13th International Conference on Membrane Computing - MTA Sztaki

L.F. Macías-Ramos, M.J. Pérez-Jiménez
is introduced, along with several examples. Finally, the simulation algorithm is
shown. Section 5 covers conclusions and future work.
2 Spiking Neural P Systems with Functional Astrocytes
In this section, we introduce SN P Systems with Functional Astrocytes.
2.1 Syntax
A Spiking Neural P System with Functional Astrocytes (SNPSFA for short) of
degree (m, l), m ≥ 1, l ≥ 1, is a construct of the form
Π = (O, σ, syn, ast, out), where:
– O = {a} is the singleton alphabet (a is called spike);
– σ = {σ 1 , . . . , σ m } is the finite set of neurons, of the form σ i = (n i , R i ), 1 ≤
i ≤ m, where:
• n i ≥ 0 is the initial number of spikes contained in σ i ;
• R i is a finite set of extended rules of the following form:
E/a c → a p
where E is a regular expression over a, and c ≥ 1, p ≥ 1 with c ≥ p;
– syn = {s 1 , . . . , s θ } ⊆ {1, . . . , m} × {1, . . . , m} with (i, i) ∉ syn is the set of
synapses;
– ast = {ast 1 , . . . , ast l } is the finite set of astrocytes, with ast j , (1 ≤ j ≤ l) of
the form
ast j = (syn o j , sync j , ω j, T j , F j , p j (0), γ j ), where:
• syn o j = {s o j,1 , . . . , so j,r j
} ⊆ syn, r j ≥ 1, is the astrocyte finite set of
operand synapses, ordered by a lexicographical order imposed on syn o j ;
• syn c j = {sc j,1 , . . . , sc j,q j
} ⊆ syn, q j ≥ 0, is the astrocyte finite set of control
synapses;
• ω j ∈ {true, false} is the astrocyte control-as-operand flag;
• T j = {T j,1 , . . . , T j,kj }, k j ≥ 1, is the astrocyte finite set of thresholds,
such that, T j,α ∈ N, (1 ≤ α ≤ k j ) and T j,1 < . . . < T j,kj ;
• F j = {f j,1 , . . . , f j,kj } is the astrocyte finite multiset (some elements in F j
can be the same) of natural functions such that for each α (1 ≤ α ≤ k j ):
∗ f j,α is a computable function between natural numbers;
∗ if ω j = true then f j,α is a unary function;
∗ if ω j = false and r j = 1 then f j,α is a unary constant function;
∗ if ω j = false and r j > 1 then f j,α has arity r j − 1;
• p j (0) ∈ N is the astrocyte initial potential;
• γ j ∈ {true, false} is the astrocyte potential update flag;
– out ∈ σ is the output neuron.
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