13th International Conference on Membrane Computing - MTA Sztaki

S. Verlan, J. Quiros
Table 2 gives some statistics concerning the experiments. As expected, linear
and 2-circular systems reach a halting configuration, while in the other two cases
it cannot be reached. It can be seen that the simulation of the non-determinism is
done correctly – in some cases all resulting configurations are different. Figure 3
shows the maximal, minimal and mean value of the number of different objects.
We show only the case of 10 rules, the other cases present a similar picture. It
can be seen that in the case of linear system there is a high chance to have a
big value for the last object and in the case of 2-circular systems the second
and before the last objects are never present. In the case of circular systems it
is possible to see an equiprobable distribution of objects, while for the opposite
systems even values have a higher value. It can be easily seen that the used rules
should exhibit exactly this behavior.
Table 2. Statistics concerning the runs of example systems.
Type N Different
final conf.
Circular
2-circular
Linear
Opposite
Halting
Y/N min max
10 982 No - -
20 1024 No - -
50 1024 No - -
10 161 Yes 5 89
20 818 Yes 11 197
50 1024 Yes 57 609
10 204 Yes 7 17
20 944 Yes 14 29
50 1024 Yes 50 65
10 4 No - -
20 938 No - -
50 1024 No - -
5 Discussion
The method discussed in Section 3 allows the construction of simulators having
a constant execution step (in terms of FPGA). While it is possible to design
ad-hoc functions that describe the rules’ execution strategy, we concentrated on
the cases where the multisets of rules that can be applied form a non-ambiguous
context-free language. This permits to easily compute the generating function
of the corresponding language and gives a simple algorithm for the enumeration
strategy.
The class of P systems where the set Appl(Π, C, δ) corresponds to a nonambiguous
context-free language is quite big and it is not restricted to the rules
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