Information Technology Reference
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from classical Formal Language theory, which is based on strings, in this framework
multisets are the basic structure, and multiset rewriting rules are usually applied in
a maximal parallel way (a set of rules which can be simultaneously applied must
be applied). Rules are located into membranes and can be applied only to objects
inside the membranes where they are located, even if results produced by the rule
applications can be moved into other membranes. Figure 2.46 shows a membrane
system and one step of computation applied to a configuration where contents are in-
dicated for each membrane (0 is the index of the
skin
, the most external membrane).
In standard membrane computing, multisets are denoted by
commutative strings
(strings where the order of symbols is not relevant), however, here for notational co-
herence with the other chapters, we adopt the multiset polynomial notation. We refer
to the topics cited above for the main results and application fields of this theory.
Here, after a short definition of a membrane system, we want to list some aspects,
related to the notion of membrane, that show its capability of modeling biological
phenomena.
Fig. 2.46
A membrane system
Membrane configurations and rules can be easily represented by bracket expres-
sions. For example, the membrane structure given in Fig. 2.46 can be written in the
following way:
[
0
[
1
[
4
]
4
]
1
+[
5
]
5
+[
6
[
2
]
2
+[
3
]
3
]
6
]
0
and the system given in Fig. 2.46 (membrane structure with initial configuration and
membrane rules) is synthetically expressed in Table 2.10.
