13th International Conference on Membrane Computing - MTA Sztaki

Membranes with local environments
A daemon actually begins to work only in the case when a shortage of objects
occurs in the inside/outside part of base multisets belonging to membrane
borders. This shortage of objects enforces a suction effect which the daemons try
to meet as far as possible. If the shortage of objects occurs in the inside/outside
part of a base multiset in a membrane border, the daemon assigned to this base
multiset tries to supplement the missing objects by the objects of the same type
from a neighbor base multiset belonging to the inside/outside space delimited by
the considered membrane. Two multisets are neighbor when their intersection
is nonempty. The first daemon execution sets off a sequence of nested daemon
calls. The nesting stops when 1) the actual base multiset does not have any
neighbor base multiset; 2) or the actual base multiset has one or more neighbor
base multisets but they do not contain any object of the required type. In this
phase, the partial multiset approximation space is changed and a new border
(from inside and outside) can be defined for regions as multisets. Hence, the
membrane computation can start again. The whole computation process stops
when there is no any applicable daemon.
It is assumed that we have a membrane system Π (Definition 6) with an
initial configuration (Fig. 1). Step 1 generates an initial partial multiset approximation
space (Definition 7). Step 2 constraints the scope of the executions of
communication (symport/antiport) rules for membrane borders.
Fig. 1. The initialization phase
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