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	Honors Theory, Spring 2002, Yap\\
	Homework 4\\
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\item (10x3 Points)
% Problem 2.16
There are three possible responses to the
following statements: True, False or Perhaps.
``Perhaps'' reflects the uncertainty that only
assume the results in chapter 2.
If your answer is True or False, you must give
brief reasons in order to obtain full credit.
% 
\\ (a) T/F/P: $\nspace(n)\ib \dtime(O(1)^n)$.
\\ (b) T/F/P: $\ntime(n)\ib \dtime(2^n)$.   
\\ (c) T/F/P: $\nrev(n)\ib \drev(O(1)^n)$. 

\ans{}{
SOLUTION:
\\ (a)
True. $\nspace(n)\ib \dtime(n^3 O(1)^n)=\dtime(O(1)^n)$.
\\ (b)
Perhaps.  There is no single constant such that we can prove
$\ntime(n)\ib \dtime(c^n)$.
\\ (c)
This is tricky: 
We know that $\nrev(2)=\RE$.  So the question amounts
to asking if $\RE=\drev(O(1)^n)$.
Based on the results of Chapter 2, the
answer is "perhaps".  But using hierarchy theorems
in later chapters, we actually know the answer is "false".
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