13th International Conference on Membrane Computing - MTA Sztaki

Spiking neural P systems with functional astrocytes
Inhibitory astrocyte, ast inh , is structurally identical to ast exc , with its formal
specification being:
ast inh = ({(p ′ , q)}, {(p, q ′ )}, true, {0, k + 1}, {g(x), f(x)}, 0, false)
and its working equation, assuming that α spikes pass through synapse (p, q ′ )
at a given instant t, being:
{
g(α) if 0 ≤ α ≤ k
ast inh (α, t) =
f(α) = 0 if α ≥ k + 1
3.2 Logic Gates
Second couple of examples shows how to implement logical gates, concretely
AND-gates and NAND-gates respectively. Implementation involves defining two
functions, f(x) and g(x), both of them unary constant functions, which associates
the 0 and 1 natural values respectively for every x ∈ N.
AND-gate astrocyte, ast and , is depicted in the Fig. 2 with its formal
specification being:
ast and = ({(p, q)}, {(A, A ′ ), (B, B ′ )}, false, {1, 2}, {f(x), g(x)}, 0, false)
and its working equation, assuming that α, 0 ≤ α ≤ 2 spikes in total pass
through synapses (A, A ′ ) and (B, B ′ ) at a given instant t, being:
{
f(0) = 0 if 0 ≤ α ≤ 1
ast and (α, t) =
g(0) = 1 if α = 2
Fig. 2. AND-gate astrocyte.
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