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Cond(
z
)=
(1
,
0) if
z
=0
(0
,
1) otherwise
Cond :
N
→{
0
,
1
}×{
0
,
1
}
,
.
1
0
s
z
j
0
s
1
s
x
y
0
t
0
0
j
s
s
1
h
Fig. 3.
The conditional construct is a function
N
→{
0
,
1
}×{
0
,
1
}
The following MP grammar defines the Conditional construct:
R
Φ
ϕ
1
=
s
r
1
:
z
→
j
S
=
{
x, y, z, j, t, s, h
}
r
2
:
j
→
zϕ
2
=1
In
=
{
z
}
r
3
:
∅→
xϕ
3
=
s
Out
=
{
x, y
}
r
4
:
x
→
yϕ
4
=
j
=
s
Start
r
5
:
x
→∅
ϕ
5
=
s
=
h
Halt
r
6
:
y
→∅
ϕ
6
=
s
r
7
:
s
→
tϕ
7
=1
r
8
:
t
→
hϕ
8
=1
s
becomes 1,
x
is incremented to 1 from the environment and,
at the same time,
r
1
:
z
Once the
Start
→
j
tries to increase the value of
j
from 0 to 1 with a
flux of
s
=1.
Input
z
=0:therule
r
1
:
z
→
j
blocks and the value of
j
remains 0. In the
next step the rule
t
→
h
signals the end of computation and the result in
Out
is (
x, y
)=(1
,
0).
Input
z
=0:thevalueof
j
actually changes to 1 and in the next step the
rule
r
4
:
x → y
inverts the values of
x
and
y
, leading to a final configuration
where the
is (
x, y
)=(0
,
1).
The reactions
r
5
:
x
Out
→∅
and
r
6
:
y
→∅
clean up the
Out
substances at
the beginning of any new computation. The rule
r
2
:
j
In
substance to its original value, if needed. However the ancillary substance
j
is
not introduced as much for the restoration of
x
but rather for its two properties.
First, it is the complementary of input
z
when needed to invert the output and,
second, being always zero at the beginning, the rule
r
4
:
x
→
z
,restoresthe
→
y
never blocks the
cleaning of
r
5
:
x
. Finally the temporary
t
is introduced for timing purposes
suggesting that the system always takes two steps to execute.
→∅
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