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\head{CSG714}{Theory of Computation}{Spring 2009}{9 January 2009}{3}

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\Large{\bf Problem of the Week -- 1}
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\noindent {\bf Unary languages}

Consider the collection of unary languages over the alphabet $\{0\}$.

\begin{itemize}
\item[{\bf (a)}]
Show that there is a one-to-one correspondence between the collection
of all unary languages and the collection of sets of nonnegative
integers.

({\em Remark:} This is an easy observation.)

\item[{\bf (b)}]
Show that if $L$ is an arbitrary unary language, then $L^*$ is regular.
\end{itemize}
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