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Fig. 2.47
A membrane system which realizes the sum of two decimal numbers of three digits.
Input numbers are represented by multisets of three symbols (
a
1
,
a
2
,
a
3
for the first input and
b
1
,
b
2
,
b
3
for the second input). The output is obtained after three steps (by maximal parallel
applications of rules) by the multiplicities of
c
in membranes
[]
1
,
[]
2
,
[]
3
. The case of the sum
325
+
478 is indicated in the Venn diagram of the initial and final state of the computation.
that instruction of order
i
is the current instruction. With this representation of the
computation states, the instructions of the register machine will be given by the
following multiset rules.
1. An instruction
i
:
inc
k
j
is expressed by the rule
P
i
→
r
k
+
P
j
.
2. An instruction
i
:
condec
k
j
,
h
is expressed by the rules:
P
i
→
S
i
+
#
S
i
+
r
k
→
Q
i
#
→
$
Q
i
+
$
→
P
j
P
h
It is easy to realize that, with maximal parallel rewriting, the above translation pro-
vides, in the membrane register representation, the effects of the corespondent Min-
ski's instructions in the original registers.
Many features of biological membranes were introduced in membrane computing
in order to analyze their computational relevance; moreover many different mem-
brane systems were introduced for expressing a great variety of distributed, paral-
lel, and non-deterministic computations [49, 50, 74, 51]. Many of them were an-
alyzed in specific papers of membrane computing (see http://ppage.psystems.eu).
S
i
+
$
→
