This preview shows page 1. Sign up to view the full content.
CS 473
Homework 10 (practice only)
Spring 2010
This homework is practice only. However, there will be at least one NPhardness problem
on the ﬁnal exam, so working through this homework is
strongly
recommended. Stu
dents
/
groups are welcome to submit solutions for feedback (but not credit) in class on May
4, after which we will publish ofﬁcial solutions.
1. Recall that 3SAT asks whether a given boolean formula in conjunctive normal form, with exactly
three literals in each clause, is satisﬁable. In class we proved that 3SAT is NPcomplete, using a
reduction from C
IRCUIT
SAT.
Now consider the related problem
2SAT
: Given a boolean formula in conjunctive normal form,
with exactly
two
literals in each clause, is the formula satisﬁable? For example, the following
boolean formula is a valid input to 2SAT:
(
x
∨
y
)
∧
(
y
∨
z
)
∧
(
x
∨
z
)
∧
(
w
∨
y
)
.
Either prove that 2SAT is NPhard or describe a polynomialtime algorithm to solve it.
[Hint:
Recall that
(
x
∨
y
)
≡
(
x
This is the end of the preview. Sign up
to
access the rest of the document.
This note was uploaded on 01/21/2011 for the course CS 473 taught by Professor Chekuri,c during the Spring '08 term at University of Illinois, Urbana Champaign.
 Spring '08
 Chekuri,C
 Algorithms

Click to edit the document details