4
BOTTOM
RIGHT
LEFT
TOP

Logic synthesis problem
Example:
fT
=
x
1
x
2
x
3+
x
1
x
4
+x
1
x
5
9 TOP-TO-BOTTOM PATHS!
x
1
x
1
x
1
x
2
x
5
x
5
x
3
x
4
LEFT
TOP
RIGHT
BOTTOM

Boolean Function Duality
Given:
Obtain:
)
,
.....
,
(
11
rc
X
X
f
)
,
.....
,
(
11
rc
D
X
X
f
f

Our synthesis method
Example:
fT
=
x
1
x
2
x
3+
x
1
x
4
+x
1
x
5
fTD
= (
x
1+
x
2+
x
3)(
x
1+
x
4)
(
x
1+
x
5)
fTD
=
x
1 +
x
2
x
4
x
5 + x3
x
4
x
5
§
Obtain the dual of
fT
.
§
Assign each product of
fT
to a
column.
§
Assign each product of
fT D
to
a row.
§
Compute an intersection set for
each site.
§
Arbitrarily select a literal from
an intersection set and
assign it to the
corresponding site.
x
5
x
1
x
1
x
2
x
1
x
5
x
3
x
4
x
1
x
2
x
3
x
1
x
4
x
1
x
5
x
1
x
2
x
4
x
5
x
3
x
4
x
5

Our synthesis method
x
1
x
1
x
1
x
1
x
2
x
3
x
3
x
4
x
1
x
2
x
3
x
2
x
4
x
5
x
3
x
2
x
3
x
2
x
4
x
4
x
5
x
5
x
1
x
4
x
2
x
3
x
4
x
2
x
4
x
5
x
3
x
5
x
1
x
2
x
5
x
1
x
3
x
4
x
2
x
3
x
4
x
2
x
4
x
5
{
x
2
,
x
3
,
x
4
}
Example:
f
T
=
x
1
x
2
x
3
+
x
1
x
4
+
x
2
x
3
x
4
+
x
2
x
4
x
5
+
x
3
x
5
f
T
D
=
x
1
x
2
x
5
+
x
1
x
3
x
4
+
x
2
x
3
x
4
+
x
2
x
4
x
5

Our method’s performance
Area of the lattice:
m×n
The time complexity:
O
(
m
2
n
2)
n
and
m
are the number of products of the target
function
fT
and its dual
fTD
, respectively.

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- Spring '14
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- Logic, BMW Sports Activity Series, X1