Information Technology Reference
In-Depth Information
A great deal of research in membrane computing was devoted to results estab-
lishing the computational universality of specific classes of membrane systems.
Many applications of membrane formalisms consist in discrete models of biological
phenomena.
The following list summarizes some important aspects of membrane that are rel-
evant to biological discrete modeling.
1. Membrane or object polarities (positive, negative, and neuter) can be consid-
ered. Therefore, rules can be applied according to the presence of certain polar-
ities and may also transform polarities.
2. Membrane thickness can prevent the membrane permeability, that is, exit/
entrance of objects from/to a membrane and rules may change a membrane
thickness.
3. Rule priorities can establish an order among the rules of a membrane, and rules
with a lower priority can be applied only if no rule with a higher priority can be
applied.
4. Catalysts are objects that participate in a rule as reactant and products, which
are not transformed during its application. They can play an important role as
controllers. In fact, if a catalyst is not available the rule cannot be applied, and
the amount of a catalyst determine the level of activity of a rule where it is
involved.
5. Synport/antiport rules realize the entrance/exit of objects from/to membranes
only in a synchronized way among pair of objects (
a
can enter/exit only if
b
enters/exits or vice versa).
6. Promoters/Inhibitors may be associated to the rules: their presence can be used
for allowing or for avoiding the application of some rules.
7. Multi-membranes may be considered, that is, membranes which occur in many
copies with possibly different contents. In this case when a rule is associated to
this kind of membrane, it may be applied to all its copies, or only to some of
them (a specific strategy has to be defined).
8. Parameters could be useful in representing physical variables which are not
objects, but may influence the applicability of rules (temperature or pressure, or
electrical potential).
9. Deterministic strategies could be imposed in several ways, for example, by
combining priority among rules with promoters and inhibitors, or even pro-
grams could be added to membranes which at each step activate at most one
rule, or groups of independent rules. The metabolic P systems, which will be
introduced in the next chapter, are a special case of deterministic P systems.
10. Non-deterministic strategies can be used in a completely free manner or with
some specific criteria. In the original formulation maximal parallelism was
adopted; however, intermediate forms of non-determinism could be considered,
where maximal parallelism could be confined to some membranes or to some
kinds of rules.
11. Movement of objects could be considered only from a membrane to an imme-
diately included or immediately including membrane.
