Biomedical Engineering Reference
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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))
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