%
% Assignment 3c for CS3530 Computational Theory:
% Turing Machines
% Fall 2024
%
% Problems taken from Sipser
%

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\textbf{\Large CS 3530: Assignment 3c} \\[2mm]
Fall 2024
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\section*{Exercise 3.5cd (5 points)}

\subsection*{Problem}

Examine the formal definition of a Turing machine to answer the following questions,
and explain your reasoning.

Note: Refer to the definition 3.3 in the textbook.

\begin{itemize}
\item [c.] Can a Turing machine's head \emph{ever} be in the same location in two successive steps?
\item [d.] Can a Turing machine contain just a single state?
\end{itemize}

\subsection*{Solution}

\begin{itemize}
\item [c.] 
\item [d.] 
\end{itemize}


\section*{Exercise 3.15cde (10 points)}

\subsection*{Problem}

Show that the collection of decidable languages is closed under the operation of

\begin{itemize}
\item [c.] star.
\item [d.] complementation.
\item [e.] intersection.
\end{itemize}

\subsection*{Solution}

\begin{itemize}
\item [c.] 
\item [d.] 
\item [e.] 
\end{itemize}


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