13th International Conference on Membrane Computing - MTA Sztaki

A formal framework for P systems with dynamic structure
deletion. This order corresponds to the actual state of art in the area of P
systems with active membranes. Other orders are also possible and this can be
an interesting topic for a further research.
The algorithm for the computation of Apply(RI, C) is the sequence consisting
of the following steps.
1. (rewriting application): L 1 = {(i 1 , l 1 , w 1) ′ . . . (i n , l n , w n)} ′ where:
⋃
⋃
w j ′ = w j − U k | j + V k | j ,
(r k ,v k )∈RI
(r k ,v k )∈RI
for each j = 1 . . . n, where (U k → V k ) = Rewrite(r k 〈v k 〉) and U k | j (resp.
V k | j ) denotes the multiset associated with the cell from U k (resp. from V k )
whose id is j, or the empty multiset if none of the cells has j as id.
2. (label change): L 2 = {(i 1 , l 1, ′ w 1) ′ . . . (i n , l n, ′ w n)} ′ where:
3. (label change): L 2 = {(i 1 , l 1, ′ w 1) ′ . . . (i n , l n, ′ w n)} ′ where:
{
l j ′ es , if ∃(r
=
k , v k ) ∈ RI such that (j, e s ) ∈ Label–Rename(r k 〈v k 〉)
l j , otherwise.
4. (membrane creation): (m 1 . . . m t+s are new ids). We define the lists of newly
created cells L c and L ′ c:
L c (r k ) =(m 1 , h 1 , u 1 ) . . . (m t , h t , u t ),
(r k , v k ) ∈ RI and
Generate(r k ) = {(1 ′ , h 1 , u 1 ) . . . (t ′ , h t , u t )}.
L c =L c (r 1 ) · · · · · L c (r n ).
L ′ c(r k ) = (m t+1 , h t+1 , w ′ n 1
− u 1 + v 1 ) . . . (m t+s , h t+s , w ′ n s
− u s + v s ), where
(r k , v k ) ∈ RI and
Generate–and–Copy(r) ={((t + 1) ′ , h t+1 , n t+1 , u t+1 → v t+1 ) . . .
((t + s) ′ , h t+s , n t+s , u t+s → v t+s )},
(i j , l ′ j, w ′ j) ∈ L 2 , 1 ≤ j ≤ n
L ′ c = L ′ c(r 1 ) · · · · · L ′ c(r n ).
By definition, we put v k | q ′ = m q , 1 ≤ q ≤ t + s.
We also consider a graph transducer CREAT E–NODES that creates nodes
m 1 , . . . , m t+s .
We put L 3 = L 2 · L c · L ′ c (this is the C m part of the result of the application
of R).
5. (membrane deletion):
Consider a vector P = (p 1 , . . . , p n ) defined as follows:
⎧
∗, if there exists (r k , v k ) ∈ RI such that s ∈ Delete(r k )
⎪⎨ and v k | s = j,
p j = v k | m , if there exists (r k , v k ) ∈ RI such that
(s, m) ∈ Delete–and–Move(r k ) and v k | s = j,
⎪⎩
j, otherwise.
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