13th International Conference on Membrane Computing - MTA Sztaki

Observer/interpreter P systems
{a↑,a−,a−,c−},skip
{a−,a−,a↓,c−},inc
{a↓,a↑,a−,c−},skip
{a−,a↓,a↑,c−},skip
q 0 q 1 q 2
Fig. 1. The system M “observes” the couples of consecutive configurations of Π and
“interprets” them.
q 2 iff all the objects a were rewritten firstly into a and then into a. Finally, by
applying the loop transition from state q 2 one gets as output 2 k−1 .
In what follows, we are interested by the computational power of these systems
and their relations with the classical families of sets of numbers.
Theorem 3. For any language L generated by an ET0L system H = (V, T, ω, ∆)
and any word w ∈ ∆ ∗ there exists an Observer/Interpreter P system Φ = (Π, M)
such that Π is a P system with symbol objects and non-cooperative multiset
rewriting rules and that halts generating 0 iff |w| ∈ length(L).
Proof. Without any loss of generality assume that card(T ) = 2. Let V −∆ = {a |
a ∈ V \ ∆} and h : V ∗ → (V −∆ ∪ ∆) ∗ such that
• h(a) = a if a ∈ V \ ∆
• h(a) = a if a ∈ ∆
• h(λ) = λ
• h(x 1 x 2 ) = h(x 1 )h(x 2 ), for x 1 , x 2 ∈ V ∗ .
Then we can construct an Observer/Interpreter P system Φ(Π, M) that simulates
the computation of H as follows.
Π = (O, C, µ = [ ] 1 , R 1 , w 1 , i 0 = 1) where
O = V ∪ V −∆ ∪ {t, e, T 1 , T 2 }
C = ∅,
w 1 = wt,
The set of rules is defined below:
R 1 = {t → t, t → λ, T 1 → λ, T 2 → λ}
∪ {A → h(α)T 1 | A → α ∈ T 1 , A ∈ V \ ∆}
∪ {A → h(α)T 2 | A → α ∈ T 2 , A ∈ V \ ∆}
∪ {A → A | A ∈ V \ ∆}
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