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Figure 4.10 shows the most parsimonious solutions designed using this
strategy. And as you can see, there is indeed a pattern in the design of this
class of exactly-one-on functions and this pattern can be easily exploited to
build extremely parsimonious solutions to any higher order exactly-one-on
function, such as the hard 11-exactly-one-on function.
2-Exactly1On (XOR)
3-Exactly1On
4-Exactly1On
A
A
A
O
N
O
N
O
N
a
c
b
A
2-1On
A
3-1On
d
A
a
c
b
O
O
d
a
c
b
O
a
b
5-Exactly1On
6-Exactly1On
A
A
O
N
O
N
e
4-1On
A
5-1On
f
A
e
O
O
f
O
O
O
O
a
c
c
e
b
d
O
d
a
b
Figure 4.10. Finding patterns to design parsimonious solutions to n -exactly-one-on
functions. Note that the simple structure that emerges here can be used to design
parsimonious solutions to any exactly-one-on function.
 
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