13th International Conference on Membrane Computing - MTA Sztaki

Mobile membranes with objects on surface as colored Petri nets
• if M 1 , . . . , M n ∈ M(Π), n ≥ 1, and w is a multiset of objects over O then
[M 1 ‖ . . . ‖M n ] w ∈ M(Π); [M 1 ‖ . . . ‖M n ] w is called a composite membrane
and M 1 , . . . , M n are called adjacent membrane configurations.
We use string representation of multisets of objects; in this way, multisets of
objects on the membranes surfaces are represented by sequences w, meaning that
every permutation of such a sequence is allowed (as an equivalent representation
of the same multiset).
Inspired from the immune system [8], we define specific rules called pino,
phago and exo in which the membranes agree on their movement by using complementary
objects a and a. Biologically speaking, the objects a and their corresponding
co-objects a fit properly.
If M and N are arbitrary membrane configurations, and u and v are arbitrary
multisets of objects, the evolution from a configuration to another is provided
by a set R of rules defined as follows:
• [ ] a u a v → m [ [ ] c u ] d v , for a, a ∈ O, c, d, u, v ∈ O ∗
pino
M 1 M 2 m M 1 M 2
cu
auav
dv
An object a together with its complementary object a indicate the creation
of an empty membrane within the membrane on which a and a objects are
attached. We should imagine that this initial membrane buckles towards the
inside, and pinches off by breaking the connection between a and a. The
multiset of objects u on the new created (empty) membrane is transferred
from the initial membrane. The objects a and a can be modified during
this step into the multisets c and d, respectively. On the surface of the
membrane appearing in the left hand side of the rule there are some objects
(others than auav) which are ignored; these objects are also not specified on
the right hand side of the rule, being randomly distributed between the two
resulting membranes. By M 1 and M 2 are denoted (possible empty) multisets
of elementary and composite membranes.
• [ ] a u ‖ [ ] a v → m [ [ [ ] c u ] d ] v , for a, a ∈ O, c, d, u, v ∈ O ∗
phago
M 1 M au 2 m M 1 M 2
cu
d
av
v
An object a together with its complementary object a indicate a membrane
(the one with a on its surface) “eating” an elementary membrane (the one
with a on its surface). The membrane having a and v on its surface wraps
around the membrane having a and u on its surface. An additional membrane
is created around the eaten membrane; the objects a and a are modified
during this evolution into the multisets c and d (the multiset c corresponds
to a and remains on the eaten membrane, while the multiset d corresponds
to a and is placed on the new created membrane). On the surface of the
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