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\handout{ps5}{Homework Assignment 5}{March 6, 1992}
\due{Friday, March 13}
%Homework Assignment 1
%Given out: Friday, January 31
%Due: Friday, Feb. 7

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Remember to write up problems 1 through 5 in such a way that each of
these problems can be turned in separately.  Put your name on each
problem, with your last name clearly written in CAPITAL LETTERS, and
with your section and the name of your recitation instructor (e.g.
Rivest/Lynch, W1).

%\reading{Martin Chs. }

\paragraph{Problems.}

\begin{enumerate}
\item[1.] (15 points) 9.11

\item[2.] (15 points) 12.5

\item[3.] (30 points) 16.11

\item[4.] (20 points) Argue carefully that a ``tree machine'' is no more 
powerful than an ordinary TM.  A tree machine doesn't have a tape, but
rather an infinite binary tree with one storage cell at each node that
can store a symbol.  We can identify the cells of the tree with words
in $\{0,1\}^*$ in the obvious way: $\Lambda$ is the root, $y0$ is the
left child of the node with name $y$, and $y1$ is the right child of
the node with name $y$.  The machine has a single read/write head that
at each move can either be left where it is, moved to the parent,
moved to the left child, or moved to the right child.  (Instead of L,
R, S, we have L, R, S, P.)  The standard starting configuration is to
have the input $x$ given is cells 1, 11, 111, etc., with all other cells
blank (including the root) and the head at the root.


\item[5.] (20 points) 17.8, 17.9, 17.10

\end{enumerate}


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