Simulating Accepting Networks of Evolutionary Processors with Filtered Connections by Accepting Evolutionary P Systems - Foundations on Natural and Artificial Computation - page 299

b α δ , the membrane of the region is dissolved
after the rule application, provided that the membrane is different from the skin
one.
The input string is initially stored in the outmost region. Then, in a fully
parallel manner all the rules are applied to the strings existing in every region
according to their priorities. The system halts whenever: (1) No rule can be
applied, or (2) The system is reduced to only one region, namely the outmost
one.
The language accepted by Π is denoted by L ( Π ). A string is in L ( Π )ifand
only if it being initially stored in the outmost region reduces the system to only
one region.

If the rule is a dissolving one ( a →

4 A Simulation of ANEPFCs by AEPSs

In this section we give just a very brief idea how an AEPS, say Π ,cansimulate
an ANEPFC, say Γ . The membrane structure of Π consists of the skin region
that includes and as many regions as connections between the processors of Γ .
For every connection between processors i and j we have the regions R ij and
R ji inside the skin membrane. Each region R ij has different structure depending
on the filter type. A symbol in the current string in Π indicates the fact that
the corresponding string in Γ has just arrived in the node i .Wediscussthe
simulation of one evolutionary step in the node i and the communication process
of the words from the node i to the node j in Γ .
Let us suppose that the set of permitting symbols for the filter on the con-
nection between processor i and j in Γ is defined by P ij .If

this filter acts in the weak mode, then the membrane structure in the region
R ij is showed in the left part of the next figure, while if the filter acts in the
strong mode, then the membrane structure is showed in the right part of the
same figure.
Inside the inner regions in illustrated membrane structures we apply the same
evolutionary rules as those associated with the node i . In addition, the new
strings are moved through the membrane structure in order to check the filter
conditions. Thus evolutionary rules having the highest priority check the pres-
ence of forbidden symbols. If such a symbol is present, then the string remains

= { b 1 ,b 2 , ··· ,b k }

R ij

R b 1
···

R ij
···

R b 1 R b k R b k

strong filters

weak filters

Fig. 1. Membrane structures for the filters