CS 70
Discrete Mathematics for CS
Spring 2005
Clancy/Wagner
HW 4
Due Thursday, February 17th
Coverage:
This assignment involves topics from the February 8 and 10 lectures (labeled as lectures 6, 7,
and 8 in the notes).
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Homework exercises:
1. (23 pts.)
Boolean decision trees
A
decision tree
is a variant of binary trees in which each
internal
node is labelled with a Boolean
DECISION TREE
variable. Each leaf is labelled with an atom
T
or
F
. The notation
h
P
,
t
1
•
t
2
i
denotes a decision tree
whose root is labelled with
P
and whose left and right subtrees are
t
1
and
t
2
.
A decision tree
t
represents a Boolean function as follows, where
m
is a model (i.e., an assignment that assigns each
Boolean variable to true or false):
If
t
is an atom,
eval
(
t
,
m
)=
t
.
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 Fall '08
 PAPADIMITROU
 Boolean Algebra, Boolean function, Decision tree model

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