13th International Conference on Membrane Computing - MTA Sztaki

On structures and behaviors of spiking neural P systems and Petri nets
focused on some structural properties of Petri nets that is fundamental to routing
tokens: the AND- and OR-splits and joins. As it turns out, even the relatively
simple mechanism of conditional routing in Petri nets, the OR-split, can be quite
complex in terms of SNP systems (an additional 2k + 1 neurons to route a spike
among k output neurons). It seems that, at least for “standard” SNP systems (as
defined in this work) without delays, the routing of spikes to specific or targeted
neurons is quite “unnatural” (again recall that splits in SNP systems are by
nature AND-splits). Perhaps a similarly complex structure is required in order
to perform AND-joins for nonsafe and nonordinary (i.e. generalized) Petri nets.
If SNP systems are to be used for modeling processes and phenomena (aside
from the more usual computability results) then results on structural and behavioral
properties are certainly desirable. Since Petri nets enjoy a rich theory
on both kinds of properties, it seems reasonable to further link Petri nets to SNP
systems, as several previous works have already done. For our part, this work
can be seen as a precursor to using SNP systems to be used in modeling processes.
Even biological processes perhaps, after further theoretical developments
are pursued, as mentioned by Păun at the beginning of [17]. Some of these processes
or phenomena might include multi or distributed processors and workflow
processes just to name a few. Many of these have been modeled and analyzed
using Petri nets such as in [15] and [21], among others.
Additionally, other classes of Petri nets such as colored and stochastic nets
(see for example [15]) just to name a few, could be simulated by SNP systems.
Other variants of SNP systems such as those with neuron budding and division
as in [16] can also be transformed and simulated by Petri nets. Such investigations
will most likely yield interesting and useful theoretical and even applicative
results for both models.
Lastly, Petri nets and their behaviors can be represented as matrix equations,
and using these equations several tools have been produced for Petri nets (see
[15] and [21]). Similarly, the behavior of SNP systems have been represented as
matrices in [23] which was used in the creation of an SNP system simulator in
[1] and [2]. One desirable feature of the various Petri net tools is their utility for
analyses and modeling of processes. It is also the hope of further realizing and
opening up connections between Petri nets and SNP systems that motivates this
work.
Acknowledgments
F.G.C. Cabarle is supported by the DOST-ERDT program. H.N. Adorna is
funded by a DOST-ERDT research grant and the Alexan professorial chair of
the UP Diliman Department of Computer Science. The authors would also like
to acknowledge the comments and suggestions of the anonymous reviewers that
helped improve this work. Both authors would like to acknowledge the help of
R.A.B. Juayong and J.B. Clemente.
157