13th International Conference on Membrane Computing - MTA Sztaki

F.G.C. Cabarle, H.N. Adorna
graphs that move tokens using two types of nodes: places and transitions. The
theory of Petri nets includes numerous works on the use of Petri nets for modeling,
analysis, and verification in business process modeling [19], in industrial
control, distributed systems, concurrent processes et al. See [15] for a comprehensive
list. Since a possible connection between SNP systems and Petri nets was
mentioned in [18], several works have been produced in transforming SNP systems
to Petri nets (including extensions of both models). Early works connecting
membrane systems and Petri nets include [11] and [22]. The transformations in
works such as [12][13][14] mostly deal with transforming a given SNP system to
a Petri net in order to check for certain properties or to “simulate” operations
of the SNP system. In [12] methods for transforming SNP systems to Petri nets
(and limited types of Petri nets to SNP systems) were introduced. An intuitive
simulation of SNP systems and Petri nets was presented, mostly focusing on
the correspondence between places and neurons, rules and transitions. In [14]
another transformation of SNP systems to Petri nets was introduced, as well as
some notes on Petri net behavioral properties such as liveness and boundedness
as applied to SNP systems. A mapping of the configurations of SNP systems
and Petri nets, by using synchronizing places, was also presented in [14]. This
mapping is similar to the idea of simulation presented in [7] between the set of
configurations of a simulating system and the set of configurations of a different,
simulated system. SNP systems with delays were modeled using timed Petri nets
in [13].
In this work we are motivated with the idea of using SNP systems to model
certain processes or phenomena, aside from the usual computability results.
Works on using SNP systems for modeling exist as in [10] and [8], however few.
Before we even begin to use SNP systems for modeling (hopefully in the near
future), we start by investigating structural and behavioral properties of SNP
systems that will prove useful for modeling processes. Several works highlight
the usefulness of Petri nets in modeling workflow processes as in [6][20][19] and
a comprehensive list and exposition in [21]. Workflow processes handle business
or organizational processes such as ordering a product, claiming insurance, and
so on, and identifying resources, defining tasks, and the order of task execution
[21]. Routing is of fundamental importance to workflow processes, and Petri nets
have been shown to be able to not only model these processes, but also to verify
the correctness of workflow process definitions and their executions. Inspired by
token routing in Petri nets, we investigate the routing of spikes in SNP systems
From our results we can answer questions about SNP systems such as: how
can spikes be routed (split or joined) in an SNP system? How “complex” do
routing of spikes turn out to be? Given structural and behavioral properties of
Petri nets related to routing, what do these properties imply to SNP systems?
Our results then indicate a possible use for SNP systems in modeling workflow
processes as an alternative to Petri nets, among other processes.
This paper is organized as follows: Section 2 provides some preliminaries for
this work, including definitions and properties of Petri nets and SNP systems.
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