Information Technology Reference
In-Depth Information
Instead of (3.) a piecewise linear (P)
canonical formula could be used for
more convenient analysis and hardware implementation [1]. For a set of
m
transi-
tion points
the canonical PL representation corresponds to:
t
,
2
t
,..,
t
1
m
>
@
m
1
m
k
w
z
0
5
1
1
s
V
s
¦
1
V
z
.)
k
k
1
with
, and
z
0
.
5
t
t
k
k
k
1
>
@
m
1
m
k
z
1
1
st
s
¦
1
t
z
1
1
k
k
1
Examined to a closer look, either formulae (3.) or (3.) are fully defined if for
any given ID (string of
N
bits) one knows the following set of parameters:
sing a simple method an optimal
b
,
1
t
,...
t
.
m
2
possible genes can be determined. In order to determine a realiation with a
minimal number of
m
(i.e. minimum number of transitions), successive integer
values for
b
are considered (until
b
becomes equal to
n
) and one keeps only the
value of
b
giving the minimum number of transitions. The successive values
m
implementation via (3.) for each of the 1,024
t
,...
1
are then recorded.
For the case of all 1,024 semitotalistic func tions with five inputs the next tables
give the corresponding realiations (
t
). The sign value
s
can be simply com-
b
,
m
puted with (3.7) and therefore is not given in the table. lso the exact transition
points
are missing from the table since they can be easily computed, as ex-
t
,...
1
plained above (Table 3.3).
t
m
Table 3.3.
A list of all semitotalistic genes indicating their optimal realiation. In each row,
the numbers indicate, ID,
b
, and
m
(the number
m
of transitions, also indicating the com-
plexity of the cell. Those cells with
b
0 are totalistic (i.e. their output depends exclusively
by the sum of the neighbor cells)
0
0 0
14 4 2
15 4 1
16
28 5 2
29 5 3
30 5 2
31 5 1
32 5 2
33 0 1
34 1 2
35 1 1
36 2 2
37 2 3
38 2 2
39 2 1
40 3 2
41
42
3 4
1
1 1
43
3 3
2
2 2
5 2
44
3 2
3
2 1
17
5 3
45
3 3
4
3 2
18
5 4
46
3 2
5
3 3
19
5 3
47
3 1
6
3 2
20
5 4
48
4 2
7
3 1
21
5 5
49
4 3
8
4 2
22
5 4
50
4 4
9
4 3
23
5 3
51
4 3
10
4 4
24
5 2
52
4 4
11
4 3
25
5 3
53
4 5
12
4 2
26
5 4
54
4 4
13
4 3
27
5 3
3 3
55
4 3
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