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CSE 200
Computability and Complexity
Homework 3
The class NP and beyond, Completeness, and
Reductions
Polynomialtime Hierarchy
Space Complexity
Due May 26
May 11, 2010
Give proofs for each problem. Proofs can be highlevel, but be precise.
You may use without giving a proof any result proved in class or in the
textbook.
In particular, to prove NPcompleteness, it suFces to give a
reduction from any of the NPcomplete problems from the text or from
class.
However, you must show your reduction is valid, by showing the
equivalence of the constructed instance and the original.
NP
and
co

NP
Consider the problem Greater Maximum Independent
Set: Given
G
1
and
G
2
, is the maximum independent set for
G
1
strictly
larger than that for
G
2
? Show that this problem is in
NP
if and only
if it is in
Co

NP
if and only if
NP
=
co

NP
.
NPCompleteness
We say that
NP
complete problems are the “hardest”
in
NP
, but intuitively that means they are the “least likely to be easy”
not that they have the greatest worstcase complexity.
To illustrate
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 Winter '12
 Edmonds

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