Biomedical Engineering Reference
In-Depth Information
2 steps, for some
m
≥ 0. The spike of neuron σ
4
(the one “prepared-but-not-yet-emitted” by using
the rule
a → a;
1 in step
t
) will reach neurons σ
1,
σ
2,
σ
3
, and σ
7
in step
t
+ 1, hence it can be used
only in step
t
+ 2; in step
t
+ 2 neurons σ
1,
σ
2,
σ
3
forget their spikes and the computation halts.
The spike from neuron σ
7
remains unused, there
is no rule for it. Note the effect of the forgetting
rules
a → λ
from neurons σ
1,
σ
2,
σ
3
: without such
rules, the spikes of neurons σ
5,
σ
6
from step
t
will
wait unused in neurons σ
1,
σ
2,
σ
3
and, when the
spike of neuron σ
4
will arrive, we will have two
spikes, hence the rules
a
2
→
a
;0 from neurons σ
1,
σ
2,
σ
3
would be enabled again and the system will
continue to work.
The next example, given in Figure 2, is actu-
ally of a more general interest, as it is a part of
a larger SN P system which simulates a register
machine. The figure presents the module which
simulates a SUB instruction; moreover, it does it
without using forgetting rules (the construction
is part of the proof that forgetting rules can be
avoided - see (Ibarra et al., 2007)).
The idea of simulating a register machine
M
= (
n
,
H
,
li:
0
,
li:
h
,
R
) (
n
registers, set of labels, initial
label, halt label, set of instructions) by an SN P
system Π is to associate a neuron σ
r
with each
register
r
and a neuron σ
li:
with each label
li:
from
H
(there also are other neurons - see the figure),
and to represent the fact that register
r
contains
the number
k
by having 2
k
spikes in neuron σ
r
.
Initially, all neurons are empty, except the neuron
associated with the initial label
li:
0
of
M
, which
contains one spike. During the computation, the
simulation of an instruction
li:
li:
: (OPP(
r
),
li:
j
,
li:
k
)
starts
by introducing one spike in the corresponding
neuron σ
li
and this triggers the module associated
with this instruction.
For instance, in the case of a subtraction
instruction
li:
li:
: (SUB(
r
),
li:
j
,
li:
k
), the module is initi-
Figure 2. Module SUB (simulating li: (SUB(r), lj, lk))
Search WWH ::
Custom Search