Information Technology Reference
In-Depth Information
Apical n-1
Global n-6
Basal n-1
Fig. 2.45
The development of Red Alga
2.7
Membrane Computing
Membranes are one of the basic ingredients in the organization of living organ-
isms. They determine a space partition in internal and external points, separated by
a surface, called skin. Biomolecules inside a membrane are selected, protected, and
concentrated. In this way, the specificity and efficiency of biochemical reactions
is guaranted. Membrane systems are mathematical objects where abstract struc-
tures of membrane organization are investigated in the perspective of information
processing.
Objects and membrane are dual concepts which can be reciprocally reduced (an
analogous situation arises in set theory duality between elements and sets). This
duality is a special case of the space/matter duality formulated in the context of a
discrete framework. In fact a physical object, having a spatial extension comprises
a portion of space, the space occupied by it, that can be delimited by an implicit
membrane delimiting its internal region. Conversely, a membrane is an object with
an internal region which can include other objects. Therefore, we may consider an
object of type
a
as equivalent to an empty membrane
[]
a
. Analogously an object
a
inside the membrane of label
j
,
]
j
, is represented by an object
a
j
with the index
denoting the localization of
a
. In general, we may reverse the relationship of con-
tainment of membranes and objects, by expressing the localization of an object by
labeling it with a
membrane address
(a string of membrane labels). Here we do not
enter into further details. However, many aspects deserve a careful analysis.
Membrane computing, introduced by Gheorghe Paun in 1998 [49, 50, 74, 51],
develops an analysis of computations and languages in terms of multisets of objects
and their localization inside compartments. The class of membrane systems he in-
troduced are also referred as
Psystems
(P is the initial letter of Paun). Differently
[
a
