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\newcommand{\SPACE}{\mbox{{\sc SPACE}}}
\newcommand{\NSPACE}{\mbox{{\sc NSPACE}}}
\newcommand{\NP}{\mbox{{\sc NP}}}
\newcommand{\RP}{\mbox{{\sc RP}}}
\newcommand{\PH}{\mbox{{\sc PH}}}
\newcommand{\BPP}{\mbox{{\sc BPP}}}
\newcommand{\IP}{\mbox{{\sc IP}}}
\newcommand{\Poly}{\mbox{{\sc P}}}
\newcommand{\polyL}{\mbox{{\sc PolyLog}}}
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\head{CSG714}{Theory of Computation}{Spring 2008}{25 March 2008}{18}

\begin{center}
\Large{\bf Problem of the Week -- 9}
\end{center}

{\noindent {\bf Complete problems in \PH}}

Prove that $\PH$ has a problem that is complete for $\PH$ with respect
to polynomial time reductions if and only if there exists $k \ge 0$
such that $\PH = \Sigma_k^p$.

\end{document}
