Honors Theory of Computation, Spring'00.

HOMEWORK 6:

Out: May 3, 2000
Due: May 10, 2000 (optimal)

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	IMPORTANT:
	1) This is an optional homework; do this if
	you think it can help your grade.  But not 
	submitting this will not lower your grade. 
	It is still useful to do this to prepare for the final.

	2) Answer each question within the page 
	limitation specified (use reasonable size handwriting,
	and leaving a 1-inch margin for grading).  
	If necessary, summarize your method or arguments.
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(Q1) 	Show that MaxOutput is in $FP^{NP}$.
	This is one half of theorem 17.3 (p.416) but the details
	are missing in the book.  I want you to use this approach:
	If $N$ is any nondeterministic Turing machine whose
	output is a binary string (each computation path may have
	a different output), and $w$ is any binary string,
	construct a Boolean formula $\phi(N,w)$ which is true
	if and only if $w$ is the prefix of some output of $N$.

	Limit: 1/2 page

(Q2)    Theorem 17.2 (p.413) shows that Exact TSP is DP-complete.

	(a) The proof refers to the proof in Theorem 9.7, and
	says that if the formula is almost satisfiable
	(but not satisfiable), then the path is broken once.
	There is a small detail that you need to add to the
	construction in Theorem 9.7 to ensure this.  What is this?

	(b) There are some minor bugs in the rest of the proof.
	What are they?

	Limit: 1/2 page
	 
(Q3) Problem 17.3.3:  Show that DP is contained in PP.

	Limit: 1/2 page