diamond B=\{xy:x\in A$ and
$y\in B$ and $|x|=|y|\}$. Show that if $A$ and $B$ are regular
languages, then $A\diamond B$ is a CFL.

Note: a formal proof is not necessary; a detailed description of a
suitable construction and an informal argument will suffice.

\subsection*{Solution}


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