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\begin{document}
\begin{center}
  Some possible Final Questions
\end{center}
The final is Friday December 20 at 8-10 am in this room.


\begin{itemize}


\item 2.5.6, 2.6.2, 3.5.28. 3.5.29. 6.1.3, 6.1.4.

\item (Essay) What is Church's thesis?  Do you believe it? Why or
  Why not? 
  
\item How would you show $f(n) = n!$ is Turing computable by
  using Church's Thesis?
  
\item (Essay) What is an universal Turing Machine?  Why is it
  important?  What algorithms can such a machine compute?
  
\item Why is the halting set not Turing decidable.  Give an
  example of a language which is not Turing decidable but is
  Turing acceptable.
  
\item Give an example of a language which is not regular but is
  context-free and one which is not context-free but is Turing
  decidable. (Or another way of phasing this given a language
  decide whether $L$ is regular, context-free but not regular or
  Turing decidable but not context-free.)
  
\item Build a Turing Machine which does ....
  
\item (Tricky) Is there an algorithm which decides
  $a^{179}b^{213} \in L (M)$, where $M$ is a finite automata?  a
  pushdown automata? a Turing Machine?

\end{itemize}
\end{document}

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